Job Family Position Classification Standard for Professional Work in the Mathematical Sciences Group, GS 1500

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

TABLE OF CONTENTS

INTRODUCTION .................................................................................................................... 2

COVERAGE ............................................................................................................................ 2

MODIFICATIONS TO AND CANCELLATIONS OF OTHER EXISTING OCCUPATIONAL SERIES AND

STANDARDS......................................................................................................................... 3

PART I – OCCUPATIONAL INFORMATION ........................................................................ 4

GENERAL SERIES DETERMINATION GUIDELINES .................................................................... 4

CLASSIFYING PROFESSIONAL SCIENTIFIC WORK.................................................................... 5

DISTINGUISHING BETWEEN PROFESSIONAL AND TECHNICAL WORK....................................... 6

OFFICIAL TITLING PROVISIONS.............................................................................................. 7

FUNCTIONAL CLASSIFICATION CODES.................................................................................... 8

INFORMATION BY SERIES IN NUMBER ORDER ......................................................................... 9

OCCUPATIONAL INFORMATION BY SERIES............................................................................ 10

GENERAL MATHEMATICS AND STATISTICS, 1501.......................................................................... 10

ACTUARIAL SCIENCE, 1510 ............................................................................................................ 11

OPERATIONS RESEARCH, 1515 .......................................................................................................14

MATHEMATICS, 1520...................................................................................................................... 17

MATHEMATICAL STATISTICS, 1529................................................................................................ 19

STATISTICS, 1530............................................................................................................................ 22

DISTINGUISHING AMONG THE COVERED OCCUPATIONS ....................................................... 28

IMPACT OF AUTOMATION..................................................................................................... 28

ADDITIONAL OCCUPATIONAL CONSIDERATIONS................................................................... 29

CROSSWALK TO THE STANDARD OCCUPATIONAL CLASSIFICATION....................................... 30

PART II – GRADING INFORMATION................................................................................. 32

HOW TO USE THIS GRADING INFORMATION......................................................................... 32

POSITION EVALUATION SUMMARY WORKSHEET .................................................................. 33

FACTOR LEVEL DESCRIPTIONS ............................................................................................ 34

FACTOR 1 – KNOWLEDGE REQUIRED BY THE POSITION..................................................34

FACTOR 2 – SUPERVISORY CONTROLS................................................................................. 37

FACTOR 3 – GUIDELINES ..........................................................................................................40

FACTOR 4 – COMPLEXITY ........................................................................................................ 42

FACTOR 5 – SCOPE AND EFFECT............................................................................................. 47

FACTOR 6 – PERSONAL CONTACTS AND

FACTOR

7 – PURPOSE OF CONTACTS..................................................................................... 50

FACTOR 8 – PHYSICAL DEMANDS.......................................................................................... 52

FACTOR 9 – WORK ENVIRONMENT........................................................................................ 53

FACTOR ILLUSTRATIONS...................................................................................................... 54

FACTOR 1 ILLUSTRATIONS................................................................................................. 54

FACTOR 4 ILLUSTRATIONS................................................................................................. 71

FACTOR 5 ILLUSTRATIONS................................................................................................. 83

PART III – EXPLANATORY MATERIAL ............................................................................ 91

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

INTRODUCTION

This job family standard (JFS) provides series definitions, titling instructions, and grading criteria

for nonsupervisory professional positions in the Mathematical Sciences Group, 1500, for General

Schedule (GS) and other “white collar” pay plans. In the General Schedule position classification

system established under chapter 51 of title 5, United States Code, the positions addressed here

would be two-grade interval positions.

This JFS is divided into three parts. Part I contains occupational information that is applicable to

Federal work covered by the JFS without regard to pay plan or classification system. Part II

provides the grading criteria for positions classified in accordance with GS grade definitions. Part

III includes explanatory material about the development of this JFS.

The term “General Schedule” or “GS” denotes the major position classification system and pay

structure for white collar work in the Federal government. Agencies no longer subject to chapter

51 have replaced the GS pay plan indicator with agency-unique pay plan indicators. For that

reason, reference to General Schedule or GS has been omitted from much of this JFS.

Coverage

This job family standard covers the following occupational series:

Series Series

General Mathematics and Statistics 1501 Mathematics 1520

Actuarial Science 1510 Mathematical Statistics 1529

Operations Research 1515 Statistics 1530

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Modifications to and Cancellations of Other Existing Occupational

Series and Standards

Issuance of this JFS establishes, renames, supersedes, or cancels occupational series and

classification standards as described in the following table.

Previous Series or Guidance Action Taken / How to Classify Work Previously Covered

Mathematics and

Statistics Group

1500

• Renames this occupational group the Mathematical Sciences Group.

General Mathematics

and Statistics

1501

• Establishes this series.

Actuary 1510

• Supersedes this classification standard, last revised in June 1967.

• Renames this series, Actuarial Science, 1510.

• Classify work previously covered by this series to the

Actuarial

Science Series, 1510

Operations Research 1515

• Supersedes this classification standard, last revised in June 1996.

Mathematics 1520

• Supersedes this classification standard, last revised in June 1965.

Mathematical

Statistician

1529

• Supersedes this classification standard, last revised in February

1961.

• Renames this series, Mathematical Statistics, 1529.

• Classify work previously covered by this series to the Mathematical

Statistics Series, 1529.

Statistician 1530

• Supersedes this classification standard, last revised in February

1961.

• Renames this series, Statistics, 1530.

• Classify work previously covered by this series to the Statistics

Series, 1530.

Cryptography 1540

• Cancels this series as a series available for general use.

• Reserves the series name and code “1540” for information purposes

only; treatment of this series will be addressed in the next edition of

the

Handbook of Occupational Groups and Families.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

PART I – OCCUPATIONAL INFORMATION

Part I is intended for use by all agencies in evaluating professional positions in the Mathematics

Sciences Group, 1500. It provides series definitions, titling instructions, and detailed occupational

information for this job family.

General Series Determination Guidelines

For a variety of reasons, selection of the correct series for a position is an essential part of the entire

human resources management process. For example, qualification requirements used in recruiting

are based on the series of the position; career ladders are influenced by the series; and organizational

structure is often designed with consideration of the series of assigned positions.

Determining the correct series for a position is usually apparent by reviewing the assigned duties and

responsibilities and then comparing them to the series definitions and general occupational

information the job family standard (JFS) provides. Generally, the series determination for a

position is based on the primary work of the position, the highest level of work performed, and the

paramount knowledge required to do the work of the position. Normally, it is fairly easy to make

this decision. However, in other instances, determining the correct series may not be as obvious.

Use the following guidelines to determine the predominant series when the work of a position

matches more than one job family or occupational group. Also, when the work of a position falls

into more than one series within this job family, it may be difficult to determine which particular

series predominates. In such situations, apply the guidelines below in the order listed to determine

the correct series.

• Paramount knowledge required. Although there may be several different kinds of work in the

position, most positions will have a paramount knowledge requirement. The paramount

knowledge is the most important type of subject matter knowledge or experience required to do

the work.

• Reason for existence. The primary purpose of the position or management’s intent in

establishing the position is a positive indicator for determining the appropriate series.

• Organizational mission and/or function. Positions generally align with the mission and

function of the organization to which they are assigned. The organization’s function is often

mirrored in the organizational title and may influence the appropriate series.

• Recruitment source. Supervisors and managers can help by identifying the occupational series

that provides the best qualified applicants to do the work. This is closely related to the

paramount knowledge required.

Although the work of some positions may require applying professional mathematical or related

knowledge and skills, classification as professional positions in the Mathematics Sciences Group,

1500, may not be appropriate. The

Additional Occupational Considerations section of this JFS

provides examples where the work may involve applying related knowledge and skills, but not to the

extent that it warrants classification to this job family.

Additional information may be found in OPM’s publication

The Classifier’s Handbook.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Classifying Professional Scientific Work

Professional scientific work involves exercising discretion, analytical skill, judgment, personal accountability and

responsibility for creating, developing, integrating, applying, and sharing an organized body of knowledge that

characteristically is:

• uniquely acquired through extensive education or training at a recognized college or university;

• equivalent to the curriculum requirements for a bachelor's or higher degree with major study in or pertinent to

the specialized field; and

• continuously studied to explore, extend, and use additional discoveries, interpretations, and applications to

improve data quality, materials, equipment, applications, and methods.

Interdisciplinary Professional Positions

An interdisciplinary position is a position involving duties and responsibilities closely related to more than one

professional occupation. As a result, you could classify the position into two or more professional occupational

series. The nature of the work is such that persons with education and experience in two or more professions may

be considered equally well qualified to do the work. In both categories the position description should show clearly

that the position is interdisciplinary and indicate the various series in which the position could be classified. The

final classification of the position is determined by the qualifications of the person selected to fill it.

For further guidance on the use and classification of interdisciplinary positions, refer to

The Classifier’s

Handbook.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Distinguishing Between Professional and Technical Work

It is important to determine whether a position is comprised of technical or professional work. It is not always easy

to differentiate between the two because some tasks are common to both. The developmental work of professional

positions and the demanding work of high level technical positions are sometimes similar. Typical distinctions

between technician and professional work follow.

Professional Work Involves:

Technical Work Involves:

• Applying a range and depth of knowledge

acquired specifically through intensive learning

of the phenomena, theories, and concepts of a

scientific body of knowledge.

• Creating, exploring, evaluating, and sharing

solutions for scientific, mathematical, and/or

statistical problems, methods, conditions, and

issues.

• Understanding theories, concepts, principles,

and their relationships underlying the practice of

a professional scientific discipline to achieve

improvements in the efficiency and quality of

work performed and/or to protect the public’s

interests in the quality of life, health,

infrastructures, and natural resources.

• Identifying, analyzing, advising, consulting, and

reporting on scientific, theoretical, and factual

data, conditions, and problems.

• Independently assessing, resolving, and

predicting the relationships and interactions of

data and findings under varying conditions.

• Reasoning using existing knowledge and

assumptions in a professional scientific field to

conceptualize unexplored areas and phenomena.

• Staying abreast of professional literature, and

analyzing and evaluating research issues and

data.

• Applying professional knowledge and skills;

scientific, mathematical, and/or statistical

theories; and assumptions, interactions, and

relationships.

• Exploring, creating, and extending solutions,

and applications of a particular professional

scientific field, discipline, industry, or

technology.

• Understanding and applying predetermined

procedures, methods, and standardized practices

or approaches in a specialized field of industry,

technology, or science.

• Understanding and applying predetermined

procedures, methods, and standardized practices or

approaches in a narrow, specialized field of

industry, technology, or science.

• Using and completing recurring methods,

standardized procedures, and established processes

for a specialized field in industry, technology, or

science.

• Handling difficult work requiring originality,

independent initiative, and practical judgment.

• Carrying out tasks, methods, procedures, and

computations based on oral instructions and/or

precedents, guidelines, and standards.

• Collecting, observing, testing, and recording

factual and scientific data within the oversight and

management of professional employees.

• Foreseeing the effects of procedural changes or

appraising the validity of results on the basis of

experience and practical reasoning.

• Staying abreast of existing and new practical

methods and applications through on-the-job and

classroom training.

• Applying practical knowledge and skills; scientific

mathematical, and/or statistical practices, methods,

and standards; and using tools in practical

situations.

• Supporting a particular industry, technology, or

professional scientific field.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Official Titling Provisions

Title 5, United States Code, requires OPM to establish the authorized official position title that includes a basic title (e.g.,

Mathematical Statistician) that may be appended with one or more prefixes and/or suffixes. Agencies must use the

official position titles for human resources management, budget, and fiscal purposes. Instructions for assigning official

position titles are provided for specific series in this section.

Supervisors and Leaders

• Add the prefix “Supervisory” to the basic title when the agency classifies the position as supervisory. If the position

is covered by the General Schedule refer to the

General Schedule Supervisory Guide for additional titling and

grading information.

• Add the prefix “Lead” to the basic title when the agency classifies the position as leader. If the position is covered

by the General Schedule refer to the

General Schedule Leader Grade Evaluation Guide for additional titling and

grading information.

Research Positions

• Add the prefix “Research” to the basic title when the work satisfies the criteria for research as defined in the

Research Grade Evaluation Guide.

Specialty or Parenthetical Titles

Specialty titles are typically displayed in parentheses and referred to as parenthetical titles. OPM has not prescribed

parenthetical titles for five of the series in this JFS:

• General Mathematics and Statistics, 1501;

• Actuarial Science, 1510;

• Operations Research, 1515;

• Mathematics, 1520; and

• Mathematical Statistics, 1529.

For these five series agencies may supplement the basic position titles with agency established specialty titles if necessary

for recruitment or other human resources needs. However, for the Statistics series, 1530, this standard prescribes the use

of the following specialty titles:

Agriculture Engineering

Biology Health

Demography Medicine

Economics Operations and Administration

Education Social Science

Agencies may use only the above listed specialty titles to supplement the basic titles for the Statistics series, 1530.

Organizational Titles

Organizational and functional titles do not replace, but complement official position titles. Agencies may establish

organizational and functional titles for internal administration, public convenience, program management, or similar

purposes. Examples of organizational titles are Branch Chief and Division Chief. Examples of functional titles are Chief

of Operations and Chief of Policy Development.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Functional Classification Codes

Functional Classification for Professional Work. The National Science Foundation (NSF) manages a system of

functional classification codes to describe the work done by scientists and engineers. NSF uses these data to

conduct studies of the science and engineering workforce. To meet the needs of the NSF, OPM requires agencies to

document and maintain functional classification codes for positions in science and engineering occupations.

The

Guide to Personnel Data Standards provides a list of the applicable occupations and definitions of the functional

classification codes. Use established internal agency procedures to assign the appropriate code for positions

covered by series in this JFS. A complete list of valid functional classification codes is given below.

Category Code

Research 11

Research contract and grant administration 12

Development 13

Testing and evaluation 14

Design 21

Construction 22

Production 23

Installation, operations, and maintenance 24

Data collection, processing, and analysis 31

Scientific and technical information 32

Standards and specifications 41

Regulatory enforcement and licensing 42

Natural resource operations 51

Clinical practice, counseling, and ancillary medical services 81

Planning 91

Management 92

Teaching and training 93

Technical assistance and consulting 94

Other – Not elsewhere classified 99

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Information by Series in Number Order

General Mathematics and Statistics, 1501

•

Series Definition

•

Titling

•

Occupational Information

Actuarial Science, 1510

•

Series Definition

•

Titling

•

Occupational Information

Operations Research, 1515

•

Series Definition

•

Titling

•

Occupational Information

Mathematics, 1520

•

Series Definition

•

Titling

•

Occupational Information

Mathematical Statistics, 1529

•

Series Definition

•

Titling

•

Occupational Information

Statistics, 1530

•

Series Definition

•

Titling

•

Occupational Information

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Occupational Information by Series

GENERAL MATHEMATICS AND STATISTICS, 1501

Qualification Standards

Series Definition

This series covers positions that manage, supervise, lead, or perform scientific work of a mathematical,

statistical, or actuarial nature. This series is applicable when the work of the position:

• is covered by two or more professional series in the Mathematical Sciences Group, 1500, and no one

professional series predominates; or

• is not covered by any one professional series in the Mathematical Sciences Group, but is related closely to

work in the Mathematical Sciences Group, 1500.

This series requires a

functional classification code.

Titling

There is no basic title specified for this series. Agencies may construct titles that appropriately describe the

work. Do not use titles authorized for other series to construct titles for this series.

Occupational Information

General Occupational Information

There is no specific occupational information for this series due to its broad coverage. See other individual

series in this job family for occupational information.

The criteria for classifying positions to this series are distinct from the criteria for classifying an

interdisciplinary position. For further guidance, refer to The Classifier’s Handbook.

⇐BACK TO TABLE OF CONTENTS

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

ACTUARIAL SCIENCE, 1510

Qualification Standards

Series Definition

This series covers positions that manage, supervise, lead, or perform scientific work in the field of actuarial

science. Actuarial science involves professional knowledge of the disciplines of mathematics, statistics,

business, finance, economics, and insurance. The work requires applying this knowledge to programs or

problems related to the financial risks posed by life, health, retirement/pension, and property/casualty entities

and contingencies.

This series requires a

functional classification code.

Titling

The basic title for this occupation is Actuary.

Occupational Information

General Occupational Information

Actuaries in the Federal Government evaluate the financial status of Federal programs designed to help protect

individuals, businesses, and pension plans against adverse financial contingencies. They also play an active

role in designing, modifying, and administering these Government programs and in providing the facts and

estimates that serve as the foundation for management decisions and actions in administering these programs.

These programs include:

– Old Age, Survivors, and Disability Insurance (commonly known as Social Security);

– Supplemental Security Income (cash assistance for low income, aged, blind, and disabled persons);

– Medicare (hospital insurance and supplementary medical insurance for the aged and disabled);

– Medicaid (health care for low income persons);

– Unemployment Insurance;

– Pension Benefit Guarantee Insurance;

– private pensions and other employee benefit plans;

– property insurance programs such as crop, hail, and flood insurance;

– life and health insurance, retirement and disability pensions, and other benefits for Federal military

and civilian employees;

– insurance plans protecting mortgages, loans, savings, and investments;

– estate, gift, and other tax regulations applicable to trusts, pension funds, insurance programs, gifts,

etc.; and

– pension and unemployment benefits for retired employees.

Many Federal programs involve Federal trust funds that have specific financing sources that must be adequate

to cover promised benefits and other expenditures.

Actuarial Functions

Actuaries deal with the financial, economic, and social aspects of a rapidly changing world. Today there are

frequent discoveries in science and medicine, and growing complexities in business and finance. Actuaries

ensure the financial viability of programs designed to protect individuals, groups, and businesses against the

uncertain risk of future financial loss. They evaluate their past projections against actual experience to

determine the economic and social forces at work. Actuaries apply these findings to create future projections.

Because most programs involve a large amount of data, actuaries often study samples. They ensure that their

study samples accurately reflect the population studied and that they are using the most suitable statistical tools

to solve a problem.

(continued)

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

ACTUARIAL SCIENCE, 1510 (continued)

Occupational Information (continued)

Major Actuarial Services

Actuaries provide the following nine principal services:

•

Cost Estimation – involves projecting future program cost estimates to form the basis for estimating

staffing needs and service capabilities.

• Financial Status Evaluation – requires the actuary to compare estimated future program revenues and

expenditures, often over long periods, to assess trust fund adequacy. Federal law frequently requires

formal public reports on program financial status.

• Insurance Valuation – involves calculating and compiling:

– mortality, morbidity, and disability tables;

– retirement, withdrawal, and remarriage rates;

– joint and survivorship values;

– annuity and insurance values; and

– reserve and trust fund values.

These valuations are used to determine the stability of programs, the value of assets and liabilities, and

compliance with legal requirements.

•

–

Financial Projection – involves estimating future expenditure levels for benefits, administration, and

other Federal program costs. In many cases, the actuaries also estimate future program revenues. The

projections involve the following activities:

estimating future program participants such as insured persons, beneficiaries, and taxpayers;

calculating growth rates for various economic and programmatic factors such as the consumer

product index, wages, health care prices, and utilization; and

projecting incidence of certain risks such as death, disability, hospital admission, and pension plan

termination.

Some of these projections are used in documents such as the Annual Budget, Social Security and

Medicare Board of Trustees reports, and the Consolidated Financial Statement of the U.S. Government.

• Legislative Proposal Evaluation – involves estimating or projecting the cost, impact, and actuarial

soundness of proposed legislation. The actuaries must prepare their study findings and supporting

evidence in nontechnical language for presentation to lay persons. To ensure proper interpretation and

implementation of their recommendations, some actuaries work closely with attorneys and other personnel

who are drafting proposed legislative and regulatory changes.

• Calculating Program Cost – involves determining pay and salary premiums, wage thresholds, health

service payment updates, cost of living benefit increases, beneficiary coinsurance levels, and a host of

other statutory factors.

• Consultation – involves advising policy makers on how to create effective and reliable programs for

addressing financial security. Some Government actuaries frequently work closely with members of

Congress and their staffs, key administration officials, national advisory commissions, and others. They

promote these relationships to ensure that their proposals will function as intended and that the financial

and operational implications are carefully considered.

(continued)

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

ACTUARIAL SCIENCE, 1510 (continued)

Occupational Information (continued)

• Improving Public Understanding – involves making presentations and participating in public forums to

explain financial status, costs, technical operations, and other program characteristics. Actuaries

frequently take a leading role in improving public understanding of complex programs.

• Publishing Professional Findings – involves presenting research, study, and analytical findings at

professional conferences and in professional journals for critical review by qualified professionals.

Critiques in these forums play a necessary and invaluable role in advancing both the profession and

individual actuaries. Actuaries may perform many functions that require an actuarial background, but do

not require writing an equation, proving a theorem, or performing any activity that involves applied

mathematics. Their unique contribution is to communicate to their readers the mathematical

considerations that underlie their and others’ research, analysis, and study findings.

Actuaries typically specialize in one or more of the following categories of actuarial work:

• Retirement Benefits – including employer-sponsored defined benefit and defined contribution pension

plans, social security, and other cash retirement income sources.

• Health Insurance – including individual policies (e.g., “Medigap”), employer-sponsored plans,

Government programs, and delivery systems such as health maintenance organizations, preferred provider

organizations, and fee-for-service indemnity plans.

• Other Group Insurance – including protection offered through employers, unions, trade and professional

associations, and other organizations against the financial risks posed by such factors as death, disability,

workplace accidents or illnesses, and legal fees.

• Other Individual Insurance – including life insurance, annuities, disability insurance, and reinsuring

other insurance products for high claim amounts.

• Finance – including corporate finance, financial intermediation, capital management, and financial risk

management.

• Investments – including pension and other accumulated reserve funds, asset management, and

asset/liability matching.

• Property and Casualty Insurance – including business insurance, malpractice and other professional

liability insurance, worker’s compensation, homeowner’s insurance, and automobile insurance.

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Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

OPERATIONS RESEARCH, 1515

Qualification Standards

Series Definition

This series covers positions that manage, supervise, lead, or perform scientific work that involves designing,

developing, and adapting mathematical, statistical, econometric, and other scientific methods and techniques.

The work also involves analyzing management problems and providing advice and insight about the probable

effects of alternative solutions to these problems. The primary requirement of the work is competence in the

rigorous methods of scientific inquiry and analysis.

This series requires a

functional classification code.

Titling

The basic title for this occupation is Operations Research Analyst.

Occupational Information

General Occupational Information

Operations research is:

• an advisory function that utilizes a structured approach to problem solving;

• a rigorous process of scientific inquiry and analysis applicable to unique or recurring problems that

confront decision makers; and

• the systematic examination and development of alternative courses of action to define and clarify the

advantages and disadvantages of available choices.

The primary purpose of operations research analysis is to provide decision makers with sound, scientific, and

quantitative information as a basis for making decisions. These decisions are often made under the following

types of conditions:

• uncertainty arising from a lack of current experience and knowledge;

• conflicts in objectives;

• a variety of possible alternative; and/or

• the failure of current systems to meet goals.

Types of Operations Research Work

Operations research analysts perform the following two broad types of work:

• Methods Development and Assessment – involves applying expert knowledge of particular classes of

problems and the ability to develop associated problem solving methods. Analysts may specialize in one

or more areas including queuing theory, optimization methods, simulation, or artificial intelligence. They

advise other operations research analysts, scientists, or engineers on techniques best suited for analyzing

their problems.

• Problem Solving – involves the ability to work directly to correct deficiencies or improve the performance

of systems, processes, or operations. Analysts doing this type of work are expert in methods of problem

solving and also have an in-depth knowledge of recurring or persistent subject matter problems.

Multidisciplinary Approaches

A key requirement of operations research analysis is the ability to work across disciplinary boundaries and to

develop multidisciplinary solutions to complex problems. For example, evaluating the capability of a high

performance fighter/bomber to reach and destroy its target may involve issues relating to:

• aeronautical, electrical, electronic, and mechanical engineering;

• physics;

• mathematics; and

• economics.

(continued)

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

OPERATIONS RESEARCH, 1515 (continued)

Occupational Information (continued)

Analysts usually deal with a variety of broad issues, subject matter areas, and problems. Each assignment

presents a different question. Over time, analysts may gain considerable knowledge of some specialty fields,

yet operations research knowledge remains paramount. Analysts often borrow and adapt analytical methods

and modify techniques from other scientific, technical, and analytical disciplines. Similarly, professionals in

other fields may use the operations research approach to solve problems in their disciplines.

The Operations Research Analysis Process

The framework for the operations research analysis process is best understood in terms of concepts and phases.

Concepts

Three key concepts⎯systems, relationships, and models⎯are important in understanding the analytical process

involved in problem solving. Each concept is described below:

• A system is a group of interrelated, interacting, or interdependent elements forming a complex whole. A

process or operation may be a system. In this job family standard, the term system refers to the process and

operation of analysis.

• A relationship is a statement about the similarities, differences, or interactions of two or more quantities or

measurements called variables. For example, a tall person probably weighs more than a short person. The

two measurements of height and weight are relative variables. There are other variables that relate to

weight, such as the person’s bone structure and body type. A person’s height and any of the other

variables may establish a relationship. Much of the work of operations research lies in identifying the

proper variables and their true relationships for use in solving a particular problem or evaluating

alternatives.

• A model is a representation of the relationships that define a system or situation under study. It may be a

set of mathematical equations, a computer program, a hand-played game, a written scenario, an

experiment, or other type of representation ranging from verbal statements to physical objects. Models

permit the manipulation of variables to determine how a process, object, or concept would behave in

different situations, without using the time, risk, or expense of actual real world implementation.

Phases

The analytical process has four phases: problem definition, model development, hypothesis testing and

investigation, and predictions/explanations. Each phase is described below.

• Problem Definition – usually takes the form of “what if” questions. In formulating problem statements,

analysts examine the objectives and criteria of systems to make sure they are studying the right problems.

They determine the context of problems to identify the:

– principal decisions made;

– relevant variables and true relationships;

– alternative choices;

– measures of effectiveness or success that distinguish among the alternatives; and

– constraints.

(continued)

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Operations Research, 1515 (continued)

Occupational Information (continued)

• Model Development – represents the important factors of the problem and their relationships to selected

features of the real world. Models permit experimentation and extend the evaluation of system

performance and reliability beyond the scope of practical testing. Analyses done with models may be the

only means to forecast performance for certain kinds of systems, for example, the world economy or

combat.

Using models leads to discovering cause and effect relationships that may otherwise go undetected.

Analysts develop or select models with which they can experiment to develop and explore choices or

hypotheses. They determine if the models describe the systems under study and test their reality by

measuring their sensitivity to various values of appropriate variables. After showing that a model is a fair

representation of reality, or that its limitations are acceptable for the current study, the model can be useful

for analyses.

Mathematical models cannot solve some problems. These problems usually include intangible

characteristics that quantitative terms cannot express. Foremost among such characteristics is the presence

of the human element.

• Hypothesis Testing and Investigation – is repeated throughout the analytical process. The process

involves successive integration of analogies, patterns, and relationships, and usually involves feedback and

further restructuring. For new types of problems, analyses constitute a continuous cycle of formulating

problems, selecting the objectives, designing better alternatives, collecting data, building new models,

weighing costs against performance, questioning assumptions and data, reexamining objectives, and

identifying new alternatives.

• Predictions/Explanations – are the end result of analyses. Analysts predict future events or explain past

events. They recommend the best alternatives, if they are found, and present relevant tradeoffs and

limitations so decision makers can make informed choices or take appropriate action.

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Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

MATHEMATICS, 1520

Qualification Standards

Series Definition

This series covers positions that manage, supervise, lead, or perform scientific work that involves:

•

conducting research on basic mathematical principles, methods, procedures, techniques, or relationships; or

developing mathematical methods to solve a variety of scientific, engineering, economic, and/or military

problems where precise specification of the relationships, rigor and economy of mathematical operations,

and logical deduction are the controlling considerations.

This series requires a

functional classification code.

Titling

The basic title for this occupation is Mathematician.

Occupational Information

General Occupational Information

Traditionally mathematics consists of two generic types of work: pure or abstract mathematics, and applied

mathematics.

• Pure or Abstract Mathematics – is sometimes referred to as basic research. Relatively few

mathematicians perform basic research. This work involves studying and developing principles for their

own sake and possible future rather than immediate usefulness. Pure or abstract mathematics applies to

areas of mathematics such as:

– differential geometry;

– topology;

– combinatorics;

– discrete equations;

– network theory; and

– graph theory.

• Applied Mathematics – concerns mathematical aspects of the physical, natural, and social sciences. In a

restricted sense, the term refers to using mathematical principles as tools in the fields of physics, chemistry,

engineering, biology, and the social sciences. Many mathematicians perform work in applied mathematics.

Typical areas of applied mathematics are:

– linear and nonlinear ordinary and partial differential equations;

– numerical analysis;

– finite element and finite differences methods;

– integral equations;

– inverse scattering;

– neural nets;

– computational geometry;

– visualization;

– virtual reality;

– robotics;

– solid and fluid modeling;

– linear and nonlinear control; and

– nonlinear dynamics.

(continued)

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

MATHEMATICS, 1520 (continued)

Occupational Information (contd)

Mathematicians perform these types of activities:

• modeling mathematical problems in various disciplines;

• analyzing mathematical models;

• developing computational methods and computer codes; and

• comparing the computational results with observations or experiments.

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Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

MATHEMATICAL STATISTICS, 1529

Qualification Standards

Series Definition

This series covers positions that manage, supervise, lead, or perform:

•

scientific work that involves designing, developing, and adapting mathematical methods and techniques to

statistical processes; or

research that relates to the basic theories and science of statistics.

This series requires a

functional classification code.

Titling

The basic title for this occupation is Mathematical Statistician.

Occupational Information

General Occupational Information

Mathematical statisticians perform duties in which the “problem” is the basic work unit. The size and

complexity of the problem varies extensively. Solving a problem usually requires that the mathematical

statistician use standard research procedures. These procedures, sometimes referred to as the scientific method,

include the following seven basic work processes:

• defining problems;

• conducting background research;

• planning;

• conducting investigations;

• reducing findings to facts;

• interpreting findings; and

• documenting findings.

The science of mathematical statistics is a body of theories and methods for obtaining knowledge.

Mathematical statisticians do not merely rely on a collection of facts; instead they are characterized by the

techniques that they develop to design models for collecting quantified data. Mathematical statisticians design

and use methods that provide the technical framework for such activities as:

• developing sampling strategies to collect data;

• discovering the meaning of facts;

• performing methodological research;

• analyzing data and generating inferences about the real world based on analysis;

• ensuring the accuracy of measurements that data represent;

• evaluating the precision and validity of estimates;

• investigating sources and magnitude of error in data;

• planning and executing sample or census surveys;

• designing and conducting experiments;

• analyzing experimental design;

• performing operations research; and

• instituting procedures for quality control in production.

(continued)

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

MATHEMATICAL STATISTICS, 1529 (continued)

Occupational Information (continued)

Mathematical statisticians apply or are guided by concepts, theories, methods, and techniques such as:

• probability;

• statistical estimation;

• data analysis;

• linear model analysis;

• time series analysis;

• survey design;

• questionnaire design;

• statistical quality control;

• sampling theory;

• methodological research and development;

• statistical and mathematical modeling; and

• random processing of problems related to testing, estimation, and prediction.

Their objective in this work is to design or use techniques that provide a basis for investigating the reliability,

validity, precision of measurement, probability of inferences, and risk of error in statistical outcomes.

Statistical means of inquiry may be applicable to any area of investigation. After mathematical statisticians

develop substantive knowledge of a subject matter, they may readily transfer their professional knowledge to

another subject matter field. The methods are fundamentally the same whether the employee applies them to:

• analyze physical phenomena;

• design, conduct, and analyze medical experiments;

• develop management control data;

• examine quantitative material in economics; or

• investigate other scientific fields.

The mathematical statisticians’ work assignments follow a variety of patterns. For example:

• As part of research teams, they:

– measure, correlate, and reduce to numerical form phenomena that is best observed using mathematical

or statistical methods; and

– frequently serve as staff advisors to various subject matter specialists on the potentials and limitations of

statistical methods.

• As leading statistical agency authorities, they:

– make recommendations to senior officials on interpreting multiple, conflicting, or incomplete data;

– advise senior officials on technical issues central to initiating new statistical programs or major

revisions to current statistical programs;

– research new sampling and/or estimation techniques for statistics;

– publish state-of-the-art statistical study findings; and

– make presentations at professional meetings and conferences.

• In collecting data, they:

– serve as program technical advisors;

– design or adapt mathematical and statistical tools;

– develop methods and select techniques that other statisticians and/or subject matter specialists use;

– conduct methodological research to improve sample surveys or experimental designs; and

– conduct evaluations of data collection, reduction, processing, and analysis methodologies.

(continued)

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

MATHEMATICAL STATISTICS, 1529 (continued)

Occupational Information (continued)

• As consultants and mathematical statistical analysts, they:

– develop or review sampling plans and all the essential elements of sample design, including:

o determining sample size;

o allocating optimum total sample size to strata or clusters;

o specifying methods of sample selection and estimation; and

o measuring the magnitude and direction of bias, if any; and

– conduct research and development to improve the design and performance of sample surveys,

experimental designs, and clinical trials, including:

o applying mathematical statistical theory, techniques, and methods to statistical studies and surveys;

o analyzing the accuracy and validity of prior statistical data;

o determining if planned operations and processes are appropriate;

o recommending improvements for collecting and analyzing statistical data;

o preparing and disseminating technical documentation of work;

o being on the forefront of developing new statistical methods and performing cutting edge research

to solve statistical problems; and

o developing and conducting statistical computing research involving record linkage, time series

modeling, seasoned adjustment, and demographic forecasting.

• In conducting mathematical statistical research, in contrast to subject matter research, mathematical

statisticians help to develop new, or improve existing, statistical theories and techniques.

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Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

STATISTICS, 1530

Qualification Standards

Series Definition

This series covers positions that manage, supervise, lead, or perform scientific work or provide professional

consultation in applying statistical theories, techniques, and methods to gather, analyze, interpret, and/or report

quantified information.

This series requires a

functional classification code.

The basic titles for this occupation are Survey Statistician or Statistician.

Use the title Survey Statistician for positions primarily concerned with:

• overall planning or executing complete surveys of any size, or parts of large surveys, including initial

negotiations or development of the survey; and

• establishing general specifications and detailed time schedules that govern the following:

– data content, collection, and dissemination;

– instrument design;

– analysis; and

– modifying systems design.

Use the title Statistician when the work of the position does not satisfy the criteria for use of the title Survey

Statistician.

Use the appropriate specialty title shown in the left column of the table below with the basic titles, Survey

Statistician or Statistician, when the work matches the corresponding bulleted criteria in the right column. If

work does not match the criteria, do not use a specialty title.

Specialty Titles Criteria

Agriculture

• crop production and crop acreage;

• livestock production and inventories;

• farm commodity prices and incomes;

• consumption of agricultural products;

• farm labor, farm property values;

• finance, marketing, and transportation; and

• related agricultural topics.

Biology

• managing and controlling biotic forms and protection;

• tracking the life processes of plants and animals including animal and

fish population inventories; and

• experiments in pest control.

Titling

Demography

• human populations and their characteristics including:

– distribution, migration and growth, fertility/fecundity, mortality,

marriage and divorce; and

– individual social and economic characteristics such as age,

education, occupation, and attitudes.

(continued)

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

STATISTICS, 1530 (continued)

Specialty Titles (continued) Criteria (continued)

Economics

• characteristics of economic activity such as:

– inputs, outputs, and product lines;

– industry concentrations, inventories, and capital expenditures;

– payroll and employment, labor force, consumption, and

international trade; and

– investments, prices, income, savings, taxation, money and credit,

value added, personal consumption expenditures, gross domestic

product, and other topics not related to agriculture.

Education

• the educational function including problems of teaching and learning,

and such topics as staff, students, income, property, organization, and

curricula of educational institutions.

Engineering

•

engineering activity and experimentation including statistical quality

control;

acceptance sampling procedures for raw materials; and

manufactured or processed products.

Health

• the causes, incidence, and cost of accidents, disease, and disabling

illness including epidemiological research and administering medical

care, disability insurance, and public health programs.

Medicine

• studies in etiology (cause), diagnosis, treatment, prevention, and cure of

human disease based on laboratory, clinical, or epidemiological

research.

Operations and

Administration

• studies on the problems of management and operations related to:

– jobs, people, material, equipment, methods, attitudes;

– working conditions, financial management, program evaluation;

and

– control, cost modeling, and statistical analysis of accounting

systems.

Titling (continued)

Social Science

• rural and urban sociology;

• criminology;

• racial problems; and

• social work, social insurance, and welfare services administered by

State and local Government, excluding economics.

Occupational Information

General Occupational Information

The word statistics means a group of facts stated numerically. Statistics also refers to:

•

the body of theory and methods used to collect, classify, and evaluate quantitative facts as a basis for

inference;

a body of techniques to obtain valid, measurable results from incomplete information; and

a scientific system for describing, organizing, analyzing, interpreting, and presenting information in

numerical form.

(continued)

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

STATISTICS, 1530 (continued)

Occupational Information (continued)

Survey Statisticians

A survey is a scientific method of gathering information from a sample of individuals, households, firms,

institutions, or other units of analysis so that results can be generalized to the entire population. The validity of

survey results depends on selecting the sample so that each unit has a measurable chance of selection and

collecting information using standardized, replicable procedures. Survey statisticians apply statistical theories

and techniques to:

• plan, organize, and operate programs for collecting, verifying, adjusting, processing, summarizing,

analyzing, and presenting information numerically; and

• conduct research to evaluate data quality.

Survey statisticians collect primary data from original sources and secondary data from records, instruments, or

reports established for historical, administrative, regulatory, or quality control purposes. They also select or

sample data.

Although the decisions of survey statisticians rest on a sound foundation of statistical principles, they also

require other specialized knowledge.

The responsibilities of survey statisticians involve the following:

• defining useful measurements for specific purposes;

• determining the best and most efficient ways to collect quantitative information;

• determining the feasibility of reducing a problem to one in which objective measurements can be taken;

• planning, organizing, and overseeing the operation of a survey;

• selecting the most appropriate survey methods within cost considerations;

• devising measurement methods to assess the completeness of a survey sampling universe;

• devising surveys or processes that will capture the missing elements in a survey sampling universe;

• developing procedures to ensure that the sampling universe for repetitive surveys are kept up to date;

• developing or reviewing questionnaires, instructions, and schedules to ensure structural soundness;

• planning the development of related data for comparison;

• establishing systems of classification and coding;

• organizing a reporting system on a production basis;

• establishing the sequence of collection, summarization, and representation;

• planning necessary quality checks and controls;

• solving statistical problems that occur in survey collection and summarization processes;

• reducing the survey process as far as possible to a routine that support personnel can manage;

• establishing procedures for data storage and retrieval;

• planning data dissemination systems; and

• conducting in-depth analysis of data and disseminating the results of those analyses.

In some situations, a single statistician may be responsible for the entire survey process. In other situations,

particularly with large statistical organizations, survey statisticians may specialize in particular functions such as

survey planning, data collection, data processing, or data analysis and dissemination as described below:

• Survey Planning – involves developing and formulating overall plans for complete surveys or parts of

surveys by using general objectives and methods. In survey planning, statisticians develop:

– overall procedures;

– forms design;

– cost estimates;

(continued)

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

STATISTICS, 1530 (continued)

Occupational Information (continued)

– activity and time schedules;

– timetables;

– specific plans for quality control and production control systems;

– staff requirements;

– general data collection specifications;

– general data processing requirements;

– general survey documentation;

– particular statistical methods and techniques applicable to the subject matter involved; and

– statistical software and computer programs to perform analysis of statistical data and findings.

• Data Collection – involves establishing general data collection specifications that translate into detailed,

practical plans for data collection systems. In data collection, statisticians:

– write training manuals, procedural manuals, and related materials;

– design scientific instruments and procedures governing the administrative and technical features of the

data collection system;

– plan and implement pretesting plans for survey instruments; and

– estimate and control budgetary and financial, supply and space, human resources, public relations, and

other general administrative management requirements of the data collection system.

Statisticians can perform the actual data collection phase of the survey in compliance with all previous plans

and procedures, quality checks appropriate for the particular survey, and troubleshooting methods applicable

to problems in the field. Their assignments typically include responsibility for explaining:

– unexpected data or trends; and

– inconsistent survey findings.

• Data Processing – involves establishing general processing specifications that translate into detailed,

practical plans for data processing systems. In data processing, statisticians:

– design large systems to control incoming data collection materials; and

– develop plans for production management that include staffing plans, procedures, backlog scheduling,

and programming for tabulation methods.

• Data Analysis and Dissemination – involves interpreting findings to draw substance and meaning from

them and planning statistical publications where knowledge of statistical presentation (e.g., tabulation,

classification, and charting techniques) is a paramount requirement. In data analysis and dissemination,

statisticians:

– conduct statistical analyses of data using appropriate statistical methodologies;

– summarize initial data;

– review, analyze, coordinate, and/or revise statistical reports, volumes, and releases; and

– consolidate published or publishable statistical research and writings into complete documents or books

such as statistical compendia (

Statistical Abstract or Historical Statistics).

The proper technical documentation of the statistical methods statisticians use is an essential part of data

publication and requires professional knowledge and understanding of the statistical principles that serve as a

basis for surveys.

In all of these activities, survey statisticians preserve the statistical validity intended in the original survey design

and must exercise professional knowledge of pertinent statistical principles and techniques.

(continued)

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

STATISTICS, 1530 (continued)

Occupational Information (continued)

Statisticians

Statisticians may use data derived from a probability sample. They are usually responsible for the design, size,

and characteristics of the probability samples that are necessary to ensure the reliability of data.

Statisticians may provide advice or be directly involved in collecting primary data. They examine data collected

by others to help them understand its implications and limitations for the problem under study. Further,

statisticians evaluate data collection and statistical methodologies, and develop better data collection methods.

Statisticians organize data into a format that facilitates the required analysis and communicates the results to data

users. The organization of data takes different forms depending upon the problem under investigation. For

example, if one is interested in changes over time, statisticians present the data in a different manner than when

one is interested in the current period’s totals. The problem may involve comparing data easily with masses of

similar data and analyzing differences, or developing complex models to support in-depth analysis of data,

illustrate and interpret findings, and disseminate findings to a variety of constituents.

Statistical functions are numerous and vary extensively, but fully qualified statisticians are typically able to

determine:

• whether the problem is amenable to statistical inquiry;

• kinds of data needed;

• necessary data sources;

• new or improved methods for obtaining data, and their estimated cost and limitations; and

• the most appropriate methods for analyzing and interpreting data.

Statisticians are responsible for:

• analyzing findings, evaluating the statistical limitations of available data, and specifying the range of

logically possible explanations of the findings;

• discovering the meaning of facts; and

• presenting original or derived data in their most pertinent form, which may include text, graphs, charts,

tables, and models.

These responsibilities require knowledge of:

• statistical theory;

• statistical methods and techniques; and

• statistical software and computer programs to perform computer analysis of statistical data and findings.

(continued)

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

STATISTICS, 1530 (continued)

Occupational Information (continued)

Some statisticians apply statistical theory and methods to solve problems in a subject matter field. To ensure

effectiveness, statisticians must acquire considerable knowledge not only about the detail but also about the

theory of the subject under study. The work requires that they become familiar with both the general and the

specific knowledge of the field. They must understand the:

• general magnitude and characteristics of the subject under study;

• various categories of data;

• technical language involved;

• major controlling factors in the field and their general relationships;

• cycles, trends, sources, validity, limitations, and interrelationships of the data involved;

• need for selecting facts to quantify, and determining which are relevant, important, or extraneous;

• agency programs and objectives and the special and continuing problems involved; and

• data collection mechanisms and limitations.

Statistical techniques apply to any subject matter field in which numerical expression may represent the facts. In

applied statistics the statistician uses these techniques to solve specific problems requiring quantitative data or

problems inherent in selecting, collecting, analyzing, interpreting, and presenting such information. The

statistician seeks to derive meaningful relationships from data, and/or to measure the significance of quantified

data usually relating to a particular subject matter field.

Examples of the various kinds of statistical techniques that statisticians use include:

• analysis of frequency distributions;

• analysis and modeling of multivariates;

• sampling;

• analysis of variance;

• determining confidence limits; and

• estimating magnitudes.

A high order of judgment is required in adapting or applying appropriate techniques and interpreting results.

Such judgment is necessary to initially determine whether a problem is amenable to statistical inquiry and to

formulate and plan the entire investigation.

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Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Distinguishing Among the Covered Occupations

Mathematical Statistics, 1529, versus Mathematics, 1520

Mathematical statistics differs from mathematics in the following areas:

• concentration on the body of mathematical theory related to probability and inference; and

• mathematical processes and techniques associated with statistics.

Mathematical Statistics, 1529, versus Statistics, 1530

Mathematical statistics differs from statistics in the following areas:

• focus on mathematical techniques and methods of the statistical process; and

• scope of mathematical theory necessary to the job function.

Mathematical statisticians design statistical tools. They are concerned less with applying statistical techniques than

with the usefulness of statistical tools in terms of the quality, reliability, and validity of the data they yield.

Impact of Automation

Automation greatly affects the way mathematical and statistical products and services are delivered. Many

mathematical and statistical professionals do scientific computation and data reduction work that involves

translating mathematical equations into compatible computer programs. Techniques that lend themselves well to

information technology include:

• computer simulations;

• optimization;

• matrix methods;

• ordinary and partial differential equations;

• Monte Carlo methods; and

• Boolean Algebra.

The information technology tools involved and the skill required to use them generally replace or supplement work

previously done manually or by machines. Automation does not change the primary purpose of the work or the

paramount knowledge required to do the work, which is a professional knowledge of mathematics, statistics, or

actuarial science. Properly classifying positions in these occupations is based on the relevant knowledge and skills

required to do the professional mathematics, statistics, and/or actuarial duties of the position.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Additional Occupational Considerations

Some positions may include professional work requiring knowledge and skills typically associated with the

Mathematical Science Group, 1500. In some cases, a closer look at the work may reveal that classification to a

series in this job family may not be always be appropriate. The

General Series Determination Guidelines section

of this JFS offers guidance on selecting the most appropriate series.

The following table provides examples of work that is similar to that performed in the 1500 job family, but not to

the extent that the paramount knowledge required, the reason for the position’s existence, the mission and/or

function of the organization, and the recruitment source for the best qualified candidates would warrant

classification to a series in this JFS.

NOTE: In the table that follows, the term job family position classification standard is abbreviated as JFS.

If Work Involves …

See This Standard or

Series Definition:

Adjudicating claims by applying knowledge of insurance laws, regulations, and

procedures.

0105, Social Insurance

Administration

0107, Health Insurance

Administration

0991, Workers’

Compensation Claims

Examining

0993, Railroad Retirement

Claims Examining

0996, Veteran Claims

Examining

Applying specialized methods to quantify, measure, and understand economic

problems, phenomena, and relationships.

0110, Economist

Performing professional work related to the behavior, capacities, traits, interests,

and activities of human and animal organisms.

0180, Psychology

Evaluating the effectiveness, efficiency, and productivity of the management of

Government programs or operations.

0343, Management and

Program Analysis

Planning and programming the budget system by applying knowledge of financial

laws, constraints, and programming rules.

JFS for Professional and

Administrative Work in the

Accounting and Budget

Group, 0500

Performing nonprofessional technical support work in actuarial, mathematical,

statistical, operations research, or other sciences, or administrative support

processes that relate to these sciences.

1521, Mathematics

Technician

1531, Statistical Assistant

1541, Cryptanalysis

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Crosswalk to the Standard Occupational Classification

The Office of Management and Budget requires that all Federal agencies that collect occupational data use the

Standard Occupational Classification (SOC) system for statistical data reporting purposes. The Bureau of Labor

Statistics uses SOC codes for the National Compensation Survey and other statistical reporting. OPM and other

Federal agencies maintain a “crosswalk” between OPM authorized occupational series and the SOC codes to serve

this need. This requirement and these SOC codes have no effect on the administration of any Federal human

resources management system. The information in this table is for information only and has no direct impact on

classifying positions covered by this job family standard. The SOC codes shown here generally apply only to

nonsupervisory positions in these occupations. As changes occur to the SOC codes, OPM will update this table.

More information about the SOC is available at

http://stats.bls.gov/soc.

Federal Occupational Series and Position Titles

and Their Related Standard Occupational Classification System Codes

Federal

Occupational

Series

Standard Occupational

Classification Code

Based on Occupational Series

Position

Title

Standard Occupational

Classification Code

Based on Position Title

General

Mathematics and

Statistics, 1501

15-2099 Mathematical

Science

Occupations,

All Other

No Specified

Title

15-2099 Mathematical Science

Occupations, All

Other

Actuarial Science,

1510

15-2011 Actuaries Actuary 15-2011 Actuaries

Operations

Research,

1515

15-2031 Operations

Research

Analysts

Operations

Research

Analyst

15-2031 Operations Research

Analysts

Mathematics, 1520 15-2021 Mathematicians Mathematician 15-2021 Mathematicians

Mathematical

Statistics, 1529

15-2041 Statisticians Mathematical

Statistician

15-2041 Statisticians

Statistician 15-2041 Statisticians

Statistician

(Agriculture)

15-2041 Statisticians

Statistician

(Biology)

15-2041 Statisticians

Statistician

(Demography)

15-2041 Statisticians

Statistician

(Economics)

15-2041 Statisticians

Statistician

(Education)

15-2041 Statisticians

Statistician

(Engineering)

15-2041 Statisticians

Statistician

(Health)

15-2041 Statisticians

Statistics, 1530 15-2041 Statisticians

Statistician

(Medicine)

15-2041

Statisticians

(continued)

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Federal Occupational Series and Position Titles

and Their Related Standard Occupational Classification System Codes (continued)

Federal

Occupational Series

Standard Occupational

Classification Code

Based on Occupational Series

Position Title

Standard Occupational

Classification Code

Based on Position Title

Statistician

(Operations and

Administration)

15-2041 Statisticians

Statistician

(Social Science)

15-2041 Statisticians

Survey

Statistician

15-2041 Statisticians

Survey

Statistician

(Agriculture)

15-2041 Statisticians

Survey

Statistician

(Biology)

15-2041 Statisticians

Survey

Statistician

(Demography)

15-2041 Statisticians

Survey

Statistician

(Economics)

15-2041 Statisticians

Survey

Statistician

(Education)

15-2041 Statisticians

Survey

Statistician

(Engineering)

15-2041 Statisticians

Survey

Statistician

(Health)

15-2041 Statisticians

Survey

Statistician

(Medicine)

15-2041 Statisticians

Survey

Statistician

(Operations and

Administration)

15-2041 Statisticians

Survey

Statistician

(Social Science)

15-2041 Statisticians

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

PART II – GRADING INFORMATION

Part II provides grading information for use in determining the appropriate grade of

nonsupervisory two-grade interval professional positions in the Mathematical Sciences Group,

1500. These grading criteria are applicable to General Schedule positions classified under chapter

51 of title 5, United States Code. They may also be used as appropriate to determine work levels

for other Federal position classification systems. You will find more complete instructions for

evaluating positions in the following OPM publications: Introduction to the Position

Classification Standards and The Classifier’s Handbook.

How To Use This Grading Information

Evaluate positions on a factor by factor basis using the factor level descriptions (FLDs) provided

in this standard. Compare each factor in the position description to the appropriate FLDs and

illustrations. If the factor information in the position description fully matches an FLD for the

series and specialty, you may assign the level without reviewing the illustrations. FLDs are

progressive or cumulative in nature. For example, each FLD for Factor 1 – Knowledge Required

by the Position encompasses the knowledge and skills identified at the previous level. Use only

designated point values.

The FLDs in this standard cover nonsupervisory positions at grades GS-5 through GS-15.

Evaluate supervisory, leader, test and evaluation, research grants, and research positions by

applying the appropriate functional guide.

Use the occupation- and specialty-specific factor illustrations following the FLDs as a frame of

reference for applying factor level concepts. Do not rely solely on illustrations in evaluating

positions, because they reflect a limited range of actual work examples. The level of work

described in some illustrations may be higher than the threshold for a particular factor level. If the

factor information in the position description fails to fully match a relevant illustration, but does

fully match the FLD, you may still assign the level.

For each factor, record the factor level used, the points assigned, and relevant comments on the

Position Evaluation Summary Worksheet. Convert the total points to a grade using the Grade

Conversion Table, and record the grade in the Summary section of the Worksheet. The shaded

portions of the table reflect the most commonly found grades in this job family.

Grade Conversion Table

Point Range GS Grade

855-1100 5

1105-1350 6

1355-1600 7

1605-1850 8

1855-2100 9

2105-2350 10

2355-2750 11

2755-3150 12

3155-3600 13

3605-4050 14

4055-4480 15

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Position Evaluation Summary Worksheet

Organization _______________________________________________________________________

Position # _________________________________________________________________________

Evaluation Factors

Factor Level Used

(FL#, etc.)

Points Assigned Comments

1. Knowledge Required

by the Position

2. Supervisory Controls

3. Guidelines

4. Complexity

5. Scope and Effect

6/7. Personal Contacts and

Purpose of Contacts

8. Physical Demands

9. Work Environment

Total Points

Grade Conversion

Additional Remarks:

Title, Series, and Grade Assigned:

Prepared by: __________________________________________ Date:_______________________

Agencies may copy for local use.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Factor Level Descriptions

FACTOR 1 – KNOWLEDGE REQUIRED BY THE POSITION

Factor 1 measures the nature and extent of information or facts that an employee must understand

to do acceptable work (e.g., steps, procedures, practices, rules, policies, theories, principles, and

concepts) and the nature and extent of the skills necessary to apply that knowledge. You should

only select a factor level under this factor when the knowledge described is required and applied.

Level 1-5 750 Points

General Mathematics

and Statistics

1501 Mathematics 1520

Actuarial Science 1510

Mathematical

Statistics

1529

Series

Operations Research 1515 Statistics 1530

FLD

Knowledge of and skill in applying:

• basic mathematical, statistical, or financial theories;

• basic authoritative references;

• routine formulas, operating procedures, and data processing practices;

• related technical tasks (e.g., computer programming, financial management, or engineering); and

• professional academic training in methods and principles

sufficient to:

• perform routine, scientific, or technical tasks and projects;

•

perform recurring tasks or calculations;

follow oral or written technical instructions and work in close cooperation with other workers; and

complete training assignments that familiarize the employee with the organization’s program requirements,

techniques, and procedures.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Level 1-6 950 Points

General Mathematics and

Statistics

1501 Mathematics 1520

Illustration(s)

Actuarial Science 1510 Illustration(s)

Mathematical

Statistics

1529

Illustration(s)

Series

Operations Research 1515 Illustration(s) Statistics 1530 Illustration(s)

FLD

Professional knowledge of and skill in applying:

• principles, theories, concepts, and methodology of the specific occupation;

• automated systems and computer programs;

• data sources;

• statutory and regulatory provisions

sufficient to:

• research, analyze, interpret, evaluate, and perform difficult, but well precedented assignments;

• learn techniques and gain knowledge through either job experience and/or extended professional training

(e.g., relevant graduate study) that supplements technical understanding;

• conduct analytical investigations using scientific methodology and problem solving;

• perform, interpret, and correlate various calculations, analyses, and computations for unknown factors or

relationships that are primarily matters of a factual nature or involve mechanisms that are well understood;

• use computers and information technology and their varied applications to accomplish projects, designs,

plans, and reports; and

• select and modify appropriate methods of operation, analyze and interpret results, and prepare reports.

Level 1-7 1250 Points

General Mathematics and

Statistics

1501 Mathematics 1520

Illustration(s)

Actuarial Science 1510 Illustration(s)

Mathematical

Statistics

1529

Illustration(s)

Series

Operations Research 1515 Illustration(s) Statistics 1530 Illustration(s)

FLD

Professional knowledge of and skill in applying a wide range of complex analytical, mathematical, statistical, or

actuarial theories, principles and practices sufficient to:

• perform the full range of specialized duties;

• plan, coordinate, and execute studies of marked difficulty and responsibility;

• apply modeling techniques and procedures;

• develop mathematical algorithms;

• write statistical computer programs;

• design and perform computer simulations;

• analyze data using probability statistics and trend analysis;

• design sample surveys; and

• modify established methods.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Level 1-8 1550 Points

General Mathematics and

Statistics

1501 Mathematics 1520

Illustration(s)

Actuarial Science 1510 Illustration(s)

Mathematical

Statistics

1529

Illustration(s)

Series

Operations Research 1515 Illustration(s) Statistics 1530 Illustration(s)

FLD

Mastery of and skill in applying broad areas of classical and modern advanced actuarial science, operations

research, mathematics, or statistics; or specialized areas within the respective disciplines sufficient to:

• complete assignments that involve initiating, applying, and planning major developmental studies;

• execute and control projects that represent an important segment of the agency’s operating programs and/or

projects;

• serve as a consultant and technical advisor to senior subject matter specialists and/or agency officials

responsible for broad program operations;

• receive recognition as an authority in a particular specialty;

• provide significant and innovative recommendations for advancing programs and/or methods;

• use findings of specialized studies, new analytical developments, and modified processes to resolve novel or

obscure problems that affect broad program operations;

• evaluate the data resulting from applying mathematical or statistical tools, models, methods, and techniques;

and

• act as the authoritative source of technical input to publications or other documents that are the basis for

formulating public policy.

Level 1-9 1850 Points

General Mathematics and

Statistics

1501 Mathematics 1520

Illustration(s)

Actuarial Science 1510 Illustration(s)

Mathematical

Statistics

1529

Illustration(s)

Series

Operations Research 1515

Statistics 1530 Illustration(s)

FLD

Mastery of and skill in applying the principles, theories, and methodologies of a specialty area as it relates to the

respective disciplines of mathematics, statistics, operations research, or actuarial science sufficient to:

• provide expert consultation to heads of major organizations, high-ranking Government officials, and key

personnel within or outside the Federal Government;

• formulate, test, and evaluate new theories, principles, concepts, and practices of the discipline;

• advance state-of-the-art theories beyond established parameters;

• serve as an authoritative representative of the agency within or outside the Federal Government (e.g., by

serving as an expert in a specialty area at professional conferences);

• earn recognition as a major contributor to published research studies or pioneering efforts that produce

advanced theories, innovative applications, new scientific principles, or new research techniques; and

• provide management with expert technical guidance and recommendations for achieving the agency’s

objectives.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

FACTOR 2 – SUPERVISORY CONTROLS

This factor covers the nature and extent of direct or indirect controls exercised by the supervisor,

or a designated individual, over the work performed, the employee’s responsibility, and review of

completed work. The controls apply to both how supervisors assign and review work. The

supervisor determines what information the employee needs to perform the assignments (e.g.,

instructions, priorities, deadlines, objectives, and boundaries). Review controls may range from

detailed inspection of work in progress, to simply confirming that the work adheres to agency

policy. The employee’s responsibilities complement the supervisory controls (e.g., if the

supervisor does not establish the sequence in which the work is to be done, it becomes an

employee responsibility). The primary components of this factor are presented below in three

categories: How Work Is Assigned, Employee Responsibility, and How Work Is Reviewed.

NOTE: These factor level descriptions (FLDs) apply to all 1500P occupational series in this JFS.

Level 2-1 25 Points

FLD

How Work Is Assigned – The supervisor or a delegated alternate assigns work that consists of routine

requirements and developmental tasks designed to prepare the employee for higher level work. They provide:

• detailed instructions on how to use and select specific methods, procedures, and techniques; and

• deadlines and priorities.

Employee Responsibility – The employee:

• performs work as instructed;

• consults with the supervisor or designated employee when clarification of instructions is necessary; and

• receives guidance on problems and work methods not specifically covered by the original instructions.

How Work Is Reviewed – The supervisor or a delegated alternate closely checks work in progress and work

results for accuracy, and evaluates the employee’s rate of development. As the employee progresses

professionally and becomes more competent in certain work areas, the supervisor gradually relaxes control over

work in progress, but continues to closely review and evaluate the work for accuracy.

Level 2-2 125 Points

FLD

How Work Is Assigned – The supervisor or designated employee instructs the employee on work objectives

and its scope, limitations, expected deadlines, and priorities. The supervisor may provide more detailed

instructions when assigning work of a type that the employee has not previously done.

Employee Responsibility – The employee:

• uses initiative in carrying out recurring assignments;

• works independently, but within the framework the supervisor established;

• conforms with established practices and prescribed procedures; and

• refers problems not covered by the instructions or guides to the supervisor for help or a decision.

How Work Is Reviewed – The supervisor or designated employee:

• reviews completed work closely to verify accuracy and conformance to policy or procedural requirements

and any special instructions;

• reviews findings and conclusions to ensure they are supported by facts; and

• reviews in detail the more difficult work that the employee has not previously done.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Level 2-3 275 Points

FLD

How Work Is Assigned – The supervisor or designated employee outlines or discusses possible problem areas

and defines objectives, plans, priorities, and deadlines. Assignments have clear precedents requiring successive

steps in planning and execution.

Employee Responsibility – The employee:

• independently plans and carries out assignments in conformance with accepted policies and practices;

• adheres to instructions, policies, and guidelines in exercising judgment to resolve commonly encountered

work problems and deviations; and

• brings controversial information or findings to the supervisor’s attention for direction.

How Work Is Reviewed – The supervisor or designated employee:

• provides assistance on controversial or unusual situations that do not have clear precedents;

• reviews completed work for conformity with policy, the effectiveness of the employee’s approach to the

problem, technical soundness, adherence to deadlines, and accomplishment of objectives; and

• performs limited review of the methods used to complete the assignment.

Level 2-4 450 Points

FLD

How Work Is Assigned – The supervisor outlines available resources and overall objectives of the work. The

employee and supervisor, in consultation, discuss scope of the assignment, approaches, timeframes, and

possible execution phases.

Employee Responsibility – The employee:

• plans and carries out the assignment;

• resolves most of the conflicts that arise;

• coordinates the work with others as necessary;

• interprets policy and regulatory requirements;

• keeps the supervisor informed of progress and potentially controversial problems, concerns, and issues;

• develops changes to plans and/or methodology; and

• provides recommendations for improvements to meet program objectives.

How Work Is Reviewed – The supervisor reviews completed work for soundness of overall approach,

adherence to requirements, achievement of expected results, and the feasibility of recommendations. The

supervisor usually does not review methods used.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Level 2-5 650 Points

FLD

How Work Is Assigned – The supervisor provides administrative direction for projects in terms of broadly

defined missions or functions of the agency.

Employee Responsibility – The employee:

• is responsible for a significant agency or equivalent level program or function;

• defines objectives;

• interprets policies promulgated by authorities senior to the immediate supervisor and determines their effect

on program needs;

• exercises a wide degree of independent professional discretion and judgment; and

• independently plans, designs, and carries out the work to be done.

How Work Is Reviewed – The supervisor:

• reviews work for potential impact on broad agency policy objectives and program goals;

• normally accepts work as being technically authoritative; and

• normally accepts work without significant change.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

FACTOR 3 – GUIDELINES

This factor covers the nature of guidelines and the judgment employees need to apply them. The

availability of specific, applicable guidelines may vary with individual assignments; thus, the

judgment employees use similarly varies with the assignment. The existence of detailed plans

and other instructions may make innovation in planning and conducting work unnecessary or

undesirable. However, in the absence of guidance provided by prior agency experience with the

task at hand or when objectives are broadly stated, the employee may use considerable judgment

in developing an approach or planning the work. The following are examples of guidelines used

in professional work in the Mathematical Sciences Group, 1500:

• Agency regulations, directives, procedures, rulings, and initiatives

• Legislation and requirements covering program operations (e.g., Employee Retirement Income Security Act,

Social Security Act, Retirement Protection Act)

• Data merging system documentation

• Professional association and private sector standards of practice, conduct, procedures, and certification (e.g.,

American Hospital Association, Blue Cross Blue Shield)

• Military directives

• Agency developed systems performance, testing, and life cycle management handbooks, specifications, and

instructions

• Agency developed technical manuals and standard operating procedure guidance (e.g., statistical analysis, cost

analysis/estimating, auditing, optimization, design of experiments, quality assurance, and mathematical

modeling)

• Computer software and hardware manuals

• Precedent data, studies, models, and cases

• Tables, charts, forms, and maps (e.g., life expectancy, properties, interest rates, productivity, mileage)

• Guidelines, circulars, and regulations of other agencies and organizations such as the Office of Management

and Budget, Office of Personnel Management, Department of Labor, Department of the Treasury, Pension

Benefit Guaranty Corporation, Internal Revenue Service, and functional regulations (e.g., the Federal

Acquisitions Regulations)

• Files and records, such as previous audit reports

• Technical reports (e.g., reports of capabilities, performance, effectiveness, test results)

• Treaties (e.g., U.S. Canada Salmon Treaty)

• Established data collection, sampling, investigative, and examining procedures

• Traditional budgetary practices, procedures, and policies

Do not confuse guidelines with the knowledge described under Factor 1 – Knowledge

Required by the Position. The primary components of this factor are: Guidelines Used and

Judgment Needed.

NOTE: These factor level descriptions (FLDs) apply to all 1500P occupational series in this JFS.

Level 3-2 125 Points

FLD

Guidelines Used – The employee uses a number of guidelines that are directly applicable to the assignment.

Guidelines prescribe established procedures and techniques and provide clear precedents.

Judgment Needed – The employee:

• uses judgment in selecting and applying the most appropriate guidelines;

• determines the appropriateness and applicability of any minor deviations within existing guidelines; and

• refers to the supervisor situations to which the existing guidelines cannot be applied or that require

significant deviations.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Level 3-3 275 Points

FLD

Guidelines Used – The employee uses a wide variety of reference materials and manuals; however, they are not

always directly applicable to the work, or they have gaps in specificity. Precedents are available outlining the

preferred approach to more general problems or issues.

Judgment Needed – The employee is expected to apply guidelines accurately and articulate the reasons for

modifying specific guidelines to address unusual situations.

Level 3-4 450 Points

FLD

Guidelines Used – The employee uses guidelines and precedents that are very general regarding agency policy

statements and objectives. Guidelines specific to assignments are often scarce, not applicable, or have gaps in

specificity that require considerable interpretation and/or adaptation for application to issues and problems.

Judgment Needed – The employee uses judgment, initiative, and resourcefulness in deviating from established

methods to:

• modify, adapt, and/or refine broader guidelines to resolve specific complex and/or intricate issues and

problems;

• deal with specific issues or problems;

• research trends and patterns;

• develop new methods and criteria; and/or

• propose new policies and practices.

Level 3-5 650 Points

FLD

Guidelines Used – The employee uses guidelines such as broad policy statements, basic legislation, recent

scientific findings, or reports that are often ambiguous and require extensive interpretation.

Judgment Needed – The employee uses considerable judgment and ingenuity and exercises broad latitude to:

• determine the intent of new or revised guidelines;

• develop policy and guidelines for specific areas of work; and

• interpret policy statements, regulations, and methods development plans.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

FACTOR 4 – COMPLEXITY

This factor covers the nature, number, variety, and intricacy of tasks, steps, processes, or methods

in the work performed; the difficulty in identifying what needs to be done; and the difficulty and

originality involved in performing the work. The primary components of this factor are: Nature

of Assignment, What Needs To Be Done, and Difficulty and Originality Involved.

NOTE: These factor level descriptions (FLDs) apply to all 1500P occupational series in this JFS.

Level 4-2 75 Points

General Mathematics and

Statistics

1501 Mathematics 1520

Illustration(s)

Actuarial Science 1510 Illustration(s)

Mathematical

Statistics

1529

Illustration(s)

Series

Operations Research 1515 Statistics 1530

FLD

Nature of Assignment – Work consists of specific related tasks that provide experience in the methods,

practices, and procedures of the field.

What Needs To Be Done – The employee decides what needs to be done by choosing from various alternatives.

The employee may rely on established procedures and practices when making these decisions.

Difficulty and Originality Involved – When doing the work, the employee must recognize differences among a

few easily distinguishable situations.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Level 4-3 150 Points

General Mathematics and

Statistics

1501 Mathematics 1520

Illustration(s)

Actuarial Science 1510

Mathematical

Statistics

1529 Illustration(s)

Series

Operations Research 1515 Statistics 1530 Illustration(s)

FLD

Nature of Assignment – Work consists of assisting and participating with senior staff in:

• responding to more complex requests for technical data concerning mathematical and statistical programs;

• consulting on the proper use of data and applying data to specific mathematical or statistical problems; and

• performing analytical services.

What Needs To Be Done – The employee decides what needs to be done by:

• analyzing scientific data through computational processes;

•

comparing data from various reference sources or research agencies to identify correlating factors; and

interpreting the data and explaining the mathematical or statistical techniques and limitations, and the

significance of their use to the specific problem; and

planning and preparing special reports, statistical materials, and mathematical documentation.

Difficulty and Originality Involved – The employee must recognize and apply an understanding of

interrelationships among different functions and activities to determine the most appropriate technique for

processing or presenting data.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Level 4-4 225 Points

General Mathematics and

Statistics

1501 Mathematics 1520

Illustration(s)

Actuarial Science 1510 Illustration(s)

Mathematical

Statistics

1529

Illustration(s)

Series

Operations Research 1515 Illustration(s) Statistics 1530 Illustration(s)

FLD

Nature of Assignment – Work consists of carrying out the technical aspects of various mathematical or

statistical programs or activities, processes, and methods.

What Needs To Be Done – To decide what needs to be done, the employee must:

• research, analyze, test, and evaluate information, unusual circumstances, and conventional issues,

conditions, and problems;

• reconcile different, incomplete, and often conflicting information and alternatives;

• evaluate problems and situations with conflicting requirements when solutions may have serious

implications for industry, commercial concerns, the environment, or the general public; and

• determine economic, effective, and feasible solutions to meet the project requirements and constraints.

Difficulty and Originality Involved – The employee uses judgment and originality to:

• plan the sequence, direction, and progress of the work;

• interpret and justify actions, determinations, and recommendations;

• discern or devise creative solutions and actions that resolve issues, conditions, and problems;

• modify, adapt, and/or refine existing applications, processes, precedents, and techniques; and

• persuade others to accept, adopt, and act on recommendations and determinations.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Level 4-5 325 Points

General Mathematics and

Statistics

1501 Mathematics 1520

Illustration(s)

Actuarial Science 1510 Illustration(s)

Mathematical

Statistics

1529

Illustration(s)

Series

Operations Research 1515 Illustration(s) Statistics 1530 Illustration(s)

FLD

Nature of Assignment – Work consists of various duties of marked complexity, significance, and importance

performed in areas where precedents are inadequate, inappropriate, or nonexistent.

What Needs To Be Done – The employee decides the most effective approach or methodology by:

• identifying, developing, and integrating pertinent information through various data collection/analysis

procedures and technologies;

• anticipating major problems; and

• recognizing future needs.

Difficulty and Originality Involved – The employee must:

• develop innovative approaches to complex situations or problems that are unique and amorphous;

• develop mathematical or statistical relationships that are new or significant departures from the relationships

established in previous problems, studies, or investigations, causing outcomes that are usually original in

nature;

• apply and adapt sophisticated analytical, mathematical, or statistical techniques and occasionally principles

of related disciplines such as engineering, finance, or economics to resolve problems;

• generate ideas for new programs, policies, or approaches;

• visualize the impact of alternative strategies and methods;

• assess the feasibility, effectiveness, and necessity of unusual approaches; and

• identify the effects associated with implementing proposed standards, regulations, and policies.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Level 4-6 450 Points

General Mathematics and

Statistics

1501 Mathematics 1520

Illustration(s)

Actuarial Science 1510 Illustration(s)

Mathematical

Statistics

1529

Illustration(s)

Series

Operations Research 1515 Statistics 1530 Illustration(s)

FLD

Nature of Assignment – Work consists of assignments that involve solving problems characterized by:

• impacts on broad functional areas and processes; and

• exceptional breadth and intensity of effort.

What Needs To Be Done – The employee must decide what needs to be done in an environment characterized

by undefined factors and conditions. The employee must conduct extensive investigations and analyses of the

nature and scope of problems to make those decisions.

Difficulty and Originality Involved – The employee must continually:

•

plan and lead efforts to address issues in areas where precedents do not exist;

develop new concepts, theories, approaches, or programs to solve problems that have previously resisted

solution; and

often pursue several activities concurrently or sequentially with the support of others within or outside the

agency.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

FACTOR 5 – SCOPE AND EFFECT

This factor covers the relationships between the nature of work; i.e., the purpose, breadth, and

depth of the assignment, and the effect of work products or services both within and outside the

organization. Effect measures whether the work output facilitates the work of others, provides

timely services of a personal nature, or impacts the adequacy of research conclusions. The concept

of effect alone does not provide sufficient information to properly understand and evaluate the

impact of the position. The scope of the work completes the picture allowing consistent

evaluations. Only consider the effect of properly performed work. The primary components of

this factor are: Scope of the Work and Effect of the Work.

NOTE: These factor level descriptions (FLDs) apply to all 1500P occupational series in this JFS.

Level 5-1 25 Points

General Mathematics and

Statistics

1501 Mathematics 1520

Actuarial Science 1510

Mathematical

Statistics

1529

Series

Operations Research 1515 Statistics 1530

FLD

Scope of the Work – Work involves:

• specific, routine duties that include a few separate tasks or procedures; and

• assignments that familiarize the employee with the organization’s programs and services.

Effect of the Work – Work results facilitate the work of others and have little impact beyond the immediate

organizational unit.

Level 5-2 75 Points

General Mathematics and

Statistics

1501 Mathematics 1520

Actuarial Science 1510

Mathematical

Statistics

1529

Series

Operations Research 1515

Statistics 1530 Illustration(s)

FLD

Scope of the Work – Work involves:

• applying specific standards, methods, and procedures to carry out tasks;

• assisting others by relieving them of routine work associated with larger studies; and

• completing a segment of an assignment or project of broader scope.

Effect of the Work – Work results affect the overall accuracy, reliability, acceptability, and timeliness of the

final work products or services developed or delivered by higher graded coworkers.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Level 5-3 150 Points

General Mathematics and

Statistics

1501 Mathematics 1520

Actuarial Science 1510 Illustration(s)

Mathematical

Statistics

1529

Illustration(s)

Series

Operations Research 1515 Illustration(s) Statistics 1530 Illustration(s)

FLD

Scope of the Work – Work involves:

• providing solutions or services that reflect a familiarity with established principles, concepts, and theories of

related professional science fields and their interrelated interests and technologies;

• adhering to precedents and established techniques to resolve a variety of traditional problems, issues, or

conditions and to provide routine customer services; and

• problem solving or research activity for a variety of conventional problems or situations.

Effect of the Work – Work results affect the:

• economy, efficiency, feasibility, security, integrity, accuracy, adequacy, and safety of a wide range of

project activities and services such as field studies and/or laboratory services;

• wellbeing of life and the general public;

• program credibility with internal and external customers; and

• utilization, development, protection, and management of natural resources in the immediate vicinity.

Level 5-4 225 Points

General Mathematics

and Statistics

1501 Mathematics 1520

Illustration(s)

Actuarial Science 1510 Illustration(s)

Mathematical

Statistics

1529

Illustration(s)

Series

Operations Research 1515 Illustration(s) Statistics 1530 Illustration(s)

FLD

Scope of the Work – Work involves:

• formulating, defining, and interpreting data presentation requirements, planning approaches, and policy;

• developing standards for analyzing, testing, or assessing emerging technology or methods;

• originating new and improved applications and strategies for existing and new concepts and principles;

and/or

• providing consultant or advisory services.

Effect of the Work – Work results affect:

• efficiency and credibility of applications that guarantee that the product meets agency and industry

specifications;

• decisions of key officials to adopt and/or accept new or conceptual approaches, technology, or materiel

(e.g., weapons or system components, ordnance);

• a large number of military or industrial operations;

• the safe and effective use of new systems or approaches; and

• systems compatibility.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Level 5-5 325 Points

General Mathematics and

Statistics

1501 Mathematics 1520

Illustration(s)

Actuarial Science 1510 Illustration(s)

Mathematical

Statistics

1529

Illustration(s)

Series

Operations Research 1515 Illustration(s) Statistics 1530 Illustration(s)

FLD

Scope of the Work – Work involves:

• formulating and exploring new theories and phenomena;

• providing expertise and advice on program planning and policy making functions covering a broad range of

mathematical, statistical, or scientific programs; and/or

• developing, testing, and advising on theoretical concepts and new or improved technologies and methods.

Effect of the Work – Work results affect the:

• work of other mathematical, statistical, or science experts;

• strategic planning of organizational resources;

• development of agency policy; and

• program mission, performance, and necessity.

Level 5-6 450 Points

General Mathematics and

Statistics

1501 Mathematics 1520

Actuarial Science 1510 Illustration(s)

Mathematical

Statistics

1529

Illustration(s)

Series

Operations Research 1515 Statistics 1530 Illustration(s)

FLD

Scope of the Work – Work involves:

• selecting productive areas for analysis, and defining and developing the technical scope and aims of

assignments;

• exploiting established and emerging methods on applications that meet industry needs; and

• a highly specialized research environment with the potential to revolutionize system design processes for an

industry.

Effect of the Work – Work results affect the:

• success and continuation of key programs essential to the agency’s mission;

• vitality and integrity of mathematical, statistical, or science programs on a long-term and/or continuing

basis;

• protection and quality of life, health, and/or property of the general public and national or international

resources;

• continuing advancement of science and technology in research, industrial activities, academia, the Federal

sector, and the private sector; and/or

• ability to evaluate changes and trends in an industry or scientific discipline.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

FACTOR 6 – PERSONAL CONTACTS

AND

FACTOR 7 – PURPOSE OF CONTACTS

These factors include face-to-face and remote dialogue – e.g., telephone, email, and video

conferences – with persons not in the supervisory chain. (Personal contacts with supervisors are

under Factor 2 – Supervisory Controls.) The levels of these factors consider the work required to

make the initial contact, difficulty of communicating with those contacted, the setting in which the

contact takes place, and the nature of the discourse. The setting describes how well the employee

and those contacted recognize their relative roles and authorities. The nature of the discourse

defines the reason for the communication and the context or environment in which the

communication takes place. For example, the reason for communicating may be to exchange

factual information or to negotiate. The communication may take place in an environment of

significant controversy and/or with people of differing viewpoints and goals.

Only credit points under Factors 6 and 7 for contacts that are essential for successfully performing

the work and that have a demonstrable impact on its difficulty and responsibility. Factors 6 and 7

are interdependent, so use the same personal contacts to evaluate both factors.

Determine the appropriate level for Personal Contacts and the corresponding level for Purpose of

Contacts. Obtain the point value for these factors from the intersection of the two levels as shown

on the Point Assignment Chart at the end of this section.

NOTE: These factor level descriptions (FLDs) apply to all 1500P occupational series in this JFS.

PERSONAL CONTACTS

Level 1

Other professionals, technicians, and support personnel in the immediate office or related units

within the agency. Limited contact with employees outside the office.

Level 2

Employees in the same agency, professionals and specialists from related occupations, and/or

members of the general public in a moderately structured setting. Typical contacts are:

• scientists and engineers;

• military personnel;

• client organization representatives.

Level 3

Individuals or groups inside and outside the employing agency representing high levels of

organizations internal and external to the Federal Government. Typical contacts are:

• management officials or senior technical staff of corporations;

• medical and legal professionals;

• contractors; and

• State and local officials;

• Government, academia, and professional organizations;

• representatives of Congressional committees.

Level 4

High ranking officials from outside the employing agency at national or international levels in

highly unstructured settings. Typical contacts are:

• members of Congress or their professional staffs/representatives;

• leading officials of foreign Governments; and

• Presidential advisors and/or cabinet level appointees of major departments and agencies;

• State governors and mayors of large cities or their professional staffs/representatives;

• presidents of large national or international firms; or

• leaders of national stakeholder and/or interest groups.

Professional Work in the Mathematical Sciences Group, 1500 September 2005

U.S. Office of Personnel Management

Purpose of Contacts

Level A

To obtain, clarify, or exchange information or facts needed to complete an assignment.

Level B

To plan, coordinate, or advise on work efforts or to resolve issues or operating problems. Contacts

involve influencing or persuading people who have a cooperative attitude and goals in common

with those of the employee. Contacts typically involve identifying options for resolving problems.

Level C

To influence and persuade persons or groups to comply with established policies or to accept

established methods. Also to negotiate or establish rapport to gain information. Contacted

personnel may be skeptical or uncooperative.

Level D

To justify, defend, negotiate, or settle matters involving significant or controversial topics. Work

usually involves active participation in conferences, meetings, hearings, or presentations.

Problems or issues are of such considerable consequence or importance that they are not

susceptible to resolution at lower echelons in Government. Persons contacted typically have

diverse scientific approaches, viewpoints, goals, or objectives. The employee must achieve a

common understanding of the problem and a satisfactory solution by persuasion, compromise, or

developing suitable alternatives.

POINT ASSIGNMENT CHART

Purpose of Contacts

Level A B C D

1 30 60 130* 230*

2 45 75 145 245

3 80 110 180 280

Personal

Contacts

4 130* 160 230 330

*THIS COMBINATION IS UNLIKELY

Professional Work in the Mathematical Sciences Group, 1500 September 2005

FACTOR 8 – PHYSICAL DEMANDS

NOTE: Laws and regulations governing pay for irregular or intermittent duty involving unusual

physical hardship or hazard are in section 5545(d), title 5, United States Code, and Subpart I, part

550, title 5, Code of Federal Regulations.

NOTE: These factor level descriptions (FLDs) apply to all 1500P occupational series in this JFS.

Level 8-1 5 Points

FLD

The work is sedentary. Some work may require periods of walking, standing, bending, or driving a motor

vehicle. Employees frequently carry research records and other similar materials. The work does not

require any special physical effort.

Level 8-2 20 Points

The work requires some physical exertion such as:

long periods of standing; •

•

walking over rough, uneven, or rocky surfaces;

recurring bending, crouching, stooping, stretching, reaching, or similar activities; and

FLD

recurring lifting of moderately heavy items (i.e., less than 22.5 kilograms (50 pounds)), or cumbersome

items (e.g., small animals, weapon components).

The work may require specific, but common physical characteristics and capacities such as above average

agility and dexterity.

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

FACTOR 9 – WORK ENVIRONMENT

NOTE: Laws and regulations governing pay for irregular or intermittent duty involving unusual

physical hardship or hazard are in section 5545(d), title 5, United States Code, and Subpart I of

Part 550 of Title 5, Code of Federal Regulations.

NOTE: These factor level descriptions (FLDs) apply to all 1500P occupational series in this JFS.

Level 9-1 5 Points

Works in an adequately lighted, heated, and ventilated environment. The work area involves everyday risks or

discomforts that require normal safety precautions typical of such places as offices, laboratories, meeting and

training rooms, libraries, or commercial vehicles.

FLD

Level 9-2 20 Points

FLD

Work involves moderate risks or discomforts that require special safety precautions and/or use of protective

clothing or gear such as masks, gowns, coats, boots, goggles, gloves, shields, or life preservers. Work is done

in an environment of moving parts, carts, or machines, and/or near or with contagious diseases or irritant

chemicals.

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

Factor Illustrations

Illustrations are provided in this part as a tool to give insight into the meaning of the FLDs for

Factors 1, 4, and 5. Consider each illustration in its entirety and in conjunction with the FLDs. Do

not rely solely on these illustrations in evaluating positions.

For additional information about the proper use of illustrations, see the How To Use This Grading

Information section of this JFS.

Factor 1 Illustrations

LEVEL 1-6: ACTUARY, 1510 (ILLUSTRATION 1)

Professional knowledge of and skill in applying the principles, concepts, and methodology of actuarial science; and

knowledge of:

•

actuarial processing of various factors;

• basic analytical and actuarial techniques; and

agency program and operating procedures

sufficient to:

analyze beneficiary and benefit data to determine actuarial relationships;

develop factors for use in expanding items in a sample by linking sample totals to related known data for a

corresponding whole group (i.e., a universe);

make logical adjustments, where necessary, to preserve consistent relationships among expanded data

elements;

review, prior to publication, worksheets and final tables showing benefit data to ensure conformance to

conventional procedures and the reasonableness of results; and

perform regulatory actuarial examinations of life underwriters’ financial statements and other official filings to

determine valuation of reserves, gross and taxable premiums, and compliance with legal requirements for

license renewal.

⇐BACK TO TABLE OF CONTENTS

LEVEL 1-6: ACTUARY, 1510 (ILLUSTRATION 2)

Professional knowledge of and skill in applying the principles, concepts, and methodology of actuarial science; and

knowledge of:

•

actuarial processing of various mathematical factors;

routine analytical and actuarial techniques; and

agency program and operating procedures

sufficient to:

• apply routine actuarial formulas to obtain rates and values for various plans of insurance and annuities;

• apply established procedures and make actuarial calculations for use in an annual statement;

• develop administrative support procedures for use in computations and compilations; and

• apply alternate mortality tables to compare an underwriter’s risk listings with the reserve funds reported.

⇐BACK TO TABLE OF CONTENTS

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 1-6: OPERATIONS RESEARCH ANALYST, 1515

Professional knowledge of and skill in applying the principles, concepts, and methodology of mathematics and

analysis sufficient to:

• perform minor phases of a larger assignment pertaining to the design, development, and testing of weapons

control software systems;

• prepare required recurring reports, correspondence, and documentation;

• work closely with a senior operations research analyst in using routine cost estimating methods such as

analogy, engineering or scientific methodology, and extrapolation;

• use cost estimating outputs to assess the impact various factors have on the costs to design, research, develop,

operate, maintain, and dispose of a particular weapon system;

• identify the most appropriate phase of the budgetary cycle (planning, programming, justification, execution,

etc.) for initiating new programs; and

• identify and analyze all elements affecting costs for a project of limited scope.

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LEVEL 1-6: MATHEMATICIAN, 1520

Knowledge of and skill in applying:

• mathematical analyses of flight data;

• standard computations;

• measurements involving advanced algorithms, specialized techniques, methods, instruments, and software;

and

• computer equipment common to the organization

sufficient to:

• document results and accomplish tasks that require only a limited degree of originality;

• consider the physical relationships pertinent to a specific phase of aerospace research;

• assist a senior mathematician or subject matter specialist;

• process or analyze test data from various sources, such as radar, global positioning satellites, or cinetheodolite

film;

• use technical software to merge, plot, or convert raw data into a usable format;

• set up differential equations on a computer to obtain calculated transient engine curves, formulate and analyze

equations, plan and initiate computer configuration, and interpret results; and

• perform assignments of limited depth and scope by independently applying mathematical methods that relate

to one narrow specialization, technique, or method (e.g., differential equations).

⇐BACK TO TABLE OF CONTENTS

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 1-6: MATHEMATICAL STATISTICIAN, 1529

Knowledge of and skill in applying general mathematics and related subject matter and tools such as:

• standard automated systems equipment, and statistical software;

• statistical philosophy, methods, and techniques;

• advanced algebra;

• differential and integral calculus;

• theory of differential equations;

• set theory and matrices;

• mathematical statistics including the calculus of probability, probability theory, sampling theory, and

systematic methods of curve fitting; and

• theory of experimental design

sufficient to:

• perform mathematical statistical work covering the entire scientific method of investigation, background

research, reduction and analysis of data, and documentation;

• execute a series of standard tasks or calculations;

• use basic authoritative references on mathematical statistics;

• analyze factual information and recognize significant factors, relationships, and trends;

• write technical reports on findings of statistical investigations;

• develop schemes for quality surveillance of parts of major continuing statistical data collection systems;

• consult with a senior mathematical statistician and with other subject matter professionals on specific

statistical problems in collecting or analyzing data, determining cause(s) of problems, and developing

solutions; and

• participate in reviewing prospective new topics in the theory of sampling and non-sampling errors and in

statistical inference.

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LEVEL 1-6: STATISTICIAN, 1530 (ILLUSTRATION 1)

Professional knowledge of and skill in applying:

• standard precedents that form the basis for assigned studies;

• statistics in a subject matter field (e.g., economics, biology); and

• common statistical techniques

sufficient to:

• plan and effectively perform limited studies that have specific, program objectives and involve recurrent and

predictable factors;

• analyze factual information and recognize significant factors, relationships, and trends;

• prepare cross tabulations or frequency listings of selected variables to assess the validity of data before a

senior statistician does more complex work;

• prepare literature searches as background for further research; and

• prepare parts of internal documentation or proof documentation with researchers.

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(continued)

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 1-6: STATISTICIAN (ENGINEERING), 1530 (ILLUSTRATION 2) (CONTINUED)

Professional knowledge of and skill in applying:

• statistical methods to engineering related projects;

• standard precedents, such as munitions systems performance, that form the basis for assigned studies; and

• information obtained from electronic devices such as sensors or radar relating to the test requirements

sufficient to:

• write technical reports, plan and prepare graphic and tabular presentations of data, and present technical

documentation in a professional manner, as in a quality assurance assignment;

• develop a study plan and assess progress in accordance with established engineering objectives and

specifications;

• recognize unexpected problems or variations in results; and

• prepare preliminary interpretations or tentative recommendations.

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LEVEL 1-6: SURVEY STATISTICIAN, 1530 (ILLUSTRATION 3)

Professional knowledge of and skill in applying:

• standard precedents that form the basis for assigned studies;

• information obtained from multiple sources of raw data that relate to the subject matter under study;

• standard quantitative techniques;

• customized software that maps geographic regions using counties and zip codes; and

• statistically sound survey methods

sufficient to:

• determine whether completed surveys satisfy established survey administration requirements;

• identify the number of survey administrators or field interviewers in an area, the number of interviews to

distribute to each interviewer, and the type of interview the respondent receives;

• ensure that respondents adequately complete a sufficient number of surveys; and

• determine whether the non-response rate is too high to be statistically valid, and as appropriate, target those

individuals who did not complete the survey for a second attempt to interview.

⇐BACK TO TABLE OF CONTENTS

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 1-7: ACTUARY, 1510 (ILLUSTRATION 1)

Professional knowledge of and skill in applying a wide range of theories, principles, concepts, and methods of

actuarial science used in the medical field; and knowledge of:

• valuation techniques;

• data obtained from multiple sources;

• special charts, tables, and guides indicating rates, trends, and historical data; and

• medical terminology, records, forms, guides, and reference materials

sufficient to:

• perform professional actuarial duties of substantial breadth relating to a variety of health care issues;

• analyze program data to advise and assist statisticians in developing methodology;

• produce appropriate medical data using the most current actuarial, computer programming, survey, and other

techniques;

• analyze data collected from a wide variety of sources to determine the nature and extent of the problem,

interpret actuarial implications, and recommend options for resolution;

• plan and conduct special recurring and nonrecurring studies of the mortality and disability experience under an

insurance program; and

• plan and lay out the work for performing investigations of such items as mortality, disability, withdrawal,

retirement, and remarriage that affect the valuation of assets and liabilities of an insurance program.

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LEVEL 1-7: ACTUARY, 1510 (ILLUSTRATION 2)

Professional knowledge of and skill in applying a wide range of theories, principles, concepts, and methods of

actuarial science used in the insurance industry; and knowledge of:

• valuation techniques;

• legislation and regulation related to life insurance;

• terminology, principles, and provisions of various types of insurance policies; and

• agency program policies

sufficient to:

• determine the use of reserve factors in the valuations of an insurance fund covering equity investment risks;

• formulate procedures for use in computing actuarial values of individual insurance contracts;

• conduct and formally report on the actuarial phases of site examinations of life insurance companies (unless it

involves unusual scope or complications such as a merger or conversion to a computerized system);

• analyze funds for soundness and trends including lapse ratios, unearned premiums, deficiency reserves, double

indemnity provisions, supplemental contracts, and other elements; and

• plan, lay out, and perform investigations of such items as mortality, disability, withdrawal, retirement, and

remarriage that affect the valuation of the assets and liabilities of an insurance program.

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(continued)

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 1-7: ACTUARY, 1510 (ILLUSTRATION 3) (CONTINUED)

Professional knowledge of and skill in applying a wide range of theories, principles, concepts, and methodology of

actuarial science; and knowledge of:

• valuation techniques;

• defined benefit pension plans;

• Employee Retirement Income Security Act (ERISA), agency regulations, and related policies and procedures;

• tax legislation and regulations pertaining to trusts, pension funds, insurance programs, and gifts; and

• agency program policies

sufficient to:

• plan and execute a variety of studies and analyses that relate to preparing periodic estimates of the future size

and composition of a population eligible for an insurance benefit;

• plan, lay out, and perform studies that affect the valuation of the assets and liabilities of an insurance program,

such as mortality, disability, withdrawal, retirement, and remarriage;

• plan and perform comprehensive actuarial analysis of a wide variety of pension plan terminations;

• develop the actuarial input into cases, including complex benefit and actuarial value calculations;

• coordinate the actuarial work on cases, including providing technical direction and expert advice to the

contractor;

• evaluate the efficiency, cost, and completeness of the contractor’s work, and serve as a liaison between the

agency and the contractor;

• analyze pension plan documents to determine benefit entitlements and ensure compliance with the ERISA;

• perform all aspects of actuarial valuation according to statute for cases, including:

– calculating guaranteed benefits and total benefits;

– calculating present values of these benefits;

– assigning benefit values to priority categories; and

– allocating assets according to priority categories;

• advise senior departmental and agency staff on actuarial issues, answer questions raised by outside actuaries,

and provide litigation support for the Office of the General Counsel; and

• modify established actuarial methods.

⇐BACK TO TABLE OF CONTENTS

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 1-7: OPERATIONS RESEARCH ANALYST, 1515

Professional knowledge of, and skill in applying a wide range of theories, concepts, and methods of analytical,

mathematical, or statistical principles and practices to military weapons programs; and knowledge of:

• analytical processes, such as:

– setting up the problem;

– conducting background research;

– collecting and reducing data;

– displaying data for analysis;

– formulating mathematical expressions; and

– drawing conclusions;

• analytical techniques such as design of experiments and computer modeling/simulation;

• subject matter specialties (e.g., aircraft survivability, risk analysis, or lethality) related to weapons systems;

• statutory provisions; and

• agency program policies

sufficient to participate in a variety of projects under the direction of a senior analyst to:

• determine tradeoff relationships between system operating costs and level of performance;

• determine the optimum test design that minimizes the amount of testing while still providing adequate data for

decision making;

• determine the effect of equipment age on system performance;

• evaluate the appropriate mix of support equipment to obtain maximum effectiveness on the battlefield; and

• work as a team member in an organization that conducts operations research investigations of military

weapons and materiel systems.

⇐BACK TO TABLE OF CONTENTS

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 1-7: MATHEMATICIAN, 1520 (ILLUSTRATION 1)

Professional knowledge of and skill in applying:

• a specialized branch of mathematics (e.g., numerical analysis, special functions, matrix theory, or computation

methods);

basic mathematical relationships unique to the area of application; •

•

precedents of related studies;

analog and digital math models and other specialized techniques; and

recent mathematical advances in the particular area of responsibility

sufficient to:

• design simulation experiments, analyze results, and prepare appropriate technical reports;

• determine test and evaluation requirements for software associated with major reconfiguration or modification

of sophisticated automated systems (e.g., weapons) including applications, diagnostic, and maintenance

programs;

• prepare evaluation of test activities;

• develop or participate in determining appropriate mathematical and statistical methods for operational

analyses, interpretation, and evaluation of specific tests for system components;

• adapt and apply existing mathematical methods and techniques in a specialized branch of mathematics to

specific subject matter applications; and

• formulate problems, select a range of values and intervals, and determine the method of solution that best fits

the essential types of calculations.

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LEVEL 1-7: MATHEMATICIAN, 1520 (ILLUSTRATION 2)

Professional knowledge of and skill in applying:

• a specialized branch of mathematics (e.g., partial and ordinary differential equations, numerical analysis,

special functions, matrix theory, or computation methods) associated with aerospace technology;

•

complex mathematical relationships and problems related to the principles of aerodynamics;

mathematical phases of research and development projects;

precedents of related studies; and

recent mathematical advances in the area of specialty

sufficient to:

investigate orbital dynamics of earth satellites;

determine methods to derive and predict dynamics; and

analyze tracking data obtained through surveillance activities, including:

– determining the objectives of such analyses and priorities of major phases;

– providing consultative services to scientists in other Federal agencies on projects associated with re-entry

studies;

– formulating mathematical models and associated computation methods to analyze special problem areas

and evaluate system performance;

– developing data to facilitate choice of optimum time of satellite launch; and

– reducing orbital equations by simplifying assumptions that cause no adverse effects on final results.

⇐BACK TO TABLE OF CONTENTS

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 1-7: MATHEMATICAL STATISTICIAN, 1529

Professional knowledge of and skill in applying:

• stratification and clustering in probability sampling;

• alternative variance estimating;

• inference procedures for complex survey data;

• design effects;

• mathematical/statistical theory;

• mathematical methods;

• survey and sample design techniques;

• complex applied sample and variance estimating;

• statistical error modeling; and

• complex computer-designed software

sufficient to:

• research, plan, and implement projects that involve developing new or modifying existing sampling,

surveying, and design methods that include:

– developing and programming imputation models to predict missing values in a demographic study or

economic survey;

– comparing variance estimation; and

– developing/programming representative samples for field survey projects;

• serve as an advisor to peers on mathematical statistical topics (e.g., theory of sampling and non-sampling

errors and theory of statistical inference);

• develop statistical standards to evaluate data quality;

• develop aspects of survey and sampling designs that ensure continuity between data collection and analysis of

data; and

• write methodological and/or technical reports of substantive survey findings for publication.

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LEVEL 1-7: STATISTICIAN (AGRICULTURE), 1530 (ILLUSTRATION 1)

Professional knowledge of, and skill in applying:

• agricultural theories and techniques;

• methods, principles, and characteristics of statistical resources and procedures associated with agricultural

sciences or of specialized agricultural studies such as farming or crop production; and

• relevant statutory provisions and objectives

sufficient to:

• serve as a commodity statistician capable of handling assignments in any of several major commodity program

groups;

• plan and conduct agricultural surveys (e.g., production of oranges in warm, rainy climates);

• prepare estimates, forecasts, and reports of considerable scope and difficulty relating to groups of crops,

commodities, or items that:

− are of major importance within the overall agricultural production and economy of a state; and

− comprise a significant segment of the assigned commodity program group.

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(continued)

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 1-7: STATISTICIAN, 1530 (ILLUSTRATION 2) (CONTINUED)

Professional knowledge of and skill in applying:

• statistical theory and techniques;

• the methods, principles, and characteristics of a particular statistical specialty (e.g., survey design) or of the

statistical resources and procedures of a subject matter field; and

• relevant statutory provisions and objectives

sufficient to:

• accomplish work that typically includes several related studies or several segments of a large data collection

project that the employee coordinates simultaneously;

• recognize and evaluate significant and critical factors in research;

• solve complex problems (or advise others on the solution of such problems);

• draw inferences using statistical data;

• ascertain what frequency listings or cross tabulations would be needed to assess data validity and to identify

inconsistencies in the data;

• calculate prevalence rates and create adjusted rates;

• prepare parts of documentation for public release;

• prepare comprehensive and publishable reports; and

• co-author statistical presentations, journal articles, or reports.

⇐BACK TO TABLE OF CONTENTS

LEVEL 1-8: ACTUARY, 1510 (ILLUSTRATION 1)

Mastery of and skill in applying advanced theories, practices, methods, and principles of actuarial science; and

knowledge of program requirements and operations of the agency sufficient to:

• provide expert consultation to senior level staff in the agency and to other actuaries, analysts, and personnel on

social or health insurance issues, study approaches, research techniques amenable to actuarial methods, and the

validity of actuarial assumptions and methods;

• plan, coordinate, and analyze recent financial experience and prepare estimates of future experience based on

general social, economic, and demographic factors using a variety of actuarial techniques;

• present recommendations, conclusions, and findings accepted as authoritative by program officials and

colleagues; and

• formulate major policy and binding commitments for the organization served;

• independently plan and execute a variety of projects and make authoritative and final decisions requiring

considerable technical and administrative judgment;

• plan, coordinate, and evaluate new estimation methodologies and models and refine existing models for

program operations and for proposed changes; and

• provide guidance to team members on methodologies and techniques used in projecting social or health

insurance expenditures.

⇐BACK TO TABLE OF CONTENTS

(continued)

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 1-8: ACTUARY, 1510 (ILLUSTRATION 2) (CONTINUED)

Mastery of and skill in applying advanced theories, principles, concepts, methods and practices of actuarial

science; and knowledge of:

• valuation techniques;

• automated systems and computer programs;

• data sources;

• specific knowledge of defined benefit pension plans; and

• program requirements and operations of the agency

sufficient to:

• perform the calculations necessary to support the present value of future benefits in the agency’s financial

statements and Annual Report to Congress;

• plan, coordinate, and evaluate new estimation methods and refine existing methods that form a part of these

liability calculations;

• conduct studies of experience in single plan and multi-employer plan populations to validate assumptions and

methods;

• recommend significant changes to valuation software, review the technical specifications of changes and test

software once the changes have been made; and

• serve as a technical advisor to other departments and financial personnel about the implications of these

results;

• coordinate large or unique actuarial work proposed for execution by contractors by evaluating the efficiency,

cost, and completeness of the contractor’s work, and serving as a liaison between the agency and the

contractor;

• perform all aspects of actuarial valuation as required under the Employee Retirement Income Security Act

(ERISA), agency regulations, and related policies and procedures, including:

− calculating guaranteed benefits and total benefits;

− calculating present values of these benefits;

− assigning benefit values to priority categories; and

− allocating assets according to priority categories; and

• provide technical advice to departmental and agency staff on actuarial issues, answer questions raised by

outside actuaries, and provide litigation support for the Office of the General Counsel on matters impacting

legal or regulatory interpretation or the agency pension program.

⇐BACK TO TABLE OF CONTENTS

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 1-8: OPERATIONS RESEARCH ANALYST, 1515 (ILLUSTRATION 1)

Mastery of and skill in applying advanced, analytical, mathematical, or statistical theories, principles, concepts,

methods, and techniques related to:

• statistical analysis;

• parametric and non-parametric analysis;

• computer modeling;

• decision theory;

• mathematical programming;

• regression analysis; and

• economic analysis

sufficient to:

• design and develop the most appropriate techniques to solve problems, enhance performance, or increase

efficiency and effectiveness;

• provide expert judgments concerning the validity of assumptions made and the criteria to evaluate alternatives;

• conceptualize systems and reduce them to the most effective, simplified, and manageable representation and

treatment; and

• simulate a process, developing a detailed model of the most critical features of the process.

⇐BACK TO TABLE OF CONTENTS

LEVEL 1-8: OPERATIONS RESEARCH ANALYST, 1515 (ILLUSTRATION 2)

Mastery of and skill in applying advanced, analytical, mathematical, or statistical theories, principles, concepts,

methods, and techniques related to:

• statistical analysis;

• parametric and non-parametric analysis;

• computer modeling;

• decision theory;

• mathematical programming;

• regression analysis; and

• economic analysis

sufficient to:

• serve as a senior analyst in an organization responsible for developing analytical models and methods;

• identify actual or potential problem areas, trends, and similar factors to improve agency program operations

and management systems; and

• recommend new or amended legislation, policies, procedures, and management systems as they relate to

agency programs and Federal or State agencies with similar program responsibilities.

⇐BACK TO TABLE OF CONTENTS

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 1-8: MATHEMATICIAN, 1520

Mastery of and skill in applying advanced theories, principles, concepts, and practices of a broad range of

techniques in mathematics, computer modeling, and mathematical programming sufficient to:

• develop specifications and apply new computer software programs and/or modify existing programs to

perform mathematical analysis of phenomena observed during experimental investigations;

• ensure quality of program design and validate that newly created software accurately simulates the desired

physical phenomena and replicates experimental findings;

• perform as an advisor and authority for other researchers in the areas of mathematical modeling, analysis, and

computer programming methods;

• provide technical advice regarding the development of simulation methods, computer techniques, and the

utilization of operational mathematics in analysis of microelectronic systems;

• devise and implement pilot programs to determine the feasibility of computer solutions to existing problems;

and

• disseminate findings through published technical reports, papers, and presentations at symposia and

conferences.

⇐BACK TO TABLE OF CONTENTS

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 1-8: MATHEMATICAL STATISTICIAN, 1529

Mastery of advanced mathematical and statistical theories, principles, concepts, and practices, and skill in applying

this knowledge to:

• statistical procedures;

•

complex mathematics;

data or quantitative analysis;

complex sample designs;

data collection techniques;

reduction of data from multiple sources;

research and experimentation techniques (e.g., observation, documentation, etc.);

computer techniques such as:

– numerical and statistical analysis;

– probability theory;

– wave propagation modeling; and/or

– numerical simulation;

state-of-the-art statistical or mathematical tools; and

publications of statistical studies in the area of specialization

sufficient to:

• translate raw data of fish populations by species and stock into mathematical models to describe and explain

fluctuations of stock in the ocean (i.e., how fish populations vary over time, growth of individual fish,

reproductive processes, and mortality rates);

• develop simulated populations for testing alternative economic theories about consumer substitution behavior

and the implications for sampling and estimation of price indexes;

write and/or present comprehensive statistical reports and scientific manuscripts based upon the data collected

and analyzed; and

make recommendations to fishery commission officials, geneticists, biologists, and other professionals

regarding the extent to which fishing should be controlled to ensure the survival of fish species;

• perform a comprehensive evaluation of the statistical properties of current or prospective complex sample

designs or estimation methods; and

make recommendations to agency officials about the viability of proposed new methodologies or the

interpretation of test results;

provide project leadership for specialized programs.

⇐BACK TO TABLE OF CONTENTS

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 1-8: STATISTICIAN (HEALTH), 1530

Mastery of :

• advanced statistical theories, principles, concepts, methods, techniques, and practices;

• specialized statistical functions (e.g., techniques of statistical surveys);

• resources, precedents, practices, and principles within an area of specialization and its related areas;

• the benefits of, and demand for, statistical research that others are doing in the area of specialization;

• agency programs; and

• skill in applying this knowledge in health sciences subject matter such as heart disease, diabetes, osteoporosis,

or injuries

sufficient to:

• provide advice and consultation on a variety of problems involving the theory or application of statistical

methods;

• evaluate new statistical methods for broad and comprehensive projects;

• plan, direct, and coordinate a variety of specialized and complex statistical research projects and make

authoritative and final decisions requiring considerable technical and administrative judgment;

• serve, either on a continuing or special assignment basis, as consultant and advisor to top level subject matter

specialists or agency officials responsible for broad research, administrative, or operational programs;

• demonstrate a specific substantive area of expertise and potentially be considered an agency resource for this

field;

• apply complex modeling techniques to determine statistical associations in the health field (e.g., logistic

regression, survival rates, and Cox models);

• serve as lead author on presentations, journal articles, or agency reports; and/or

• initiate agreements with officials from other agencies for joint projects and research.

⇐BACK TO TABLE OF CONTENTS

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 1-9: ACTUARY, 1510

Mastery of and skill in applying advanced actuarial theories, principles, concepts, and practices (e.g., cost

estimating, insurance valuation) in one or more specialized areas, and knowledge of agency operations, systems,

and practices sufficient to:

• develop special techniques, formulas, assumptions, and methods to resolve unprecedented actuarial problems

associated with insurance plan termination;

•

review requests for financial and/or actuarial data required for planning and/or policy purposes;

provide authoritative evaluations of projected program costs, impact, and actuarial soundness;

make presentations before Congress or at national or international professional meetings and conferences, or

have significant involvement in drafting proposed legislative changes to ensure proper interpretation and

implementation of actuarial recommendations;

add to or advance the state of the art in actuarial processes;

represent the agency on interagency work groups established to develop industry actuarial polices and

solutions to critical issues; and

serve as an agency senior consultant to agency/corporate officials, and actuarial and/or computer science

peers on highly complex actuarial issues, debates, studies, research, and analysis projects.

⇐BACK TO TABLE OF CONTENTS

LEVEL 1-9: MATHEMATICIAN, 1520

Mastery of and skill in applying the theories and advanced state-of-the-art concepts and principles of one or more

specialized areas of mathematics (e.g., numerical analysis, numerical methods, theoretical and applied numerical

mathematics, or mathematical modeling) sufficient to:

• serve as the department or agency expert on highly complex mathematical issues/debates for a wide range of

mathematical and/or computer science peers;

• review theoretical assumptions, conduct hypothesis testing, and evaluate the appropriateness of proposals;

• produce results in areas of particular interest to the scientific community that have eluded the efforts of highly

competent investigators and researchers; and

• author a number of professionally acclaimed publications that advance the state-of-the-art in mathematical

methods.

⇐BACK TO TABLE OF CONTENTS

LEVEL 1-9: MATHEMATICAL STATISTICIAN, 1529

Mastery of and skill in applying advanced:

• mathematical and statistical theories, concepts, and practices; and

• concepts, principles, and practices of a biological or scientific discipline

sufficient to:

• serve as a leading regulatory agency authority in the areas of:

– clinical evaluation, design, and methodology;

– bio-statistical analysis; and

– evaluation of combination drugs and mortality trials for specialized drugs (e.g., cardio-renal drugs);

• define, develop, and implement significant data collection methodologies for a complex and comprehensive

nationwide survey and research program;

• make presentations at national and/or international professional meetings and conferences; and

• publish study findings that advance state-of-the-art approaches to the work.

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U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 1-9: STATISTICIAN (HEALTH), 1530

Mastery of and skill in applying advanced principles and concepts of applied statistical methods and health

sciences to a specific subject matter area within the field of medicine or health, or to a particular statistical

function; and comprehensive knowledge of the laws, policies, and regulations governing the agency’s major

programs sufficient to:

• anticipate new developments and emerging trends in the field;

• conduct strategic planning with respect to survey design, analytic direction, and workload management;

• conduct research into methodological issues in measuring biases in data from various subpopulation groups;

• serve as an expert consultant to officials of foreign countries, foreign research organizations, and university

staff on the design and analysis of collaborative international studies; and

• coordinate and direct large international studies to make comparisons and develop conclusions.

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U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

Factor 4 Illustrations

LEVEL 4-2: ACTUARY, 1510

Nature of Assignment – Work consists of onsite training related to the organization and functions of the agency.

Duties are designed to prepare the employee for high level professional assignments.

What Needs To Be Done – The employee:

• analyzes the issues involved in assignments;

• evaluates particular circumstances of each situation; and

• chooses an appropriate problem resolution approach.

Difficulty and Originality Involved – Exercises judgment to:

• apply standard actuarial techniques;

• evaluate the results of the assigned task; and

• prepare reports, memoranda, or descriptive materials that summarize accomplishments.

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LEVEL 4-2: MATHEMATICIAN, 1520

Nature of Assignment – Work consists of a limited range of activities that require using standard or established

procedures. Duties are designed to prepare the employee for higher level professional assignments.

What Needs To Be Done – The employee:

• identifies problems;

• evaluates the particular circumstances of the assigned task;

• recommends changes and procedural improvements; and

• selects alternative methods for problem resolution based on standard professional principles.

Difficulty and Originality Involved – Exercises judgment to:

• apply mathematical principles and practices;

• evaluate results for the assigned tasks; and

• prepare reports, memoranda, or descriptive materials that summarize accomplishments.

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LEVEL 4-2: MATHEMATICAL STATISTICIAN, 1529

Nature of Assignment – Work consists of onsite training on the effective use of standard mathematical and

statistical techniques as they relate to the organization and functions of the agency.

What Needs To Be Done – The employee applies established methods and procedures to the problems being

studied.

Difficulty and Originality Involved – Exercises judgment to:

• plan assignment details;

• examine source material; and

• adapt standard mathematical and statistical techniques to the particular requirements of the assignment.

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U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 4-3: MATHEMATICIAN, 1520

Nature of Assignment – Work involves projects in which complex features are limited and problems generally

require using various standard methods.

What Needs To Be Done – The employee operates independently to:

• evaluate alternative methods or approaches to problem resolution; and

• select a method from a variety of mathematical analyses, computations, measurements, and evaluation

options.

Difficulty and Originality Involved – Exercises judgment and limited originality to:

• use and, as appropriate, modify and adapt standard mathematical methods and procedures;

• do required calculations;

• analyze and interpret findings; and

• prepare technical correspondence such as reports, graphs, tables, or other descriptive documents.

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LEVEL 4-3: MATHEMATICAL STATISTICIAN, 1529

Nature of Assignment – Work consists of assisting and participating with senior staff in experimental design and

interpretation of information for biological studies (e.g., impact of Alaskan fisheries on Pacific salmon).

What Needs To Be Done – The employee:

• ensures statistical accuracy in planning data collection procedures;

• analyzes the issues involved;

• designs experiments (e.g., selects the most effective means of tracking salmon from infancy to mortality);

• performs data analysis;

• maintains statistical databases;

• writes reports;

• chooses the appropriate approach to solve problems from available agency alternatives; and

• assists senior staff with computing statistical problems related to the Pacific Salmon Treaty.

Difficulty and Originality Involved – Exercises judgment and limited originality to:

• recognize subtle distinctions in statistical results that require deviation from conventional rules;

• define the data analysis problems;

• select and adapt techniques if necessary; and

• establish the sequence of activities.

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U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 4-3: STATISTICIAN (AGRICULTURE), 1530

Nature of Assignment – Work consists of processes such as:

• reviewing project plans and procedures to conduct agricultural surveys;

• analyzing and preparing estimates, forecasts, and reports; and

• examining survey forms to determine validity of data and to ensure that they are representative of actual

conditions at the county, district, and State levels.

What Needs To Be Done – The employee:

• decides such matters as the type of data to collect, and the type of questionnaire to use; and

• selects, from several alternatives, the most appropriate method or procedure for these purposes.

Difficulty and Originality Involved – Exercises judgment and originality to:

• design general data collection and analytical procedures;

• recognize significant factors, relationships, and trends while analyzing pertinent facts, such as the

discrepancies between crop and livestock activity, the size of farms, and the history of production;

• determine appropriate checks and necessary calculations;

• analyze results;

• develop recommendations; and

• write technical reports on specific assigned studies or prepare preliminary drafts of more comprehensive

reports.

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LEVEL 4-4: ACTUARY, 1510

Nature of Assignment – Work consists of various professional actuarial problems related to pension plan

funding levels. Work requires adapting actuarial techniques and methods to salvage potentially under-funded

pension plans and calculating individual pensions for plans in trusteeship.

What Needs To Be Done – The employee:

• conducts comprehensive actuarial analyses of terminated pension plans;

• processes plans with several hundred participants, a large present value of guaranteed benefits, and unique

benefit features;

• analyzes plan documents to determine benefit entitlement and amount of accrued benefit for all participants;

and

• explains mathematical methods used to determine benefits for participants entering pay status and

participants in pay status with benefit changes.

Difficulty and Originality Involved – Exercises judgment and originality to:

• evaluate the relative importance of benefits and present values of those benefits to assign priority categories

to the benefit values according to legislation and agency regulations;

• make decisions regarding the valuation and the present and/or actuarial soundness of terminating plans and

plans having reportable events;

• modify plans that are not in compliance with current laws, regulations, and policies; and

• plan and complete all processing steps and actions from the time a plan is placed in trusteeship until final

benefit determinations are issued for all participants.

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U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 4-4: OPERATIONS RESEARCH ANALYST, 1515

Nature of Assignment – Work involves adapting a variety of established analytical techniques to accomplish a

variety of tasks such as:

• modeling the cumulative amount of emissions from mobile sources at the local, State, or Federal level;

• analyzing the relationship between recorded emissions on short tests and Federal test procedures using

regression analysis and associated techniques;

• modeling and analyzing the effects of various fuels and fuel additives; or

• correlating emissions test results from various division laboratories to ensure a high level of quality control.

What Needs To Be Done – The employee:

• assesses conditions such as variables, expected outcomes, and anticipated problems of the assignment;

• recognizes the relative significance of applicable relationships and their potential impact on the project;

• examines a variety of methods, techniques, and processes; and

• chooses the appropriate process for completing the project.

Difficulty and Originality Involved – Exercises judgment and originality to:

• plan, organize, and perform the chosen process;

• recognize and evaluate the importance of critical factors relative to the assignment;

• determine the limitations of available guides and precedents;

• solve problems despite the fact that available guides do not fully cover the assignment; and

• complete the assignment despite the presence of conflicting or inconclusive data.

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LEVEL 4-4: MATHEMATICIAN, 1520

Nature of Assignment – Work consists of a wide range of assignments involving mathematical reduction of

time, space, and position information used to identify the location of bombs, airplanes, boats, missing tanks, and

other military acquisitions. Work demands careful evaluation and interpretation of findings and conclusions.

What Needs To Be Done – The employee works in an environment where issues and problems are not always

susceptible to conventional analysis. In this environment, the employee:

• develops an approach to the assignment;

• decides whether conventional guidelines, such as operation manuals, are reliable or feasible for use relative

to the specifics of the assignment;

• selects appropriate methods or techniques from a variety of possible alternatives; and

• calculates corrections to variables such as velocity to reflect wind speed, angles, air pressure, and other

environmental effects.

Difficulty and Originality Involved – Exercises judgment and originality to:

• investigate significant variables such as position, acceleration, velocity, and direction;

• examine underlying relationships such as instrument accuracy, location, and angle; and

• develop recommendations and/or conclusions.

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U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 4-4: MATHEMATICAL STATISTICIAN, 1529

Nature of Assignment – Work consists of various mathematical statistics problems requiring the mathematical

modeling of numerous variables or parameters; modeling simulates natural or actual occurrences in a specialized

area. Examples include genetics, aircraft flight patterns, or weapons testing.

What Needs To Be Done – The employee:

• develops mathematical models and performs mathematical analysis to indicate trends, the likelihood of

various outcomes, performance levels, and ideal conditions;

• selects and adapts the mathematical statistical tools or techniques used to reduce data and to prepare reports

and/or recommendations;

• constructs histories of behavior changes;

• determines the appropriate sample size and technique to address all relevant concerns; and

• assesses that data indicate what is technically expected to occur.

Difficulty and Originality Involved – Exercises judgment and originality to:

• recognize limitations of precedent studies;

• modify survey design and methodology;

• solve problems where pertinent specifications, models, or data are not available; and

• test many mathematical models for projects that involve parties with diverse interests and missions (e.g.,

whole weapon testing versus testing components of a weapon).

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LEVEL 4-4: STATISTICIAN, 1530

Nature of Assignment – Work involves planning, researching, and implementing the full scope of analytical

projects requiring application of statistical theory.

What Needs To Be Done – The employee:

• evaluates Medicare trust fund operations;

• conducts and evaluates surveys;

• directs studies on prices, utilization, and factors related to health care costs;

• provides consultative services on matters related to Medicare, Medicaid, and national health care programs;

and

• bases interpretations, forecasts, and recommendations on statistical findings.

Difficulty and Originality Involved – Exercises judgment and originality to:

• reconcile merged data and develop statistically reliable methods and strategies to impute missing data

elements;

• develop and implement methods and procedures for collecting, processing, compiling, editing, and analyzing

statistical and actuarial data; and

• participate in data handling and survey quality control, including:

– detecting errors and biases;

– developing statistical imputations;

– comparing other data sources; and

– assessing data matches.

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U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 4-5: ACTUARY, 1510

Nature of Assignment – Work involves difficult and diverse projects requiring in-depth analysis of actuarial

issues and related information technology and data issues.

What Needs To Be Done – The employee:

• designs sophisticated tests to ensure that the valuation system is producing accurate results consistent with

both actuarial principles and audit standards;

• develops new techniques to accurately reflect changes in the agency’s reporting requirements, data needs, or

procedures; and

• develops innovative approaches to incorporate into a system that is subject to audit the effects of new

legislation and guidance, changes in the software environment, and unique issues raised by complex plans.

Difficulty and Originality Involved – Exercises considerable judgment and originality to:

• choose aspects of the program to be improved or modified;

• weigh computer processing as well as the actuarial aspects of a problem; and

• craft mathematical solutions that involve innovative approaches and applying concepts outside the normal

bounds of actuarial theory.

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LEVEL 4-5: OPERATIONS RESEARCH ANALYST, 1515

Nature of Assignment – Work involves planning, designing, and developing performance requirements and

methods to ensure valid user tests of complex systems in an operational environment.

What Needs To Be Done – The employee:

• evaluates the organization’s performance information needs;

• identifies available performance measurement alternatives;

• analyzes each alternative in terms of public safety, cost to the agency, and cost to the industry;

• develops advantages and disadvantages of each alternative; and

• presents decisions to management.

Difficulty and Originality Involved – Exercises considerable judgment and originality to:

• evaluate advice of experienced and respected professionals with different opinions and interpretations;

• assess alternatives that have political or economic sensitivities;

• address local community and public action groups that may challenge conclusions; and

• recognize, in mathematical and analytical findings, relationships that may be new or may significantly depart

from the relationships discovered in previous studies.

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U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 4-5: MATHEMATICIAN, 1520

Nature of Assignment – Work involves leading long-term weapon employment projects in which the employee:

• acts as mathematical consultant to ballistics personnel on problems involving theory of dynamic stability and

analysis of mechanisms;

• provides expert advice on simulation methods, computer techniques, and use of operational mathematics in

weapons systems analysis; and

• conducts comprehensive evaluations of projects/programs related to ballistics.

What Needs To Be Done – The employee:

• formulates and solves complex mathematical problems;

• identifies ways to improve mathematical processes;

• develops optimum system parameters and boundaries;

• performs mathematical analyses and computer simulations to determine dynamic properties of particles, rigid

and non-rigid bodies, and structures;

• determines impact of temperature or force on structural designs and electronic circuitry;

• determines configuration and develops equations of motion for dynamic analysis of systems; and

• applies numerous mathematical techniques to solve optimization problems.

Difficulty and Originality Involved – Exercises considerable judgment and originality to:

• test munitions when the state of the weapon varies from experimental to production to termination phases;

• develop entirely new or vastly improved test, evaluation, and application standards, techniques, and

instructions to process and present ballistic data; and

• use computer applications that are evaluative or developmental in nature.

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U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 4-5: MATHEMATICAL STATISTICIAN, 1529

Nature of Assignment – Work involves technical direction and coordination of major wildlife (e.g., salmon or

seal) preservation, management, and tracking projects. As a leader on one or more projects, the employee

provides technical direction and ensures collaboration for a team of scientists and/or technicians at remote sites.

Assignments include working in a broad range of activities and making onsite decisions in highly specialized data

collection and analysis functions.

What Needs To Be Done – The employee:

• explores mathematical, statistical, information handling, and other techniques from related fields for potential

application to the problem at hand;

• acquires a thorough understanding of the substantive problems that relate to the program area or scientific

discipline;

• applies a variety of mathematical and statistical principles and techniques such as:

− probability theory;

− estimation;

− inference;

− quality control;

− acceptance sampling;

− sequential and other sampling plans;

− experimental design;

− clinical research methods;

− tests of significance; and

− data reduction to a myriad of situations and problems; and

• develops analytical and/or mathematical models for use in preparing evaluation criteria or data

collection/reduction requirements.

Difficulty and Originality Involved – Exercises considerable judgment and originality to:

• solve novel, obstinate, and obscure problems that require:

− extending existing methods;

− developing new mathematical or other approaches; and

− working under time pressure without compromising data quality.

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U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 4-5: STATISTICIAN (AGRICULTURE), 1530

Nature of Assignment – Work involves estimates of the production of specific specialty crops or commodities

such as fruits and vegetables. Varying complexities require the employee to:

• determine the most appropriate technical methods to apply for each commodity;

• plan and conduct surveys, and prepare estimates, forecasts, and reports related to crops production;

• adapt or develop necessary statistical input, edit, and output specifications for specialty commodities; and

• analyze data for major regional agricultural commodities to advise and assist others in developing

methodology.

What Needs To Be Done – The employee:

• formulates and recommends new or revised programs relating to the functions and activities of statistical

estimation, including survey design, implementation, summarization, and analysis;

• reviews and evaluates the accuracy of all survey input and output parameters and related data for assigned

commodities;

• stays informed about economic and weather related factors that may affect the crops assigned;

• uses knowledge of geographic centers of specific crop production areas to evaluate potential changes in

production levels; and

• interprets survey and related data to make recommendations and decisions regarding estimates and forecasts.

Difficulty and Originality Involved – Exercises considerable ingenuity and originality to:

• complete assignments in areas where precedents often do not exist;

• develop new and improved methods and techniques for computation, formulation, and assembly of data

forecasts, questionnaires, and crop survey and forecast reports;

• initiate or modify technical policy, conduct preliminary analyses, evaluate proposed projects and studies; and

• establish technical regulations and instructions for statistical work.

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U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 4-6: ACTUARY, 1510 (ILLUSTRATION 1)

Nature of Assignment – Work involves functioning as a senior agency actuary for preparing cost estimates on

legislative proposals to change the Medicaid or Medicare programs.

What Needs To Be Done – The employee, as an agency representative and technical authority:

• determines the appropriate course of analysis;

• conducts extensive simultaneous studies in largely undefined areas;

• devises and presents the agency’s implementation plan based on these studies; and

• provides advisory services to the agency head or corporate officials in the medical community regarding

preparation of briefing materials, Congressional testimony, Congressional inquiries, and the impact of new

regulations on existing procedures (e.g., forms, systems, computer programming, and operations).

Difficulty and Originality Involved – Exercises considerable judgment and originality to:

• define implications of legislative proposals for which no precedent exists;

• develop new concepts;

• design new computational models;

• calculate the agency impact of proposed legislative changes; and

• provide technical assistance and expertise to agency attorneys in litigation.

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LEVEL 4-6: ACTUARY, 1510 (ILLUSTRATION 2)

Nature of Assignment – Work involves providing expert advice to agency officials on:

• the impact of new or changing actuarial policies on the financial status of the agency, defined benefit pension

plans, or actuarial systems, procedures, and practices;

• issues that require study and evaluation and for which precedents are not applicable; and

• options and recommendations for management decisions.

What Needs To Be Done – The employee, as an agency representative and technical authority:

• provides analysis, technical insight, advice, and recommendations on:

– unprecedented, complex, sensitive actuarial matters with national impact;

– rulings and decisions that affect the agency as a whole; and

– proposed recommendations and laws;

• evaluates advantages and disadvantages of various approaches; and

• conducts special studies on the effects of proposed regulations and/or legislation.

Difficulty and Originality Involved – Exercises considerable judgment and originality to:

• provide analysis, prepare estimates, and make recommendations with potentially large financial

consequences to the agency and/or plan sponsors, often in a short time frame and with little data; and

• develop creative techniques to address issues.

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U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 4-6: MATHEMATICIAN, 1520

Nature of Assignment – Work involves:

• serving as a senior mathematician responsible for developing and conducting analytical and simulation

studies necessary to define and evaluate advanced combat control systems;

• directing and participating in developing models and analyzing results; and

• participating on an agency development team responsible to conceptualize and design new combat control

systems and techniques.

What Needs To Be Done – The employee:

• develops mathematical models and simulation requirements;

• designs, conducts, and evaluates simulation experiments;

• prepares complex, technical reports;

• identifies and considers previously undefined human/machine interface situations and problems in combat

situations; and

• acts as expert advisor to agency management in combat systems simulation.

Difficulty and Originality Involved – Exercises considerable judgment and originality to:

• perform work in undefined and unprecedented areas;

• solve combat systems problems not previously addressed; and

• develop new mathematical processes compounded by requirements for simultaneous analysis.

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LEVEL 4-6: MATHEMATICAL STATISTICIAN, 1529

Nature of Assignment – Work involves functioning as a senior advisor and project leader engaged in planning,

developing, and carrying out broad, complex agency statistical analyses.

What Needs To Be Done – The employee, as a technical authority:

• develops new statistical methods necessary for accomplishing assignments;

• defines the associated statistical problems so that solutions will be scientifically sound, relevant, and comply

with regulatory requirements; and

• provides advisory services to the agency head regarding congressional testimony, inquiries, and the impact of

new legislation on existing procedures.

Difficulty and Originality Involved – Exercises considerable ingenuity and originality to:

• resolve problems that require multidimensional approaches; and

• establish concepts and theories to resolve unyielding problems for which traditional mathematical/statistical

methods are neither applicable nor easily adaptable.

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U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 4-6: STATISTICIAN (HEALTH), 1530

Nature of Assignment – Work involves:

• serving as a primary agency consultant in specialized statistical activities such as data collection and analysis

of the performance of health care providers in a nationwide program;

• defending and achieving acceptance of new, controversial statistical methodologies;

• providing authoritative counsel to senior agency officials on the optimum use of statistical technology; and

• recognizing and advising on the possible expected contribution of statistics and the limitations of statistical

methods in the solution of complex problems.

What Needs To Be Done – The employee, as a lead agency consultant:

• reviews clinical trial protocols for adequacy of study design, sample size, and statistical methods used by the

regulated industry;

• develops new, controversial, and officially untried analytical methods; and

• provides advisory services to the agency head regarding Congressional testimony, inquiries, and the impact

of new legislation on current survey or census methodologies.

Difficulty and Originality Involved – Exercises considerable originality and creativity to:

• visualize statistical methods as they relate to broad studies;

• research advanced statistical techniques to resolve complex, philosophic problems; and

• establish policy relating to complex statistical and administrative problems.

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U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

Factor 5 Illustrations

LEVEL 5-2: SURVEY STATISTICIAN, 1530

Scope of the Work –Work involves performing specific statistical calculations to support a variety of projects

assigned to higher grade statisticians.

Effect of the Work – Work facilitates timely completion of broader projects.

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LEVEL 5-3: ACTUARY, 1510

Scope of the Work – Work involves conducting a variety of conventional actuarial assignments that are limited

in scope and difficulty. Assignments are well precedented and have short-term objectives that require using well

established mathematical statistical methods and concepts.

Effect of the Work – Work generally becomes the foundation for subsequent phases or processes.

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LEVEL 5-3: OPERATIONS RESEARCH ANALYST, 1515

Scope of the Work – Work involves developing target performance history that results from statistical and

mathematical analysis of data from the appropriate repositories. Typically, higher grade employees establish the

goals, constraints, measures of effectiveness, and value criteria.

Effect of the Work – Work facilitates the work of other professionals. Data analysis results support other studies

or identify problems that require immediate action.

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LEVEL 5-3: MATHEMATICAL STATISTICIAN, 1529

Scope of the Work – Work involves participation in a team environment to evaluate potential impacts of

pollutants on fish population and marine communities. Chemical and biological data are used to identify

threshold levels for contaminant effects on bottom dwelling fish and assess these effects using multivariate

statistical models.

Effect of the Work – Work affects the quality and usefulness of field and laboratory results and the ability to

meet research and administrative deadlines and objectives.

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U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 5-3: STATISTICIAN (DEMOGRAPHY), 1530

Scope of the Work – Work involves conducting recurring or continuing studies that consist of clearly defined

units, parts of major projects, or segments of higher grade statistician assignments.

Effect of the Work – Work affects conclusions of demographic studies. Reports provide technical details that

may facilitate similar or more extensive investigations.

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LEVEL 5-4: ACTUARY, 1510

Scope of the Work – Work involves leading projects that are broad in scope and require considerable advanced

planning. Work requires:

• dividing the project into sections and overseeing completion of each section; and

• documenting the results of the project(s).

Effect of the Work – Valuations and cost estimates form the basis for:

• short-range projections concerning beneficiary population;

• benefit outlay contribution rates and incomes;

• fund transfers, budget preparation, legislative proposals; and

• administrative cost distributions.

Accuracy of the results is essential to current and short-range operational and agency administrative planning.

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LEVEL 5-4: OPERATIONS RESEARCH ANALYST, 1515

Scope of the Work – Work involves providing expert analytical advice and guidance to managers and scientists

within or outside the agency. Work requires:

• conducting data analysis, modeling, and special studies of endangered species in a designated geographical

area;

• analyzing the tracking data of sea turtle migration patterns;

• monitoring birth and mortality rates;

• providing advice on experimental design (i.e., the best way to collect data to ensure statistically significant

findings); and

• developing computer programs to conduct analysis and simulations.

Effect of the Work – Work minimizes field experimentation costs. It also affects the agency’s ability to study

endangered species and to ensure program efficiency.

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U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 5-4: MATHEMATICIAN, 1520

Scope of the Work – Work involves planning, developing, evaluating, and executing assignments that are broad

in scope and of marked complexity, significance, and importance. Work requires:

• a specialized knowledge of a subject matter area (e.g., orbital dynamics) or of a specific branch of

mathematics (e.g., numerical analysis); and

• providing consultative and/or advisory services.

Effect of the Work – Work facilitates the work of engineers who assess dynamics of motion, trends, or changes

over time. Work results also allow the display of scientific data in an understandable and useable form.

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LEVEL 5-4: MATHEMATICAL STATISTICIAN, 1529

Scope of the Work – Studies and projects usually represent an important segment of the agency’s primary

research program or statistical projects. Work involves:

• developing sampling or data tabulation specifications, assessing the completeness of the sampling universe,

or preparing statistical reports;

• using broad, highly varied methods to perform statistical calculations and analyses and to prepare estimates

and projections for large statistical data collection projects;

• analyzing various mathematical statistical issues; and

• formulating, planning, executing, and controlling major statistical studies or continuing projects.

Effect of the Work – Work output has an important impact on planning efforts and provides a basis for

introducing process improvements to the data merging functions.

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LEVEL 5-4: SURVEY STATISTICIAN, 1530

Scope of the Work – Work involves:

• determining and analyzing hazardous trends in the mining industry;

• analyzing contributory causes and conditions of mining accidents, injuries, and illnesses;

• in-depth studies to define true causes of accidents or illnesses; and

• maintaining statistical databases to obtain information on fatal accidents.

Effect of the Work – Work has considerable effect on the reliability of data that researchers collect in their

specialized surveys throughout the agency. Work results may affect:

• the agency’s policy making activity;

• factors to be assessed when analyzing data;

• application and use of final statistics;

• the design, rewording, and restructuring of survey questionnaires so that they better meet the growing and

changing needs of the basic statistical function;

• the regular and orderly transmission of employment and injury tabulations and summaries; and

• identification of mining hazards and improvement of safety policies, practices, and enforcement.

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U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 5-5: ACTUARY, 1510

Scope of the Work – Work involves empirical studies to:

• design methods of modeling complex pension plans;

• influence the direction and scope of studies and certify the accuracy of the assumptions, methods, and data

for research use;

• propose new approaches/theories including recommendations to change software and test updated software

to facilitate the evaluation of actuarial practices and assumptions (e.g., actuarial interest rates); and

• develop and refine the specific methods used in calculating the agency’s financial statements.

Effect of the Work – Work:

• opens significant new avenues for further study;

• results in important changes to existing or proposed systems; and

• directly affects consolidated budgets, Governmentwide financial statements, and pension benefit systems.

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LEVEL 5-5: OPERATIONS RESEARCH ANALYST, 1515

Scope of the Work – Work involves originating ideas for a series of self-initiated projects. Project results may

have an impact that extends beyond the immediate organization.

Effect of the Work – Work:

• provides the scientific and quantitative basis for critical agency decisions, policy, and subsequent regulatory

actions;

• influences the direction and scope of studies conducted by subordinate organizations;

• answers important questions;

• opens significant new avenues for further study;

• represents an important contribution to the validation or modification of methodology relating to the topic

area; and

• results in important changes to existing or proposed systems.

⇐BACK TO TABLE OF CONTENTS

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 5-5: MATHEMATICIAN, 1520

Scope of the Work – Work involves the precise specification of relationships (e.g., calculating the specific

impact of proposed changes on the time it takes to complete the design of an aircraft/spacecraft). Work requires:

• examining the quality of a tool such as a grid, and participating in grid design to make sure that the grid is

suitable to obtain necessary information;

• developing models and methods of analysis using expertise in a particular discipline or field;

• representing the agency in internal activities for topics related to geometry (e.g., how to improve the

mathematical definition of the aircraft);

• coordinating laboratory activities such as task selection, which hardware/software to use, which project the

laboratory will take; and

• keeping up with technological changes.

Effect of the Work – Work:

• frequently contributes to improving processes, tools, or construction of mathematical models. For example,

the mathematician adapts computer software to process thousands of independent variables at a time for use

in the multidisciplinary science of aircraft or spacecraft design;

• forms the theoretical basis for further research or planning, and impacts Government regulation, policy, and

procedure in specialized areas of electronics, data visualization, video imaging, and software development;

and

• assists other mathematicians and those who apply mathematics to a specialized subject matter area such as

Atmospheric Sciences, Structural Engineering, or Aerodynamics.

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LEVEL 5-5: MATHEMATICAL STATISTICIAN, 1529

Scope of the Work – Work involves controlling the amount of fish caught to prevent low reproduction rates for

particular species and stocks of fish. Work requires:

• providing estimates of likelihood and sampling error rates; and

• estimating the number of fish being caught and how many should be caught to sustain adequate fish

populations.

Effect of the Work – Work:

• facilitates biologists in determining country of fish origin and thereby, fish ownership;

• indicates when stock abundance is low;

• results in recommendations on how intensely certain stocks are to be fished and the vulnerability of particular

stocks fished in given locations;

• influences policies, penalties, and operations of fisheries where vessels used for industry fishing go to

intercept fish on their way to spawning ground; and

• affects national and international fishing practices to ensure adequate fish populations.

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U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 5-5: STATISTICIAN (MEDICINE), 1530

Scope of the Work – Work involves resolving technical aspects of regulations and policy relating to biologic-

type products. Work requires:

• conducting data collection research programs that involve a wide variety of issues from designing and

selecting samples to tabulating and analyzing results;

• documenting the statistical aspects of any research when new theory and methods need development; and

• providing expert and authoritative advice to officials and scientists of the agency in the areas of

biomedical/biometrics statistical applications.

Effect of the Work – Work represents major segments of broad statistical research programs. Advisory and

consultation services affect other national and foreign Government agencies and regulated industry with respect

to statistical aspects of specialized (e.g., biostatistical) applications.

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LEVEL 5-6: ACTUARY, 1510 (ILLUSTRATION 1)

Scope of the Work – Work involves:

• planning, developing, and directing actuarial analysis of critical projects that could affect defined benefit

plans nationwide;

• dealing with representatives of the pension, insurance, financial, and investment communities as an

authoritative agency official;

• serving on external and internal panels and committees; and

• meeting with members of Congress or their staff to discuss complex pension policy issues.

Effect of the Work – Work affects legislative/policy recommendations or guidance, and may affect defined

benefit pension plan sponsors and participants in all Federally defined benefit plans. Policy recommendations

may affect the long-term financial health of the agency.

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(continued)

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 5-6: ACTUARY, 1510 (ILLUSTRATION 2) (CONTINUED)

Scope of the Work – Work involves:

• maintaining primary responsibility for all actuarial aspects of the Pension Insurance Management System

(PIMS); including managing outside actuarial contractors and overseeing actuarial assumptions and data used

in the model;

• designing and certifying all actuarial aspects of the model;

• developing guidelines that serve as quality control measures for actuarial data used in the model;

• overseeing empirical work designed to evaluate actuarial practices and assumptions (e.g., actuarial interest

rates);

• approving financial estimates for the model; and

• designing and certifying alternative funding rules evaluated in the model.

Effect of the Work – Work facilitates the agency’s ability to:

• evaluate long-term impact on actuarial practices, assumptions, and trends;

• develop reports to monitor particular actuarial developments with long-term impact on the agency’s financial

condition; and

• prepare statements and evaluations that serve as the basis for the agency’s study of future potential legislative

proposals and policy development.

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LEVEL 5-6: MATHEMATICAL STATISTICIAN, 1529

Scope of the Work – Work involves serving as a consultant to high level officials and counterparts in other

agencies, educational institutions, professional associations, and Governments. The mathematical statistician

works on projects of general interest and significance to the Government (e.g., endangered wildlife species).

Work requires:

• conducting extensive applications in time series analysis, sampling, analysis of variance, etc., to resolve

critical agency problems;

• ensuring proper interpretation and implementation of technical recommendations by drafting proposed

legislative changes to a critical agency program or system;

• planning, developing, and directing major programs where the analysis and original studies are of such major

importance and scope that extremely large data sources or legislative coordination is required; and

• representing the agency or command at conferences, briefings, and meetings concerning long-range goals,

state-of-the-art technology, or the advantages or disadvantages of various complex methods.

Effect of the Work – Work has ongoing, far reaching implications and may be the basis for evaluating the

sustainability of major programs. The employee provides technical leadership that affects numerous industries

(e.g., fisheries, lumber), political activist groups, nations, treaties, natural resources, wildlife, and general

populations. Work attracts attention from others in the scientific community seeking to make comparisons or

develop similar tools.

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U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

LEVEL 5-6: STATISTICIAN (HEALTH), 1530 (ILLUSTRATION 1)

Scope of the Work – Work involves planning, developing, and directing extensive (e.g., nationwide) statistical

analysis programs. Work requires conducting nationwide analyses of health care services to:

• identify areas that need improvement;

• quantify levels of customer satisfaction by geographic area;

• establish trends and predictors of good health among different age groups; and

• assess the integrity of billing and collection procedures.

Effect of the Work – Work affects agencywide and/or Governmentwide scientific procedures and may serve as a

catalyst for legislative coordination, or may have a major impact on national legislation. The work may also

impact programmatic activities and operating policies of a major department or agency of the Federal

Government.

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LEVEL 5-6: SURVEY STATISTICIAN, 1530 (ILLUSTRATION 2)

Scope of the Work – Work involves advanced statistical methodologies, procedures, or programs with

significant impact on the nation, and planning, developing, and directing extensive statistical data collection

projects (e.g., nationwide). The work impacts many agency surveys by:

• identifying methodologies that need improvement;

• assessing the impact methodological changes have on results; and

• developing novel methodologies that result in dramatic changes in statistical data collection programs

throughout the profession.

Effect of the Work – Work affects agencywide and/or Governmentwide statistical data collection projects and

may serve as a catalyst for legislative coordination or have a major impact on national legislation. The work also

may impact procedures and operating policies of major departments or agencies of the Federal Government. For

example, national census data provides indicators of the need for Federal programs and may influence the way the

Federal Government distributes billions of dollars.

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U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

PART III – EXPLANATORY MATERIAL

KEY DATES AND MILESTONES

In 1998, the Office of Personnel Management (OPM) notified agencies that we were continuing an

earlier effort to develop a Job Family Position Classification Standard for Professional Work in the

Mathematical Sciences Group, 1500. We had suspended the earlier effort because of a lack of

staffing resources. The 1500 occupational group includes the Computer Science Series, 1550. We

excluded the 1550 series from the effort because we believed it might be better aligned with the

Information Technology Group, 2200. The 1550 series will be the subject of a separate study to

determine its final disposition.

In conjunction with the study, we conducted factfinding at 15 installations representing collectively

10 major agencies. After completing the factfinding, we developed a draft job family standard (JFS)

which we released electronically in 2001 for agency review, comment, and test application. At that

time, we arranged with those agencies that had the largest covered populations to take the primary

role in reviewing and commenting on the draft. OPM calls this arrangement the “lead agency”

approach. In addition to the lead agencies, we invited and encouraged all agencies to comment on

the draft. This appendix addresses concerns expressed by reviewing agencies and describes our

responses to them. It also provides information that may help agencies to manage transition from

cancelled occupational standards to this JFS.

Another important milestone is that many Federal “white collar” positions are no longer evaluated

by the General Schedule grading criteria. In recognition of this situation, OPM now defines series

without a prefix of GS (e.g., series GS-1501 is now shown as 1501). We have also changed the

format of this JFS to support those users who do not classify positions according to the General

Schedule. Part I contains occupational information that is applicable to Federal work covered by the

JFS without regard to pay plan or classification system. Part II provides grading information for

positions classified according to the General Schedule grade definitions in chapter 51 of title 5,

United States Code. Part III explains the development of this standard.

RESULTS OF AGENCY REVIEW, COMMENT, AND TEST APPLICATION

A. JOB FAMILY STANDARDS – GENERAL INFORMATION. During the development of this

job family standard (JFS), we exploited every opportunity for simplifying and streamlining its

content. We relied heavily on the help of agency subject-matter experts and human resources

management officials to do this. We also incorporated changes into this JFS based on lessons we

learned from our work on earlier JFS issuances.

1. Name Changes. We changed the name of the occupational group, “Mathematics and Statistics

Group” to “Mathematical Sciences Group.” We made this change to reflect broad agency

recognition of statistics, actuarial, and mathematical work as scientific in nature. For consistency,

we also changed the designation of this job family standard to include the words, “Mathematical

Sciences Group.”

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

Our policy is to prescribe functional names for occupational series, and position titles for positions

performing work in that series. For example, “accounting” is a function and is the name we use for

the accounting occupation (i.e., Accounting Series, 0510). “Accountant” is the title we prescribe for

positions that involve doing work predominantly in the accounting series. Consistent with this

policy, we changed the names of three occupational series in the Mathematics and Sciences Group

as shown below.

Series Former Series Name New Series Name

1510 Actuary Actuarial Science

1529 Mathematical Statistician Mathematical Statistics

1530 Statisticia

Statistics

2. Classifying Professional Scientific Work. In response to the draft of this JFS and earlier

standards, agencies requested that we provide guidance on classification issues related and perhaps

unique to professional scientific work. One specific request was that we provide instructions for

assigning functional classification codes to professional scientific positions. The guidance is

available in

The Classifier’s Handbook. As a convenience for the agencies, however, we have

incorporated the guidance into this JFS.

3. Issue – Distinguishing Between Professional and Technical Work. We have included in

this job family standard (JFS), guidance to determine whether work is professional or technical in

nature. The guidance is available in The Classifier’s Handbook. We have added the material to

this JFS in recognition of the fact that line managers and others who use it may do so infrequently.

By placing this guidance in this JFS, we eliminate the need for them to reference another document.

We believe this change in a small way contributes to the efficiency and convenience of the

classification process.

B. THE 1500 JOB FAMILY STANDARD FOR PROFESSIONAL WORK – SPECIFIC

ISSUES. When we announced this study, we requested agency comments on a number of specific

issues. This section describes those issues and provides a summary of the agency comments on

them. It also describes the actions we have taken in response to the agency comments, and the

rationale for our actions.

1. Issue – Establish a General Mathematics and Statistics Series, 1501

Agency Comments: The majority of agencies indicated a strong preference for establishing a

“miscellaneous” series for the Mathematical and Statistical Occupational Group.

Our Response: We established a miscellaneous series, the General Mathematics and Statistics

Series, 1501. This new series gives agencies the capability to appropriately classify work that

consists of a mix of mathematical, statistical, and related work. The new occupation gives agencies

a classification option that for many years has been available for other occupational groups.

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

2. Issue – Retaining Specialty Areas (represented by parenthetical titles) in the Statistics

Series, 1530.

Agency Comments: Most agencies commented that the existing parenthetical titles facilitate

recruitment efforts and should be retained. A couple of agencies with medical and health research

functions suggested the addition of a “Biomedical” specialty. One agency suggested combining

some of the specialties to eliminate any overlap in current specialty titles. Only one agency opposed

the use of parenthetical titles for specialty areas.

Our Response: With one exception, we retained the existing 1530 parenthetical titles. The one

exception is that we abolished the parenthetical title, “General.” We did this because we are

allowing agencies to use any basic title with the newly-established General Mathematical and

Statistic Series, 1501. The agency choice of a basic title with the 1501 series eliminates the need for

a parenthetical title, General, with the 1530 series.

We did not authorize use of a new parenthetical title, “Biomedical.” We disapproved that change

because we already authorize use of relevant parenthetical titles (e.g., Health, Biology, and

Medicine) with the 1530 series.

In response to agency comments, we clarified that agencies may apply parenthetical titles to both

Survey Statisticians as well as to Statisticians.

3. Issue - Establish Specialty Areas and Parenthetical Titles for Series in this JFS in

Addition to Those Authorized with the Statistics Series, 1530.

Agency Comments: The majority of agencies indicated that there was no need for specialty

areas/parenthetical titles for any series other than the Statistics Series, 1530.

Two agencies recommended parenthetical titles for the Mathematical Statistics Series, 1529. One of

the two agencies suggested we authorize the specialty areas and parenthetical titles defined for the

Statistics Series, 1530 for use with the series, 1529. The other agency recommended we recognize

health, biology, and medicine specialties and establish for them the related parenthetical titles,

“Biomedical Research,” “Bioinformatics,” and “Health.”

A third agency suggested we recognize specialty areas for the Operations Research Series, 1515.

The agency also recommended we establish for the specialties, the related parenthetical titles

“Various Engineering Fields,” “Ships,” “Aircraft,” “Cost Analysis,” and “Computers.”

Our Response: The Introduction to Position Classification Standards provides guidance on this

issue. The guidance instructs agencies that when we do not prescribe use of parenthetical titles, or

specifically proscribe their use, agencies may append official position titles with any meaningful

parenthetical title of their choosing. We believe there is no compelling argument to rescind the

flexibility that this guidance gives to the agencies. Accordingly, we have not prescribed

parenthetical titles for series other than the Statistics Series, 1530.

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

4. Issue - Assessing Impact on Grades. We observed our usual practice of requesting that

agencies test the draft job family standard by applying it to actual positions. We requested also that

they report to us the impact of the draft application on the grades of tested positions.

Agency Comments: Agencies applied the draft JFS to 421 positions. They reported no grade

impact due to its application. They did report five downgrades, but acknowledged they were due to

inaccurate grade evaluations based on application of the existing standard.

In addition to grade impact, agencies indicated that the test showed the need for clearer distinctions

among factor level descriptions (FLDs) 1-7, 1-8 and 1-9 in Factor 1, Knowledge Required by the

Position. Agencies also asked for more occupation-specific illustrations.

Our Response: We made significant changes to the FLDs for Factor 1 and also (although not

specifically requested to do so) for Factor 4, Complexity. We also added a number of occupation-

specific illustrations for Factors 1 and 4, and also for Factor 5, Scope and Effect. As requested,

many of the newly-added illustrations are companion to the higher level FLDs. We believe these

changes, taken as a whole, will improve the accuracy of classification efforts.

C. THE 1500 JOB FAMILY STANDARD FOR PROFESSIONAL WORK –

MISCELLANEOUS ISSUES.

1. Issue - Distinguishing between Grade 15 and Executive Level Positions

Agency Comments: One group of reviewers suggested that many of the higher factor level

descriptions (FLDs) for several factors in this job family standard (JFS) seemed “…more descriptive

of a Senior Executive Service (SES) position than a GS position.”

Our Response: The law at 5 U.S.C. 5104 defines the criteria for all GS grade levels. Some years

ago, the Civil Service Commission (predecessor agency to the Office of Personnel Management)

developed a Primary Standard in Factor Evaluation System (FES) format to provide the

classification community with a generic tool that might be applied to positions in all occupations.

All interested parties have long accepted the Primary Standard and its FES higher factor level

descriptions (FLDs) as consistent with the law.

We prepared this JFS in FES format. When we prepared this JFS, we confirmed that its FLDs met

FLD criteria in the Primary Standard and as a consequence were in compliance with the law. We

understand and recognize that the higher FLD criteria may be quite demanding. However, we are

obligated by statute to develop standards that are consistent with the law’s current grade level

criteria. Accordingly, we have not made changes to weaken the higher FLDs in this JFS.

2. Issue – Cancellation of the Cryptography Series, 1540

We proposed canceling series, 1540 because our records showed it had no population.

Agency Comments: A few reviewers suggested that we not cancel series 1540. The reviewers

believed that a number of executive agencies used the series, but for security reasons did not report

employment in it.

U.S. Office of Personnel Management

Professional Work in the Mathematical Sciences Group, 1500 September 2005

Our Response: We contacted the agencies the reviewers believe employ personnel in series, 1540.

None of the contacted agencies expressed concern with our proposal to cancel the series.

Accordingly, we cancelled 1540 as a series available for general use. We have reserved the code

“1540” and the occupational series name, “Cryptography,” for use by the intelligence community.

This information will be placed in the next revision of the Handbook of Occupational Groups and

Families with a list of reserved series.

U.S. Office of Personnel Management