VOLUME 78

Number 4

| Our nal of the December, 1988

WASHINGTON

CIENCES

ISSN 0043-0439

oe |

Issued Quarterly

at Washington, D.C.

CONTENTS

Editor’s Introduction:

DR. R. CLIFTON BAILEY

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Articles:

DR. RICHARD ALLEN: The Washington Statistical Society and Its

History

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DR. MILES DAVIS and DR. DONALD WOLFE: Clustering of Senators

AICO NUMRY CULES en ne NE 2 cin, oon S GE ee dies QUES S Mee te Sowa 296

DR. EDWARD J. WEGMAN: Computational Statistics: A New Agenda for

SEALISHEA MMC ORV RANG UE LACIICE! «ancl es. 5 ole cele ae ee ele ct nee ene gees Here 310

DR. KEITH R. EBERHARDT: Statistical Analysis of Experiments to Mea-

SLPS VERT aU Gees Oo ae Se cee nr eee ee ea

DR. N. PHILLIP ROSS and DR. GILAH LANGNER: Environmental

Statistics

DR. R. CLIFTON BAILEY: Some Uses of a Modified Makeham Model to

Evaluate Medical Practice

Washington Academy of Sciences

Founded in 1898

EXECUTIVE COMMITTEE

President

James E. Spates

President-Elect

Robert H. McCracken

Secretary

Donald O. Buttermore

Treasurer

R. Clifton Bailey

Past President

Ronald W. Manderscheid

Vice President (Membership Affairs)

M. Sue Bogner

Vice President (Administrative Affairs)

Jo-Anne A. Jackson

Vice President (Junior Academy Affairs)

Marylin F. Krupsaw

Vice President (Affiliate Affairs)

John G. Honig

Academy Members of the Board of

Managers

William M. Benesch

Carl E. Pierchala

Lawson M. McKenzie

Marcia S. Smith

Jean K. Boek

Thomas N. Pyke

BOARD OF AFFILIATED

SOCIETY REPRESENTATIVES

All delegates of affiliated

Societies (see inside rear cover)

EDITORS

Irving Gray

Joseph Neale

Lisa J. Gray, Managing Editor

ACADEMY OFFICE

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Telephone: (703) 527-4800

The Journal

This journal, the official organ of the Washing-

ton Academy of Sciences, publishes historical

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sue contains a directory of the Academy mem-

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Back Issues

Obtainable from the Academy office (address

at bottom of opposite column): Proceedings:

Vols. 1-13 (1898-1910) Index: To Vols. 1-13

of the Proceedings and Vols. 1—40 of the Journal

Journal: Back issues, volumes, and sets (Vols.

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Published quarterly in March, June, September, and December of each year by the

Washington Academy of Sciences, 1101 N. Highland St., Arlington, Va. 22201. Second

class postage paid at Arlington, Va. and additional mailing offices.

Editor’s Note

The Washington Statistical Society (WSS) was founded in 1926 and joined the

American Statistical Association (ASA) in 1935. The American Statistical Associa-

tion, founded in Boston in 1839 at No. 15 Cornhill, will celebrate its sesquicentennial

in 1989. The ASA was founded because of concerns with the inadequate and inaccurate

national statistics. An excellent account of the early history of the American Statistical

Association can be found in its 1918 publication The History of Statistics, Their De-

velopment and Progress in Many Countries, collected and edited by John Koren and

published for the American Statistical Association by the Macmillan Company of New

York in 1918. John Koren recounts some of the early history of the ASA (1839-1914)

and its concern with issues of national statistics such as the Census and vital statistics,

interests clearly consistent with the provisions of their bylaws which state (Koren, pp.

4—5) that “‘the operation of this Association shall principally be directed to the statistics

of the United States; and they shall be as general and as extensive as possible and

not confined to any particular part of the country ...” I also highly recommend

Revolution in United States Government Statistics 1926-1976, for an overview of sta-

tistical issues as they evolved with the Federal Statistical System. It was prepared by

Joseph W. Duncan and William C. Shelton and issued October 1978 by the U.S.

Department of Commerce, Office of Federal Statistical Policy and Standards.

With the forthcoming sesquicentennial of the ASA, many special publications are

anticipated. My purpose in this brief note is to let the reader know of the roots of

the statistical profession in the U.S. The articles in this special issue demonstrate in

a very limited way the range and richness of the science of statistical application and

methodology.

This special issue of the WAS Journal is devoted to a collection of articles by

members of the Washington Statistical Society, an affiliate of the Washington Acad-

emy of Sciences. This special issue appears as the American Statistical Association

enters its 150th year.

The articles in this issue convey the broad scope of statistical activities. The lead

article by Richard Allen, President of the Washington Statistical Society provides an

overview of WSS activities and its history.

The article by Miles Davis and Donald Wolfe applies the classical statistical meth-

odology of principal components for multivariate data to the voting records of the

U.S. Senate. Their insights and graphs will capture your imagination and encourage

you to ask of the data your own thought provoking questions.

Edward Wegman’s article examines the implications of computational statistics on

statistical theory, education, and practice. This article provides an elegant description

of some recent advances in graphical techniques for exploring multivariate data of

many dimensions.

Keith Eberhart’s article on ignition propensities of cigarettes follows in a long

tradition of the National Bureau of Standards (NBS) recently renamed the National

Institute of Standards and Technology (NIST). Traditionally, Bureau statisticians work

closely with their colleagues to design and analyze statistical studies. The tradition at

NBS is long and includes such notaries as W. J. Youden, John Mandel, Joseph Cam-

eron, Churchill Eisenhart, Harry Ku, Mary Natrella, Joan Rosenblatt and many others

who have had the good fortune to work there. The article by Joan Rosenblatt in the

Encyclopedia of Statistics (Volume 6, pp. 148-155, John Wiley and Sons, New York)

is a valuable reference to this tradition.

The article by N. Philip Ross and Gilah Langner examines the tradition of statistical

agencies in government and argues the case for credible centralized environmental

statistics for the U.S.

My own article addresses some methodological issues in medical statistics and dis-

cusses some uses of administrative data and its augmentation for special studies.

It has been my pleasure to bring these articles together for this special issue. I hope

the Washington Academy regularly will feature articles devoted to statistical science

and its applications.

Journal of the Washington Academy of Sciences,

Volume 78, Number 4, Pages 291-295, December 1988

The Washington Statistical Society

and its History

Richard Allen

President, Washington Statistical Society

ABSTRACT

The Washington Statistical Society (WSS) serves 1500 statisticians in this Washington,

D.C. based chapter of the American Statistical Association (ASA). Each year, WSS

organizes and sponsors 35—40 technical sessions, a tradition that began when WSS was

organized in 1926. Accomplishments over the years are described.

About the Washington

Statistical Society

The Washington Statistical Society

(WSS) is the Washington, D.C. based

chapter of the American Statistical As-

sociation (ASA), the leading professional

society for statisticians in the world. The

WSS normally has about 1,500 members

which is approximately 13 percent of the

members of all chapters of ASA.

While one of the strengths of the WSS

is the contributions of members from the

Federal statistical agencies, its member-

ship is broad based. Approximately 55

percent of members are from govern-

ment, 10 percent from academia, 30 per-

cent from private and nonprofit organi-

zations, and 5 percent self-employed or

retired. Members of the WSS form the

backbone of many ASA activities and

committees. WSS members can be found

in leadership roles for nearly every ASA

Correspondence should be sent to: Richard Allen,

President WSS, c/o USDA/NASS/DAP Room 4133

So. Bldg., Washington, D.C. 20250.

291

section, committee, and publication. For

example, two of the last three presidents

of the ASA have been WSS members.

One of the major goals of the WSS is

to organize and sponsor a wide variety

of technical sessions relating to statistics

each year. These sessions are advertised

through the monthly WSS Newsletter and

newsletters of organizations which might

be interested in a specific session. Usually

35—40 sessions are offered each year rang-

ing from very technical sessions on work

in progress to presentations of general in-

terest from renowned professionals. Many

of these sessions are cosponsored with

other professional organizations and uni-

versity departments. Sessions are planned

by anumber of program committees which

currently include agriculture and natural

resources, economics, methodology, pub-

lic health and biostatistics, physical sci-

ences and engineering, social and demo-

graphic statistics, computing technology,

and quality assurance. In addition to the

regular program sessions, the WSS has

organized and presented a few short

292 RICHARD ALLEN

courses in each of the recent years. These

short courses have brought in leading

speakers and video tape presentations on

developing statistical methodologies. At-

tendance has been upwards to 200 partic-

ipants for some of these short courses.

One special activity of the WSS News-

letter is a monthly employment column

for both employers and prospective em-

ployees. The society participates in Wash-

ington, D.C. area science fairs by judging

all projects for noteworthy statistical con-

tent. Prizes and other recognition are pro-

vided. The society also sponsors an an-

nual award at all local universities for

outstanding graduate students with inter-

ests in statistics. This award consists of a

year’s membership in both WSS and the

ASA. The Society also cooperates with

six other government agencies and profes-

sional associations in the annual Julius

Shiskin memorial award for economic sta-

tistics.

Most members of WSS are also mem-

bers of the ASA. However, WSS does

offer associate memberships for individ-

uals who may be professionals in related

fields and who wish to keep up on infor-

mation in statistical activities in the Wash-

ington area.

Below is listed a brief description of the

history and development of WSS.

Brief History of the Washington

Statistical Society”

The WSS was organized in 1926 with a

short constitution that proclaimed it was

to be achapter of the American Statistical

Association. Officers established were

President, Vice-President, Secretary, and

two Representatives-at-Large. However,

a charter for ASA membershp was not

applied for until November 1935.

The names of most early Society offi-

cers are lost in the mists of history. Wil-

‘Acknowledgement: Credit goes to Al Mindlin for

the original history version.

liam M. Stewart, Director of the Census

Bureau, was President in 1928 and in 1930.

The 1930 Secretary-Treasurer was E. A.

Goldenweiser.

Although the 1926 constitution set the

annual dues at $1, during the Great

Depression no serious effort was made to

collect dues. Instead, the Secretary, who

by 1935 was the ASA District Repre-

sentative, stood at the meeting house door

and collected 15 cents from each attendee

(25 cents at luncheon meetings). Dinner

meetings cost $1.25 for dinner.

Apparently, in the earliest years, WSS

program meetings were held about once

a month. Information on topics and

speakers for meetings before 1940 is scarce

but there is a reference that in a 1939

meeting titled “Irrelevant Remarks on

Trivial Matters in Modern Statistical

Theory,”’ addressed by Leon Henderson,

Arne Fisher and Bassett Jones, the dis-

cussion got so ribald that “the doors were

closed.”

The informal financial management of

the Society’s early days was simply in-

adequate, and in 1941 WSS was insolvent

(a $10 deficit). The regular meeting door

fee of 15 cents could not be raised because

most of the meetings were held at George

Washington University, where a charge

greater than 15 cents would make the

University liable for taxes as conducting

meetings for pay. WSS discontinued door

collections and ordered collection of $1

from each member at the beginning of the

season. Heretofore, chapter membership

had been defined as every ASA member

living in the Washington area. With the

increasing number of statisticians migrat-

ing to Washington because of the “Peo-

ple’s War of Survival,” WSS trumpeted

to the world that the membership in 1942

was a thousand persons—approximately

one third of the total membership of

ASA. However, when the Board of Di-

rectors sought to collect its dues only

about 200 persons responded to the call.

WSS membership grew steadily after

World War II. The 1953 report of the Sec-

retary-Treasurer stated that more than

WASHINGTON STATISTICAL SOCIETY 293

700 of the nearly 900 ASA members in

the Washington area were WSS members.

Membership increased particularly rap-

idly in the period 1958 to 1964 and con-

tinued inching up to a temporary peak of

1,500 in 1967. Membership declined in the

period 1969-1974 to about 1,350. How-

ever, the trend reversed in 1975 and a

probable membership peak of 1,773 was

reached in 1979.

The first Annual Dinner meeting was

held in 1947, with Isadore Lubin as

speaker. The event has been held each

year thereafter with the exception of five

years.

Through the 1950’s and early 1960’s at-

tention of the Society’s Board of Direc-

tors focused heavily on scheduling meet-

ing. It was mainly a program committee,

leaving little time to develop additional

activities. For the most part an evening

meeting was held each month thru a seven

or eight month season. In 1963 a special

committee was established to develop over

the summer the entire year’s set of seven

meetings. Under the leadership of T. D.

Woolsey the first program committees

were established in 1964—Economics un-

der Hyman Kaitz, Public Health and Bio-

statistics under Oswald Sagen and Mon-

roe Sirken, and Social and Demographic

under David Kaplan. The program com-

mittee system flourished from the begin-

ning, rapidly taking over the main burden

of meetings and freeing the Board of Di-

rectors for further improvements.

As it became apparent that daytime

meetings were more popular than evening

meetings, more and more meetings were

held during the day. In the 1969-70 sea-

son there were no evening meetings at all,

except the Annual Dinner.

The 1960’s saw other dramatic expan-

sions of Society activities. In 1962 an

award of one-year membership in ASA

and WSS to an outstanding graduate stu-

dent in each of seven universities in the

Washington-Baltimore area was initiated.

Also in 1962 a Methodology Committee

was established under Jerome Cornfield

and Seymour Geisser. Under the subse-

quent leadership of Samuel Greenhouse,

and with an enabling revision of the con-

stitution, this evolved by 1963 into a semi-

autonomous Section of the Society with

its own elected officials and separate pro-

gramming. In 1966 a Baltimore Commit-

tee was established under Harold Gross-

man. WSS financed the growth of a

Statistical program in the Baltimore area,

until by 1969 it felt sturdy enough to cut

the parental tie and strike out as a ‘““Mary-

land” chapter of ASA. In 1967 an Em-

ployment Service was established under

Marie Eldridge. Also in 1967 an Out-

standing Paper Award Committee. for

young statisticians was established under

Churchill Eisenhart. In 1968 a WSS Com-

mittee on ASA Fellows was established

under Margaret Martin.

The increase in Society activities during

the 60’s and rapidly rising costs spelled

the end of the $1.00 dues in 1967 even

though a number of economy measures

such as switching to bulk rate newsletter

mailings were taken. Dues were raised to

$2.00 a year in 1967 and remained at that

level for 10 years. Increases in mailing

costs necessitated raises to $3.00 in 1977,

$4.00 in 1979, and $6.00 in 1984 which has

been maintained since then.

A major membership survey was con-

ducted in 1969 which pointed out a gen-

eration gap. The majority of members of

WSS were age 40 or above and favored

nontechnical meetings. Nontechnical

meetings tended to have higher attend-

ance, but technical meetings drew more

of the younger members. The WSS pro-

gram attempted to provide a balance of

the two types of sessions.

The 70’s saw WSS attempt a number of

new programs. Some of them were en-

visioned as annual programs but did not

prove to have such permanence. In 1973

a W. J. Youden memorial scholarship was

established in conjunction with the Amer-

ican Society for Quality Control. The

program was to provide scholarship

assistance for a worthy student at the

Washington Technical Institute. Appar-

294 RICHARD ALLEN

ently the scholarship was awarded only in

1973 and in 1976.

In 1974 WSS participated with a dozen

other private and government sponsors in

a three-day symposium on Statistics and

the Environment. This symposium fol-

lowed other similar presentations in Cal-

ifornia and was very successful, with over

200 participants. There was considerable

interest in establishing such a symposium

as an annual event but it was not to be.

In 1976, to commemorate the 50th an-

niversary of the Society, five past presi-

dents of the American Statistical Asso-

ciation addressed the WSS annual dinner

on the topic of ‘““The Past as Prologue to

the Future.” This proved to be one of the

most interesting annual dinner meetings

of all time.

Another notable accomplishment of the

1975-76 Society activities was the estab-

lishment of a “local associate member-

ship” program. That feature allows a non-

ASA member such as a retired statistician

or an individual working in some other

field to receive the WSS newsletter and

keep abreast of statistical activities in the

Washington, D.C. area.

The 1977-78 program year was marked

by two very popular activities. A short

course On variance estimation was planned

which ran on six consecutive Fridays. Over

140 people applied for the 50 available

spots and a random process was used to

select a lucky 50 participants. A reception

was held for visiting statisticians from

Latin America. Since the room would hold

only 135 people over 60 individuals had

to be turned away.

A major new award program was started

during the 1978-79 program year, the

Julius Shiskin Memorial Award for Eco-

nomic Statistics. WSS is joined in this pro-

gram by the Bureau of Labor Statistics,

the Bureau of the Census, the National

Association of Business Economists, the

Bureau of Economic Analysis, the Na-

tional Bureau of Economic Research, and

the Office of Management and Budget,

all of which Julius Shiskin was associated

with during his career. This award has

been presented annually with the selec-

tion made by a committee of represen-

tatives from each participating organiza-

tion.

The fundraising activities for the Shis-

kin Award led WSS to separate the two

positions of secretary and treasurer, an

arrangement which had been provided for

in the WSS Constitutions. Other changes

over time in the structure of the elected

positions of the Society was the establish-

ment of the Vice President as the Presi-

dent Elect in 1966 and the establishment

of two-year terms for Representatives at

Large, Secretary, and Treasurer in 1984.

The emphasis on maintaining continuity

of WSS activities has been reflected in the

encouragement of two-person teams for

organizing various program sessions.

The thawing of relations with China led

to one of the most successful activities of

the Society. Five statisticians from the

National Statistical Society of China vis-

ited Washington, D.C. for nearly a full

week in conjunction with their visit to the

1981 ASA annual meetings. WSS served

as the host for the D.C. part of the trip.

Activities arranged included visits with

statistical organizations, a reception at the

National Academy of Sciences, an eve-

ning “pot luck”’ dinner, chaperoned sight-

seeing, and a most successful evening din-

ner in honor of the visitors.

The success of China delegation visit

led to the sponsoring of other special pre-

sentations by the Society. In the spring of

1982, an all day program was scheduled

to commemorate the 200th anniversary of

the birth of S. D. Poisson. That fall, W.

E. Deming’s birthday was celebrated in

an evening social session. Morris Han-

sen’s 73rd birthday was recognized in 1983

with a similar evening social.

The 1984-86 time period led to several

important developments in the operations

of the Society. The interest in the Deming

and Hansen birthday parties was institu-

tionalized into an annual WSS holiday

party. This early evening event held every

December provides a second social activ-

ity to accompany the June annual dinner.

WASHINGTON STATISTICAL SOCIETY 295

During the 1984-85 program year,

Terry Ireland urged WSS to try some WSS

sponsored short courses. These were not

to compete with universities or private

vendors but were intended to provide in-

struction or knowledge on statistical top-

ics of broad interest. A short course might

involve the use of video tapes from an

ASA tutorial, with a knowledgeable in-

dividual available as a resource person.

These short courses were to be provided

on a fee basis, with fees covering rentals,

printing of materials, and travel expenses

of speakers.

The short courses were an instant suc-

cess. All had been well researched and

participants felt they got a fair return for

their investment. From the simple begin-

nings of low key one-day sessions in the

Martin Luther King Library the complex-

ity of courses and arrangements in-

creased. The 1987-88 program year was

marked by a very ambitious two-day sym-

posium on quality assurance in the gov-

ernment. This proved to be a landmark

session bringing together a unique com-

bination of quality professionals and

agency staff members. Very professional

materials were available and registration

included meals and receptions for speak-

ers. This session, planned for 150 partic-

ipants, drew over 200 people.

Another key development during the

1984—86 time period was the beginning of

WSS’ involvement in judging local science

fairs in the metropolitan area. Susan EI-

lenberg, in her position as a Represent-

ative-at-Large to the WSS Board, initi-

ated contact of all local school systems

and found volunteers to do the judging.

Since no Statistics category was offered,

WSS members judge all projects for sta-

tistical content. Prizes have included books

on statistics appropriate to high school age

individuals.

The success of the short course program

led to another change in WSS program

philosophy. WSS normally does not pay

any honoria for presentations. Many of

the name speakers each year from outside

the Washington, D.C. area have spoken

for free when they are in the area for other

commitments. In the 1986-87 program

year, the concept of one invited lecture

was originated. Based on the fact that some

extra proceeds were available from short

course operations, one outside speaker a

year would be brought in. The concept

was successful in 1987 and was repeated

in 1988. In that case, the science fair win-

ners were invited to display their projects

at the invited lecturer.

In 1984, WSS started its own internal

award program. This Presidents’ Award

goes annually to a member or members

for outstanding contributions to the So-

ciety. The award carries no monetary

value but since it is presented at the An-

nual Dinner, it does provide good recog-

nition to the recipient.

Many WSS members are actively in-

volved in the celebration of the 150th an-

niversary of the American Statistical

Society. This celebration will last from

August 1988 through December of 1989.

WSS has planned a series of 10 monthly

special presentations on broad topics such

as Statistics and the law and statistics and

the media.

Journal of the Washington Academy of Sciences,

Volume 78, Number 4, Pages 296-310, December 1988

Clustering of Senators and

Their Votes

Miles Davis and Donald Wolfe

Loyola College, Baltimore, Maryland

ABSTRACT

Votes by Senators of the United States of America on major bills are analyzed by

principal components and clustering techniques. Clusters of Senators and bills are shown

in graphs. The three classes of Senators elected in successive Senatorial elections are

studied to detect systematic differences in their voting patterns. A dimension of liberal-

conservative gradation and a pattern of change over time are found from the voting

records.

Introduction

Voting in the Senate of the United

States of America is an interesting and

important source of complex data. Al-

though it is highly structured by party af-

filiation, by ideology and by regional

interest, it is still sufficiently unpredicta-

ble to be interesting. We analyze voting

on key bills by all senators from 1969 to

1986, using principal component analysis.

We offer the data as a readily understood

and important body of illustrative but real

data for experimentation with statistical

methods.

Voting Data

We abstracted data from the complete

record of voting in the Senate appearing

regularly in the Congressional Quarterly?

Correspondence should be sent to: Dr. Miles

Davis, 1214 Bolton Street, Baltimore, Maryland

21217-4111.

296

for key bills as selected by Michael Bar-

one in the Almanac of American Politics.'

We identify the 144 key bills in Table 1.

They are selected to reflect the decisive

action on issues that often come to several

votes. They are thus more closely con-

tested than the entire record of votes and

represent the high drama of decision.

The actors in the drama are the 217

senators who served from 1969 to 1986.

Their classes, party affiliations, states,

names, and the bills on which they voted

appear in Table 2. The term “‘class”’ refers

to the three divisions of the Senate de-

termined by the year of election. Since

senators are elected for six year terms,

and one-third of the Senate is elected

every two years, each Senator holds a seat

in one of the three classes.

The Senators’ votes on the key bills ap-

pear in Table 3 as the data for our study.

To show the votes compactly, the rows of

Table 3 are identified by class and state,

and the columns are identified by bill

number. For example, the first row of Ta-

Table 1

1069/54

2069/142

30@69/245

4070/11

5070/19

6070/89

770/103

8070/112

9@70/157

10@70/180

11@70/195

12€70/206

13070/211

14070/240

15070/249

16070/251

17070/252

18070/256

19070/328

20070/380

21071/23

22071/354

23071/355

24071/361

25071/417

26072/54

2772/97

28072/110

29072/144

30072/215

31072/219

32072/226

33072/262

34072/292

35072/296

36072/334

37€@72/339

38072/383

39072/391

40073 /27

4173/34

42073/154

43073 /286

44073/372

45073/400

46073/551

47@73/571

48074/66

49074/69

50©74/138

51074/156

52074/187

53074/194

54074/212

55074/225

56074/286

CLUSTERING OF SENATORS AND THEIR VOTES 297

Senate Bills

Prevent funds for Safeguard.

Reduce depletion allowance on oil & gas.

Reject Philadelphia Plan amendment.

Drug Control, striking “‘no-knock”’ provision.

Drug Control. Hughes amendment reducing further marijuana penalties.

Voting Rights Act—Voting at 18.

Corundum disposal.

Carswell Nomination to Supreme Court.

School bus in desegregated districts.

Bar U.S. military in Cambodia.

Consumer Products Warranty and Guaranty Act.

Limit agricultural subsidy to $20,000 to any producer in a single year.

Bar price support for tobacco.

Require weapons systems be tested.

Increase funds for Bureau of Prisons.

Create volunteer army.

Prohibit military use of defoliants.

Reduce authorizations for defense.

Elect Senate committee chairmen.

Reduce defense public information.

Restore funds for supersonic transport

Presidential campaign fund from tax.

Extend to single persons tax rates applicable to married persons.

Limit US military in Europe to 250,000

Rehnquist Nomination to Supreme Court.

Bar school busing on basis of race.

Table National Voter Registration Act.

Equal Rights Amendment.

Unfair Billing Practices.

Delete criminal penalties in 1972 Food, Drug and Consumer Product Act.

One-year authorization for Corporation for Public Broadcasting.

Delete National Legal Services Corporation from Economic Opportunity Amendments.

Delete minimum wage for domestics.

Give states exclusive authority to manage fish and wildlife, unless endangered species.

Reduce annual crop subsidy maximum.

Refer no-fault auto insurance to Judiciary Committee.

Outlaw Saturday-night special guns.

Table reduction of exemption on preference income for minimum tax.

General Revenue Sharing.

Senate committee meetings closed only by public vote at start.

Highway Trust Fund for bus opr rail.

Prohibit U.S. combat in Cambodia or Laos.

Permit Alaska Pipeline.

Restrict limousines for officials.

Reduce military headquarters overseas.

New northeast rail labor agreements.

Halt import of Rhodesian chrome.

Table required registration of handguns.

New standards for death penalty.

Federal Election Campaign Financing.

No-Fault Auto Insurance.

Prohibit required student testing.

Table prohibition of school busing.

Freedom of Information Amendment.

Demobilize 76,000 U.S. oversea military.

Repeal no-knock provision of Drug Abuse Control Act of 1970.

298

MILES DAVIS AND DONALD WOLFE

Table 1.— Continued

570@74/395

58074/479

590@74/496

6075/55

61075/67

62@75/130

63075/190

64075/382

65075/431

66075/516

67€76/27

6876/65

69076/93

70€@76/103

71076/141

72076/180

73076/333

74076/471

75€@76/521

76076/554

77@77/11

78@77/41

79@77/42

8077/59

81077/164

82077/232

83077/263

84077/275

85077/280

86077/320

87€77/523

88078/66

89078/161

90078/166

91078/435

92078/447

93078/480

9479/70

95079/169

96079/206

97@79/438

98079/445

99@79/490

100080/60

101@80/101

102€80/197

103@80/272

104080/315

105@80/345

106080/441

107080/466

108080/496

109081/140

110081/182

111€81/239

112081/275

113081/335

Senate Bills

Consumer Protection Agency.

Prohibit food stamps for strikers.

Foreign Aid Authorization.

Amend Cloture Rule.

Rescind F-111 fighter-bombers.

Table barring Medicaid abortions.

Resume military aid to Turkey.

‘“‘Redlining”’ Disclosure.

Emergency Natural Gas.

Common-Site Picketing.

Prohibit arms sales to Chile.

Federal Employees’ Political Activities.

Prohibit federal supersonic air funds.

Recommit no-fault auto insurance.

Reduce national defense budget.

Bar production of B-1 bomber.

Utilities pay for Clinch River reactor.

Retain nitrogen oxide standards.

Delete House ban on abortion funding.

Water Pollution Control Amendment.

Presidential Pardon for Draft Resisters.

Warnke SALT Nomination.

Warnke as Director of Arms Control and Disarmament Agency.

Halt Rhodesian Chrome Imports.

Reduce target price for wheat.

User fees for water resources.

Prohibit federal funds for abortion.

Limit Clinch River reactor spending.

Prohibit production of neutron bomb.

Federal tax fund for Senate elections.

Natural Gas Pricing.

Ratify Panama Canal Treaty.

Disapprove mideast figher plane sales.

Amend National Labor Relations Act.

Extend ERA ratification deadline.

Revenue Act of 1978.

Medicare-Medicaid Cost Containment.

Establish Department of Education.

Defer new nuclear power plants.

Food Stamps.

Windfall Profits Tax.

Indexing individual income tax.

Chrysler Loan Guarantees.

Spending Limits.

Fiscal 1981 Budget Targets.

Draft Registration Funding.

Aid to Nicaragua.

Exempt small business from OSHA.

Invoke cloture on Alaska Lands.

Kill federal funds for abortion.

Cut MX missile funds.

Fair Housing Act Amendments.

Require paying for food stamps.

Budget reconciliation.

Cut individual income tax rates.

Helms (R-NC) Foreign Aid Amendment.

Disapprove AWACS sale.

CLUSTERING OF SENATORS AND THEIR VOTES 299

Table 1.— Continued

Senate Bills

114081/368 Legal Services Corporation.

115@82/2 Bar court-ordered school busing.

116@82/118 Chemical weapons.

117@82/288 Balanced Budget/Tax Limitation Amendment to the Constitution.

118@82/420 Bar MX missile procurement.

119@82/422 Eliminate Clinch River reactor funds.

120082/463 1982 Transportation Assistance Act.

121083/35 Social Security Disability.

122083/65 Postpone date for resident status.

123@83/101 Immigration Reform and Control Act.

124083/169 Human Life Federalism Amendment.

125083/170 Tax Rate Equity Act.

126083/293 Martin Luther King, Jr. Holiday.

127€83/355 Table tuition tax credits.

128084/34 School Prayer Amendment.

129084/51 Table combat troops in El Salvador.

130084/132 Table ban on new MX missiles.

131084/252 Prohibit activities against Nicaragua.

132084/266 Table freeze on nuclear weapons.

133@85/142 Firearm Owners’ Protection.

134@85/191 Immigration Reform and Control Act.

135@85/300 Textile Import Quotas.

136@85/310 Discount sales of tobacco.

137085/371 Sequester funds for national defense.

138086/51 Aid to Nicaraguan “‘contras’”’.

139@86/176 Table limit to “star wars’’.

140@86/209 Reduce limits on PAC’s.

141©86/266 Rehnquist Nomination as Supreme Court Chief Justice.

142086/296 Tax Overhaul.

143086/300 Omnibus Drug Bill.

144086/311 South Africa Sanctions.

ble 3 shows votes by the senators occu-

pying the seat reserved for Arizona in

Class I. Reference to Table 2 shows that

this seat was held by Senator Fannin (R,

AZ) while voting on bills 1 through 76

and by Senator DeConcini (D, AZ) for

bills 77 through 144.

Votes are recorded as letters or sym-

bols:

y = yea vote n = nay vote

# = pairedfor x = paired against

f= CQpollfor « = CQ poll against

+ = announcedfor -— = announced

against

voting present

= not voting to avoid conflict of in-

terest

? = unknown

space means not a senator for that vote.

Bills are identified in Table 1. Our se-

quential bill numbers are followed by the

years of the Congressional Quarterly

(CQ) volumes and the numbers assigned

by CQ to the bills. Bills marked @ were

passed, but those marked O were rejected.

Short descriptions of the bills follow the

numbers. Much more thorough descrip-

tions are in CQ.

Analysis of the Data

We began to analyze the data by con-

centrating on the process of voting. We

formed a matrix of 217 rows and 144 col-

umns containing a +1 wherever a yea

vote (y) was cast and a —1 wherever a

nay vote (n) was cast. Elsewhere, the ma-

300 MILES DAVIS AND DONALD WOLFE

Table 2

Senators listed by class, party, state and name, with

the numbers of the earliest and latest bills in their

terms of office.

1 RAZ Fannin 76

1 DAZ DeConcini 77 144

1 RCA Murphy ies)

1 DCA Tunney 2k), 76

1-RCA Hayakawa TT 20

1 RCA Wilson 121. 144

1p CT Dodd, T. oy 20

LR Weicker 21 144

1 RDE Williams, J. fi 20

1 RDE Roth 21 144

1,DFL Holland Keg 20

LD BE Chiles 21 144

1 RHI Fong Ly 6

1 DHI Matsunaga 77 144

1 DIN Hartke TKS)

1 RIN Lugar 77 144

1 DME Muskie L 10%

1 DME Mitchell 102 144

1 DMD Tydings ey 20

1 RMD Beall ZA 6

1 DMD Sarbanes 77 144

1 DMA Kennedy 1 144

1 DMI Hart dG

1 DMI Riegle 77 144

1 DMN McCarthy 20

1 DMN Humphrey, H. Pasi te

1 DMN Humphrey, M. S8r 195

1 RMN Durenberger 94 144

1 DMS Stennis 1 144

1 DMO Symington P76

1 RMO Danforth 77 144

1 DMT Mansfield ire WS)

1 DMT Melcher 77 144

PR INE Hruska LOG 7 6

1 DNE Zorinsky 77 144

1 DNV Cannon 1.120

1 RNV Hecht 121 144

1 DNJ Williams, H. MWe ibis)

1 RNJ Brady 116 120

1 DENy Lautenberg 121 144

1 DNM Montoya Wie, 76

1 RNM Schmitt TE OY

1 DNM Bingaman 121 144

1 RNY Goodell 20

1 RNY Buckley PA BETS)

t DNY Moynihan 77 +144

1 DND Burdick 1 144

1 ROH Young, S. Lf 920

1 ROH Taft, Jr. PAINS | TAG)

1 DOH Metzenbaum(II) 77 144

1 RPA Scott, H. © LW IK

1 RPA Heinz 77 144

1D RI Pastore 1s 6

1 RRI Chafee 77 144

1 DTN Gore, A., Sr. tna 20

1 REN Brock PAV TKS)

NONNMNMNMNNNMNMNMNNNYNNMNMNMNNNNNNNNMNMNNNNMNNNNNNNNNNNNNNNNN NMR RRR RRR RRP RRR Rr re

Sasser

Yarborough

Bentsen

Moss

Hatch

Prouty

Stafford

Byrd, H., Jr.

Trible

Jackson

Evans

Byrd, R.

Proxmire

McGee

Wallop

Sparkman

Heflin

Stevens

McClellan

Hodges

Pryor

Allott

Haskell

Armstrong

Boggs

Biden

Russell

Gambrell

Nunn

Jordan

McClure

Percy

Simon

Miller

Clark

Jepsen

Harkin

Pearson

Kassebaum

Cooper

Huddleston

McConnell

Ellender

Edwards, E.

Johnston

Smith, M. C.

Hathaway

Cohen

Brooke

Tsongas

Kerry

Griffin

Levin

Mondale

Anderson, W.

Boschwitz

Eastland

Cochran

Metcalf

Hatfield, P.

Baucus

Curtis

WWWWW WWW WWW WWW WWW WW WWW WWWWWWWWWNNNYNNNNNNNNNNNNNNNNNN NH NNN NW HW NW PY

CLUSTERING OF SENATORS AND THEIR VOTES 301

Table 2.— Continued

EOomtagS

Exon

McIntyre

Humphrey, G.

Case

Bradley

Anderson, C.

Domenici

Jordan

Helms

Harris

Bartlett, D.

Boren

Hatfield, M.

Pell

Thurmond

Mundt

Abourezk

Pressler

Baker

Gore. A; 55.

Tower

Gramm

Spong

Scott, W.

Warner

Randolph

Rockefeller

Hansen

Simpson

Allen, J.

Allen, M.

Stewart

Denton

Gravel

Murkowski

Goldwater

Fulbright

Bumpers

Cranston

Dominick

Hart

Ribicoff

Dodd, C.

Gurney

Stone

Hawkins

Talmadge

Mattingly

Inouye

Church

Symms

Dirksen

Smith, R. T.

Stevenson

Dixon

Bayh

Quayle

Hughes

Culver

Grassley

3 RKS Dole 1 144

a DRY. Cook 1) 7-59

3¢) KY. Ford 60 144

3 sD LA Long 1 144

3 RMD Mathias 1 144

3 DMO Eagleton 1 144

300 D NN: Bible Lex59

3 RNV Laxalt 60 144

3 RNH Cotton(I) E50

3 RNH Cotton(II) 64 64

eet DM BI Durkin 65 108

3 RNH Rudman 109 144

3 RNY Javits 1 108

a7 RNY D’ Amato 109 144

3 DNC Ervin 1°) 59

a INC Morgan 60 108

3.4 Rk NC East 109 138

SS ING Broyhill 139 144

3 RND Young, M. 1 108

3 RND Andrews 109 144

3a OH Saxbe Len 47

3.9 DOH Metzenbaum(I) 48 59

3. DOr Glenn 60 144

3 ROK Bellmon 1 108

3 ROK Nickles 109 144

Ewa el GIF Packwood 1 144

3 RPA Schweiker 1 108

3 RePA Specter 109 144

3) SC Hollings 1 144

3) DSD McGovern 1 108

Samed its) B) Abdnor 109 144

SPROUT Bennett PUP 'S9

SR Ae WG Garn 60 144

3. RVE Aiken Le. 59

3-4 -DeViE Leahy 60 144

3 DWA Magnuson 1 108

3 RWA Gorton 109 144

Sh WI Nelson 1 108

3 RWI Kasten 109 144

trix contains zeroes. This matrix was con-

densed into Table 3 by placing the votes

of all Senators into rows corresponding to

the Senate seats that they hold, identified

by class and state. Rows in the data ma-

trix, unlike Table 3, correspond to sena-

tors. The columns of the data matrix

correspond to bills, as in Table 3. Gra-

dations of support short of voting are ig-

nored by this choice, and an alternative

analysis might well take them into ac-

count.

A spectral analysis of the matrix was

done, following the ideas of Good*. The

302

MILES DAVIS AND DONALD WOLFE

TABLE 3.1

Votes in the Senate. Senate seats arranged by class and state identify the

rows,

DONNONNNNNNNNNNNNNNFRFPKPRPBPBPBPBP BR BPP RPP RPP RPP PRP BPP BPP RP RPP BPP PPP PP

and senate bill numbers identify the columns.

111111111122222222222333333333444444444455555555556666666666777

123456789012345678901234567890123456789012345678901234567890123456789012

nnnnnyyy ?n?n?xnyn- ?nynnnyyynnyyyyynyny? ?nnyynynyynnyn?nnnyn?nnynnnnnnynn

nn?n-yyyxnnx+n?#--xnnynnn-nyy ?nnnnnnynytyyn. nnynnyynyyyyynyyyynyyyyty? ?x

nnynn-+n+—-++—-ntnn-? ?nnynynyyn?nnyn?nnyyyy#ynxnyynnyyyy ?yynnnnynynyynynyn

nynnnnyynnnyyynynynynnnnyyyynyyyynynyyyyynnnyyyyynyynynyyynnynnnn?nnnyn?

nnnynynynnnnnxnnnnnnnyynyy-#y?? ?anyyynnyyynn?nnyyynynynnyynnyyynynyynynn

nn?nnn#nynt+nn-ny ?-?nynynyyyynynyynnyyyynyty ?nyy?? ?cynynyynynyyynnn.nnec.n

VYYY? ?nyn?yy?? ?yy ?+?ynyytn.nyynnnnnynyyynnyynynyynynnn?yyyn?y?nn?yyyy?y?y

yyyyynnn#yyyn?ynyy ?yny? ?n-?y??? ?nn?ny ?yyy *nnnnynnyynyyyyyNyyVVVYVyvyy ?ynny

yyyntnnn?yytntyn-#? ?ynnnyyyynyyyynynyyyyynyynynyyyyynynnynyynynynnynnynn

YYYY ?n?nyyyyn? ?nny#ynynynnnyynnnnnyny . fyyynnfnynnyynyyyy+nyyyynfyyyyynyy

yyyyyn?ntyyy#+yyyynynyyynnny fnnnnn#nynyyyynnfnynnyynyyyyynyyfyyfyyfynny?

yy ?yy--nty++-yynty-ynyynnx-y ?nnnann#nyxyynynnynynnyynyyyyynytyy .tyyyyxnyy

nnnynynynnynnnnnnnnnynnnyyynnynyynnynynxx? ?yn?nyyxnynnnnnyn ?nnynnnnannynn

y# ?nnxnnyyy-—? ?yny-nyyyyynnyynnnnnnnynnnyynny?ynyty ?yy#yynnynyyynyyyxynn

yni#yynnn#yyyx?y#yyyynynyxnny??? ?nnnnnnnxnynnyny? ?y#yyyynynny ?yyyyyy*x=nny

nnnnnyt+tynnnnannnannnnnynnnyyyynyyyyynyyyynnnyy.ynyynnynnnnny.nnnynnnn-nynn

ynnnnnnnny ?y#x?x?x ?nyynnyynyynnny fnynnynnt+ynnnnyyyynnnnnynnyn?yyynyynynn

yyyyynnnyytyyy ?yyyyynyyynxnyyn.nn. ynyyy+#ynnynynnyynyyyyynyyyy-yyyyyynyy

yyynynyn#yyyy#yyyy##ynnnyyynnyyyy-nyyyynynny fynyynnyn ?nnn? ?n ?nynn ?nnyynx

ynnynnynyyynnnyy-ynynyyyynnyynnnyynnyynnnynnfnyynyynyyyyynnyyynynyyyynnn

yy ?yynnntyyt+t+y-yyynyynnnytyyny.xyn#nnynyyny? ?ynyynyyyynynny#f£+yynynnnyn-

nnynnyxy#nnynnt+ynnnnynnnynyy.yynyy##yyynynyynyyyyyyyynnnynyyytyynnnn-nnn

nyyyynynyy+tyyy-yny-nnynyynny+nnnnn#nyyynyynnnnynnyyyytyyynnyynnyyyt#yny#

yynynnnnny??x??n?? ?yynnnyyyyNyyyVyNn?yyyyyny.- -ynyynnynnnynynnnyynnnnn.nn.

ynx#nnnn?y ?nnn-ynnnynynnyynynnnnnnnynynynyyn?nyyyyn?nannyyyyynynnnnn?nyn?

ynyy-ntnyyyty-yyyttyyynynnnyynnnnnnnnnyyyyn. -nyyyyy-yyfyynyyyyxfyyyy.-yn.

nyy??n?nyn?yn-nynn-nnnnyynyyyynnnntyntyyyynynnyyyyynyynyynyynyyyyynxnyyn

nnnyyyyynnyyn?nnnnnnnnnnyyyynyyyynyyyynnnyynnynyyxnynnnynynnynnnnannnyynn

nyynynnnyyyyyntnnnnnyyynn--t++nnnannnnynynynnnnnyyyyynyynyynyynynyyyty-xyn

nynnxnyynyyynnnnnynyyynyyynyynnynnnanyynnnyynynnyynyynnynynnynyynnynynnny

yynynnynyyyynynyyynynyyyyynyynnnnnynynnyyynnynyynyyynyyyynnyynnyyyynynny

nn? ynnnnyny-? ?ynnn?nyyynynnyynn?nynnxytnn?yynnyyytynyyxyynynnn#ynyny?n??

nnnyyytynny-—-nnnnn?nyynny?yy -nnyynnyyftnnxyynnnyffin.nf.ynnynnnyynnyynyn.

nn?+nnnyyyy? ?--#-nynynynynyyfynnnynnnyynnyyynnyyyyynnynyynyyny+tnyn#nn. —

nnnnny+ynnnnnnnnnnnnynyyy#?#?? 7nynnynyynnyyynnnyynnynnynnyn?nnynnnnnn#?n

nnxnny#ynnxynnnnnnnnynynyyyyxyyynyxyyt#yytny fnyyyyynnyyyyn?yyy-yyyyyynyy

nyynnnyyynnynnnynnnnynnnynyynyyynyynyyyyyynnynfynyynyyyyy ?nyynnyyyyy#nyy

nnnnnnt+ynnnynnnynnnnnnnnyyyynyyynyF#yyyx#nynnnynyynnyn?nannynnnnynnnn?ny-n

y-yxnnxnyy###nyynnyynnnn#¥n-ynnnnn-ynyynyyyny#nynnyy ?yynyy ?yynynynyn-nnn.

nnynnyyynnnnannnnnnntnnnny.yynynyynnyyt+#yyynnynyynyynyyyyynyyyy-yyyyyynyy

yn?nnnyyyyynnnxynynyynynynyyynn?yynnyyynyyny .yyynyyyyynyynyynyyynnynynnn

yy ?ynnyyyynnnyynnynynn ?nynyyyyyynnnyyyynnyyn ?nnyyynynnnyynyyyyypnnyynyny

ynxnnyyynn+nnnnnnnnnyynyyyyyy#nyt ?xyyyyynyynn?yyynnynnn?nynynnyynnnynyn.

yynnnnnnnny+t+y-nnnnnnnnntynynyyynnnnyyyyyynnyyynnyynyyyyynynyy ?yyyyynyyy

yyynynynyyyyynyynnynnnynnnnyynnnnnynyyyyyyyynnynnyynyynyynyyyynyyyyvyy *yy

n#ynnyyyyn?y#nynnnnnnnynyyyyn?y#tynyxynynynyynyyyynyynnnnnyyynnynnnnx?nnn

yyyyynynyyyy? ?ynyyyynyyynnnyynnnnn#n#nyyyynnyny? ?yynyyyyynyy ?y ?yyyyyynyy

nn?ynynynn?nn?nnnxnnynnnyyyxnyn#ynny-yynnnyy ?nny ?nnynnnnn ?n? ?n?nnnn?nynn

CLUSTERING OF SENATORS AND THEIR VOTES 303

TABLE 3.2

Votes in the Senate. Senate seats arranged by class and state identify the

rows,

WW WWW WWW WW WWW WWW WWW WWWWWWWWWWWWWWWNNNNNNNNNNNNNNN ND

and senate bill numbers identify the columns.

111111111122222222222333333333444444444455555555556666666666777

123456789012345678901234567890123456789012345678901234567890123456789012

yy#yyxtntynnt+y-~-yynynyyynn.yy. .nnynnxnyxyynnynynnyyyyyyyynyyy- fyyyyyynyn

nnnnnyyynnnx-nnnnnnnynnnyyyynynyyynyyyxnnnyyxynyynntnnnnnynxnnynnnnnnynn

yyynnn?nyyyynnnnnnnnnyyyyn?ty? .nnnynynt+n?ynynnyynyynyyyyynyy ?ynyyn?y?nnn

yytyynynyyyyyyynyyyynynnnnnyynnnnnynyyyyyynnynynnyynyynyynyyyyyyyyyyynyy

n-?n?n? ?yy?? ?nnnn?nnnyny ?nnyn?n? Pnnyyy ?nnyyynynyyynynnnyyyynynynnnnnnynn

nnn#nyt+tynyy-xnnnnn?n-ynnyyyy ?yny? ?xyyyynnnynnynyynnynnnnnynnynynnnynnynn

yy#nnnxnyyyyy#yyyyy#nnyyynyy#-—-nyytyyynyyyn. #yyt+-yynyyyyynnyyny-ynyyyny#

yyyyynyxyytyyynnny ?ynyynynnyynn?nn#n? ?ynyynnynynnyyny ?yyynnyyynyyyyynnyy

nnnnny#ynnnnnxnnnnnnynynyyyynyyyynnyyy#xnnyynynyynnyn-nnnyynnnynnnnnnynn

n-nnn-t+ynnnnx?+ynnnnynynyyyynyy?? ?xyn?yny ?y ?nynyynnynnnynyynn? Pnnnannnyn?

nn?xn+nynnxnnnnnnnnxynnnyyyynyyyyynynyynnnyynynyynnynnnnnyynnyynnnnnnynn

nynynnynnyyyny ?nnnnynynnyyyyyynnyn#ny#ynnnynny ?yy ?nynnynnynnnynnnnnnnynn

ynnynnnynyyynynnnyyyyynyyynyynnnnnxyyyynnyynynnyy#n-ynyyynnynx. nnyyynyyn

nnnnnnyynnnnn-nnannnnnannnyyynnyyyyynynfynnnyynynyynnynnnannynnnnynnannnnynn

nnnynyyynnynnnnnnn?nnynnyyyynynyynnynyynn. ynnynyynnnnnnynynnynn.nnnnnynn

yn##?-nnyyy? ?#+++# ?yyyyynnnyt. -xnyxnnny#nyyny? ?ynyy. ft+tyfynynyynynyyfc-?n

nN???n??y?n?n?n?yn?ynyn?nyyyNn?? ?y?yxyn?xnnxynnynyy-Nn?nnnnnyn?nnynnnn-nynn

yxnn?nyn?y ?nyynx?ynynynyny-yynnn?nnyyyynnynnyny. ??x????y??? ?yyynynyyyynn

ynyy ?nnnyyynynyyy#yynyyynnnynnnnnnnny ?yyyy ?nynynnyynyyyyynyyyynyyyytynyn

nnnx-nyyynnynnnannnnxynnnyyyynyyyyyxynyynytyn. yn? ?nnnn?nnnyyyyynyyy -yynny

yy#ty#n#nyy++?#yyy #nynyyynn-yynnnnnynyyyyyynntnynyyynyyyyy ?yynyn?yyy-ynyy

nnnnnt+yynnnnnxnynxnnynnnyyyynyyyynnyyyyynynn.nnyyy? ?nannnn?nyynnnnnyynynn

nn?ynynynnynnnnnnnnnyynyyyyyyynyynnyyyynn#ynnnnyynnnnnynny? ?yy ?7nnnnynynn

yyyyy-nnyytnnn+++-yyyyyyn.nyyffnnnxnyyyxyyynynynnfy.fffyynyyn#tfyyyy??n.n

ynynyn+nyyyynnnyny-ynyntnnnyynnnnnfynnxnytnnynfyy#ny#tyyyy ?nninnyyyf#ynftt+

nxyn-#yyny-yyyyyyx#ynyynynnyynnnnnynynnyyynnynynnnynyyyyynyyyynyyyfynnny

yyynnnnnyyyynyyny?yy-yyyn-nynnnnnnynyny#xynnynyyyyynyyyyynnyfynfy+fy#nyy

yyyyyn+nyyyynyy#yyyynyyynnnyyx .nnnynynyynyn. fnynnyynyfyyynnyyynyyyyyynyy

nnnnnnyyyynnnntynnnnynynyyyy ?yVYVynyyyyynnnynynyynnynnnyyynyynnnnnnnnynn

yn?nnnt+nynn?xnnynny ?ynnnyyyynnnynynyynyynynnnynyynn?nynyynyyyyYNyyVVYVVY°?y

nnxnn#?yxxynnnnnn-?yyynyy#nynnnyynnnyyynnnynynyyytnnnny ?nynyyn? ?nynnnnny

yny# ?n?nyynyn? # ?nyyyyynnynnyynnnnn#yyyyyyynnfyyynyynyyyyy ?yYyyvy ?yynny ?y

yyynnnnnyyynn? ?nyyyynyyyynnyynnnn? ?yynn#?yn?ynyynynnyyy ?ynn? ?nnynyyy#y?n

nnnnnnnynyyyn-nnnnnnyynyyyny -nnnnnnynynnnt+ynynnyyynnnnynnnnannynnnn?nnynn

nn?nnnyyxnnynn?nn?nnynn?yyynnyyyyv#yyyynnty? ?y?? ?nnnnnnnnyy nyyyyynyy

yyyttnynyy##?nynny ?ynnnnnnnyynnnnnynyyynyynynnynnyy ?yynyy ?yynynftnyyyynyy

nnxynynynnynnnnnnnnnnnnnyyyn#ynyynnyyynxnty.ny-yynnynnnyny. ?y??xnnnyny-n

nnnnnnnynnnnnnnnnnnnynyyyynynyn.yynyyynnnyyynnnyyynyny .nnynynnynnn.nnyn.

yn?nn? ?yyyyynn?x?#yyynn?y-yyyynnyyyynynn?yyy ?ynnn#ynyyyyynyyyynfnnnynnnn

nnynnxnyynnnn?nnnn?nynnnynnynyyynynyy ?yynyyy ?ynyyn?y ?nn?ny ?nynynnnnnnynn

nny? ?nynyynyyyyy? ?ynnnyyy ?y+?nyyynxynyy#yynynyy? ?yy ?yy ?yyynyyyy ?yynnnyny

ynynnnnnyyyyyyyynnyynnynynnyynnnnnynnyyyyyynnnyyyyynnyyyynytynnyyyyyynny

n?xynnnynyynnn-nn-xyyynyyynynftnnynnyynyynyynyy???xn?x? ?Pnyynn.yn.ynny?ynn

yyy ?ynnnyyyy ?y ?yyyyynyy+tn-n+xnn?n?t+ny?#yyynnynyynynny ?yyynnyyynyyyy ? ?nyy

nnynnyn#nnnnannnnnnnnynnntyynnyyyyyxynyyny.yy-y-ffnyf. .nnn?yynnynnn.nnynn

yyynnnyyyynnny-nnn?nnnnyynyyyyyynnnyyyynyynnnnyynnynyyyyynyyyy-yyyyy ?nny

yyynynxnyyy ?#nnnyxnnyyyynnnyt+nnnnnnnynyn#y-nnnyyyyynyyyyyn-yntn#tyyyynnnn

yy#yy-yny# ?ynyyyyyyynyyynnnyynnnnnynynnyyynnyny? ?yyyyyyyynn?yynyyn?yynyy

304

MILES DAVIS AND DONALD WOLFE

TABLE 3.3

Votes in the Senate. Senate seats arranged by class and state identify the

rows,

NNNNNNNNNNNNNNNNNFRPEFPRPRPRPRPRPRPRPRPRP PRP PRP RPP PRP RPRPRPRPRPRPRPRPRPRERP

and senate bill numbers identify the columns.

pbalalabakatataeakabalatababalalalababalababatavababalabal at alah abot au lob SL 1 ab aL Tab

777777788888888889999999999000000000011111111112222222222333333333344444

345678901234567890123456789012345678901234567890123456789012345678901234

nnyyyyyyyyMnyyyyyynnyyyyyynnnyyyyyny ?#ynyyynyynyyyxyyynn?#ynynyynnnyynny

?++-nnnnynynnnyynnyyynnynynyyynyynnnyyyyn?yyyyyynynnnynyyynyyynyyyyyyyny

nyy -nnnyynynynyyyynn.ynnynnynyy ?yn?ynyynyynnnnyynnynnyynnnynyyyynnnnnnyy

ynnnnny ?yynnnnynynyyyynyyyyyynyyyynnyyyyynynyynynnynnynyyynyyyynnyynynny

nnyynnyyynnnnyyyynynnynnynynyynyynnynyynynynyynyynyyyyyyynnyyy? ?#ynyynny

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n?xynnnnnnnnnnynnnyyynnynyyyyyyyyynnyyyynnyyyynynnyynynyyynyyynyyyynyyny

nnynyyyyy-nyyynynynnn?ynynyn?nynyynynyynyynnnnnnynnnyyynnnynynynynnynyyy

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nny+nnnnnnynnnynnnyyyn-ynynyyynynn ?nnyyynnyyyyynenynnnnyyynyyynyyyynyn?n

nnnyyyyynyyynnnynnnynynyyyynyynnnynnnyyyyynyyyynyn ?ynyyyyynyynyyyyyyynny

nn#ynnyynyynnnynnyyyyynyn?yyyyyynn ?nnyyynyyyyyyynnynnynyyynyyyyyyyynyynn

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nnyyyyyynyynnyyyny+nynnynynyyny ?ynynnyynnnynnnnynnynnyynyyyyyynynynyyyny

nyyyynyynynnnyny ?yynyynnynynyyyyyynnnyynnyynynyynnyyyynyynynyyyyyyynyyny

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nyynyyyyynyyyynyyynnny ?nyyynnnynynyynnnnyynnnnnyyyynyyyn ?nynnnynynnyny ?y

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nnnynyynnyn?nnynnnynyynnnynyyynyyynnnyyynnynyyynnnyynyyyyynyyyyyyyynyy?n

CLUSTERING OF SENATORS AND THEIR VOTES 305

TABLE 3.4

Votes in the Senate. Senate seats arranged by class and state identify the

WWW WW WW WW WWW WWW WWW WWWWWWWWWWWWWWWWNNDNNNNNNNNNNNN DN DY

and senate bill numbers identify the columns.

oc e213 We BW Dee ie ph a Lg Ue Bs Ya ta Up Dp Le a Ol Do OT a OB

777777788888888889999999999000000000011111111112222222222333333333344444

345678901234567890123456789012345678901234567890123456789012345678901234

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ynnynnnnnnnnnnynnnyyynnynynyyynynynnyyyynnyyyyynnnnpnnnyyynyynyyyyynynnn

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nnnynnnyynynnnyynnyynynynnnyynyynnnnyyyynnyyyynnnnyynnyyyynyyynyyyyyynnn

yyynnnyynyynnnyyyynyyynnyynyyn?yynnnnyyyy ?nnynny ?nynnynnynynyynyynnyyyny

y ?nnnnnyyynnnnynyyyyynynyynyynny ?#nnnyynyynnynyynnynyyynnnnnyyynynnyyyny

ynynnyy .-yyynnnnynnynyynnyn?nyynyyn?ynynnyyy ?ynn?y? ?nyyyynnnnyyyyyyyyyyny

y ?ynyyyynnyyyynynynnnyyn? ?ynnn?yy? ?yyyyynyyyyyyynnyynnyyyynyyynyyyyyynny

?n.ynnnnyynnnnynnnyyyynynynyyn?ynynnyyyynnyyyyynnnnynnyyyynyynynyyynt-??

yyynyyyynnnyyynynynnnyynyyyn?n?nynyynnnnytnnnnnynyynyyynnnynyyynynnynyny

~y# ?nxyynyynnynynynnnynnyyynnxynynnynyyynyynnyyynnynnyynyynyyynyynyyyy ?y

yyynyyyynnyyyynyyynnnyynynynnnynynnyyyyyynyyyyynnnyynynyyynyyynnyyyyyyny

306

SENATORS - CLASS |

Second

Principal

@ NE-Hruska Component

@ AZ-Fannin

e@ NY-Buckley

@ TN-Grock

NM-Bin

@ PA-Scott

Hi-Fong @ @ OH-Taft

MILES DAVIS AND DONALD WOLFE

MD-Sarbanes @®D OH-Metzenbaum

gaman © © MT-Melcher

WV-Byrd ©@ Ri-Chafee

FL-Holland © AZ-DeConcini © @ CT-Welcker

MS-Stennis © © VA-Byrd © MD-Beall © ND-Burdick

@ CA-Mur phy

CT-Dodd, T. ©¢@ DE-Williams ® V7-Stafford MA-Kennedy ©

NV-Cannon © © MN-Humphrey, M.

VT-Prouty @q@ TX-Yarborough

a © TX-Bentsed © TN-Gore, Sr.

FL-Chiles © | © PA-Heinz © WA-Jackson First Principal Component

NJ-Brady ee WA-Evans © MD-Tydings

MN-Ourenber ger

OH-Y bungee NY-Goodell

@ CA-Wilson

NM-Schmitt ¢e © VA-Trible

@ CA-Hayakawa © CA-Tunney © ME-Muskie

@ NV-Hec. IN-Hartke © © MN-Humphrey, H. © NJ-Williams

@ DE-Roth MT-Mansfield @® RI-Pastore

NE-Zorinsky ©@ MO-Danforth

@ WY-Wallop

UT-Hatch ee /N-Lugar

Fig. 1. Principal components for Senators in Class I.

mathematics involves a singular value de-

composition by the Jacobi method”’. Per-

haps more efficient methods would be

found in LINPACK?* and EISPACK".

Faddeeva® wrote about older but inter-

esting methods. MacRae’ and Easterling?

used the related method of factor analysis

to analyze voting in the Senate. Davis and

McCoy? analyzed survey responses in a

similar way. The analysis by principal

components is far from new, but it seems

useful as a first look at the data.

Results

In the figures, the principal component

vectors corresponding to the largest and

the next largest principal values are plot-

ted, following the widely used methods

named “‘biplots” by Gabriel’. In Figures

1, 2 and 3, the senators are divided among

the classes to which they belong. The

three classes of the Senate differ in their

characteristics, which may be seen in the

figures. Figure 4 shows the Senate bills,

CLUSTERING OF SENATORS AND THEIR VOTES 307

which are also identified by name in Ta-

ble 1.

Inspection of the figures allows us to

interpret the first, or largest, principal

component as a liberal-conservative gra-

dation. The second is not so easily under-

stood, but the sequence of bills in Figure

4 helps us to see a pattern. Early bills,

from 1969 and the early ’70’s, seem to fall

along a diagonal line from upper left to

lower right. As time passes, the line pivots

about the origin until, in the mid-1980’s,

SENATORS - CLASS I

Second

Principal

Component

NE-Curtis ee WY-Hansen

the line passes from upper right to lower

left. A further rotation of the axes might

well simplify the picture.

In Figures 1-3, the party affiliation of

the Senator is shown by @ Republican or

ators are more Democratic or north-east-

ern; more conservative Senators are more

Republican or south-western. These ob-

servations are well known, but it is inter-

esting that the spectral analysis was

performed with no reference to state or

1A-Miller ee CO-Allott

e@ (D-Jordan

MI-Griffin @ © DE-Biden

®@ Oxk-Bartlett

@ VA-Scott

@ TX-Tower

@ TN-Baker

@ OR-Hattield

@ SC-Thurmond 8 First Principal Component

CO-Haskel/ @ @ SD-Abourezk

SD-Pressler @ © OK-Bofen

@ MN-Beschwitz

@ /L-Percy

@ NM-Domenici @ MA-Brooke

NC-Helms @ @ /D-McClure © MT-Metcalf

@ /A-Jepsen

AkK-Stevens @ WyY-Simpson ® ® MS-Cochran

NH-Humphrey @® VA-Warner

® NJ-Case

Fig. 2. Principal components for Senators in Class II.

308 MILES DAVIS AND

SENATORS - CLASS III

Second

Principal

Component

® UT-Bennett

GA-Talmadge ©@e NH-Cotton

NC-Ervin © @ CO-Dominick

®@ OK-Bellmon @ FL-Gurney

@ NO-Young

DONALD WOLFE

>|SC-Ilollings

NV-Bible © IL-Dixon©e PA-Specter

KY-Cook ©@ O;

FL-Stone ©

@ AZ-Goldwater

NC-Broyhill @

NY-O'Amato @® /N-Quayle

NC-East @® WI-Kasten

GA-Mattingly @ @ AK-Murkowski

Al-Denton ee OK-Nickles

!0-Symms @ @ SD-Abdnor

UT-Garn @

@ NV-Laxalt

-Saxbe

@ MO-Mathlas

First Principal Component

d ® © AR-Fulbright

AK-Gravel © © 1ID-Church

® NY-Javits

® PA-Schwelker

Fig. 3. Principal components for Senators in Class III.

party affiliation. Only the voting record

contributed to the results.

In Figure 4, bills that were adopted are

shown as solid circles @ and those that

were not are shown as open circles O.

There is a pattern reflecting the legislative

leadership at varying times. In the earlier

years, more liberal bills, appearing in the

lower right corner, are passed more often;

but in later years, more conservative bills,

appearing in the lower left corner are

more often carried. Bills toward the edges

of the patterns are not often passed, per-

haps reflecting a moderating tendency of

the Senate to avoid support of extreme

legislation.

As Colin Mallows remarked on seeing

the graphs in the poster session at the

Joint Statistical Meetings in New Orleans,

the data would be usefully explored fur-

ther by computer graphics and shown

on videotapes. We are working on that

possibility, and we invite others to do so.

The data are available on a floppy disc

in an ASCII file in IBM-PC compatible

form.

CLUSTERING OF SENATORS AND THEIR VOTES 309

SENATE BILLS

Second

Principal

Component

8 036

033

043

320 ©26 25

300 €27

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044

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102

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119 138

116 136

12400110

e115

1120 0128

1300 0139

133@ @117

118 0129 e141

132

Fig. 4. Principal components for Senate Bills.

Acknowledgment

We thank Charles Stembler for pre-

paring a draft of the voting data in Ta-

ble 3.

References Cited

1. Barone, Michael: Almanac of American Poli-

tics, Washington, DC, National Journal, 1972-

1987.

2. Congressional Quarterly: Washington, DC,

Congressional Quarterly, Inc., 1970-1986.

3. Davis, M. and McCoy, J.: “A multivariate

model for response reliability in surveys,”’ Pro-

037 First Principal Component

28 @61 075 69

$9e of 073 Tlo @68 074

o40 = 62@ ~860

350 019 4024 «41 064

ol3 = @11 e112 072 550 @67

160 o14

ceedings of the Section on Survey Research

Methods of the American Statistical Associa-

tion, 603-608, 1978.

. Dongarra, J. J., Moler, C. B., Bunch, J. R.

and Stewart, G. W.: LINPACK Users’ Guide,

Philadelphia, Society for Industrial and Applied

Mathematics, 1979.

. Easterling, Doublas V.: Political Science: Using

the Generalized Euclidean Model to Study Ide-

ological Shifts in the U. S. Senate, Chapter

10 in Young, Forrest W.: Multidimensional

Scaling: History, Theory and Applications,

Hillsdale, NJ, Lawrence Erlbaum Associates,

1987.

. Faddeeva, V. N.: Computational Methods of

Linear Algebra, New York, Dover, 1959.

310

EDWARD J. WEGMAN

Gabriel, K. R.: The biplot graphic display of

matrices with application to principal compo-

nent analysis, Biometrika, 58:453—467, 1971.

. Good, I. J.: The Estimation of Probabilities,

Cambridge, MA, The MIT Press, 1965.

. MacRae, D.: Issues and Parties in Legislative

Voting-Methods of Statistical Analysis, New

York, Harper and Row, 1970.

Journal of the Washington Academy of Sciences,

Volume 78, Number 4, Pages 310-322, December 1988

10. Ralston, A. and Wilf, H. S.: Mathematical

Methods for Digital Computers, New York,

John Wiley, 1960.

11. Smith, B. T., Boyle, J. M., Dongarra, J. J.,

Garbow, B. S., Ikebe, Y., Klema, V. C., Moler,

C. B.: Matrix Eigensystem Routines-EISPACK

Guide, 2nd ed., New York, Springer-Verlag,

1976.

Computational Statistics:

A New Agenda for

Statistical Theory and Practice

Edward J. Wegman*

Center for Computational Statistics

4400 University Drive

George Mason University, Fairfax, VA 22030

ABSTRACT

The impact of workstation and personal computing has important implications for the

future of statistics. We argue that the capabilities of new computing environments will

change methodological focus because computationally intensive algorithms free of onerous

restrictions are feasible in place mathematically tractable but potentially nonrobust al-

gorithms. Moreover electronic instrumentation allows us to collect data substantially dif-

ferent from traditional data collection. In particular, we argue that in place of small, low

dimensional homogeneous data sets chosen according to a well designed experiment, we

are more likely to see very large, high dimensional nonhomogeneous data sets collected

opportunistically. We outline a comparison between traditional statistics and what we call

computational statistics. We give several examples a computational statistics and complete

our thesis with a discussion of the implications for graduate curricula.

1. Introduction

The spectacular growth in the field of

computing science is obvious to all. In-

*Correspondence

deed, the most obvious manifestations,

the ubiquitous microcomputer, is in some

ways perhaps the least significant aspect

of this revolution. The new pipeline and

parallel architectures including systolic

arrays and hypercubes, the emergence of

COMPUTATIONAL STATISTICS: A NEW AGENDA 311

artificial intelligence, the cheap availabil-

ity of RAM and color graphics, the impact

of high resolution graphics, the potential

for optical, biological and chemical com-

puting machines and the pressing need for

software/language models for parallel

computing are all aspects of the compu-

tation revolution which figure promi-

nently in the other sciences.

While not as obvious to the casual ob-

server, the fields of statistics and proba-

bility have experienced equally spectac-

ular technical achievements including

weak convergence theory, the almost sure

invariance principle, exploratory data

analysis, nonlinear time series methods,

bootstrapping, semiparametric methods,

percolation theory, simulated annealing

and the like principally within the last dec-

ade. The computing and statistical tech-

nologies both figure prominently in the

manipulation and analysis of data and in-

formation. It is natural then to consider

the linkage between these two discipline

areas. The interface between these two

discipline areas has been labeled by the

phrase, “‘statistical computing,” and more

recently, ““computational statistics.”’ We

should like to distinguish between the two

and, indeed, argue that the latter embod-

ies a rather significantly different ap-

proach to statistical inference.

In thinking carefully about the rela-

tionship between computing science and

statistical science it is possible to describe

a large number of linkages. Two that come

immediately to mind are the stochastic

description of data flow through a com-

puter and the characterization of uncer-

tainty in expert systems. In the former

case, we can view a computing architec-

ture, particularly a parallel or distributed

architecture as a network with messages

being passed from node to node. This is

essentially a queueing network and the

characterization of the distribution state

of the network becomes a problem in sto-

chastic model building and estimation. In

the latter example, a rule-based expert

system is invariably characterized by im-

precision in the specification of the basic

predicates derived from the expert or ex-

perts. This may be because either the rule

is a “rule-of-thumb” and hence inherently

imprecise or because the rule is a not yet

fully formulated and verified inference

and hence exogenously stochastic. The as-

signment of probabilities (or such alter-

natives to probabilities as belief functions

or fuzzy set functions) in a useful way is

another application of statistical meth-

odologies to computing science. In both

of these examples statistical methodology

is employed in the development of com-

puting science. Both of these examples

might legitimately be called statistical

computing since the focus is on computing

with statistics as an adjectival modifier.

Traditionally, of course, this is not at

all what statistical computing means. Sta-

tistics is fundamentally an applied sci-

ence, hence, a computationally oriented

science. A statistical theory is useless

without a suitable algorithm to go with it.

Statistical computing has traditionally

meant the conversion of statistical algo-

rithms into a reasonably friendly com-

puter code. This enterprise became fea-

sible with the development of the IBM

360 series in the early 1960s and the slightly

later development of the DEC Vax series

of computers. Of course, the trend has

accelerated with the ubiquitous PC. Pack-

ages such as SAS, BMDP, Minitab, SPSS

and the like represent a very high evo-

lution in statistical computing. When we

use the phrase, “computational statis-

tics,” we have in mind a rather stronger

focus on the exploitation of computing in

the creation of new statistical methodol-

ogy. We shall give some explicit examples

shortly.

2. Statistics as an Information

Technology

Statistics is fundamentally about the

transformation of raw data into useful in-

formation. As such statistics is a funda-

mental information technology. It is,

312

therefore, appropriate to see statistical

science as intimately related not only to

computing science, but also communica-

tion technology, electrical engineering

and systems engineering as part of the

spectrum of modern information proces-

sing and handling technologies. Statistics

is perhaps the oldest and most theoreti-

cally well developed of these information

technologies.

It is thus important to understand how

the changing face of these technologies

affect statistics and, more importantly,

how they offer new opportunity for the

development of statistical methodologies.

In particular, it is important to understand

how the computer revolution is affecting

the accumulation of data. Electronic in-

strumentation implies an ability to ac-

quire a large amount of high dimensional

data very rapidly. While such capabilities

have existed for some time, the emerg-

ence of cheap RAM in the 1980’s has given

us the ability to store and access that data

in an active computer memory. Satellite-

based remote sensing, weather and pol-

lution monitoring, data base transactions,

computer controlled industrial automa-

tion and computer controlled laboratory

instrumentation as well as computer sim-

ulations are all sources of such complex

data sets. We contend that this new class

of data represents a challenge for statis-

ticians which is substantially different in

kind. In many ways the characteristics of

automated data are different from tradi-

tional data. Automated data is generally

untouched by human brain. While there

are fewer transcription errors, there are

also fewer checks for reasonableness.

There are likewise different economic

considerations. In many traditional data

collection regimes, the cost per item of

data is expensive. In the automated mode,

set-up costs are expensive, but once ac-

complished there is low incremental cost

for taking additional data. Thus it is often

easy to replicate, hence, increased sample

size, and it is easy to take additional mea-

surements on each sample item (vari-

ables), hence an increase in dimensional-

EDWARD J. WEGMAN

ity. As an adjunct, it is worth pointing out

that when an individual datum is expen-

sive, we collect no more than absolutely

needed to complete the inference. How-

ever, when the marginal cost of additional

data is low, we tend to collect much more

both in sample size and dimension moti-

vated by the belief that it might be useful

for some not-yet-precisely-specified pur-

pose. Thus, the computing revolution

often implies that there are less sharply fo-

cused reasons for collecting data.

The majority of existing methodology

is focused on the univariate, IID random

variable model. Even in the circumstance

that a multivariate model is entertained,

it is usually assumed to be multivariate

normal. We contend, in addition, that

while arbitrary sample size is frequently

assumed, the truth of the matter is that

these techniques implicity assume small

to moderate sample sizes. For example,

a regression problem with 5 design vari-

ables and 1000 observations would rep-

resent no problem for traditional tech-

niques. By contrast, a regression problem

with 40,000 design variables and 8 million

observations would. The reason is clear.

In the former case the emphasis is on sta-

tistical efficiency which is the operational

goal for most current statistical technol-

ogy. However, with massive replications

the need for statistical efficiency is much

less pervasive. Indeed, we may find it de-

sireable to exchange highly efficient,

parametric procedures for less efficient,

but more robust, nonparametric proce-

dures to guard against violations of (pos-

sibly untestable) model assumptions. The

emphasis on parsimony in many contem-

porary books and papers is a further re-

flection of the mind-set that implicitly fo-

cuses on small to moderate sample sizes

since few parameters do not necessarily

make sense in the context of very large

sample sizes. Finally, we note that the

very fact of largeness in sample size im-

plies that it is unlikely we would see IID

homogeneity.

Thus, the computer revolution implies

a revolution in the type of data we are

COMPUTATIONAL STATISTICS: A NEW AGENDA 313

Table 1.—Comparison of Traditional Statistics

Traditional Statistics

Small to Moderate Sample Size

IID Data Sets

One or Low Dimensional

Manually Computational

Mathematically Tractable

Well Focused Questions

Strong Unverifiable Assumptions relationships

(linearity, additivity) error structures

(normality)

Statistical Inference

Predominantly Closed Form Algorithms

Statistical Optimality

able to accumulate, i.e. large, high-di-

mensional nonhomogeneous data sets.

More importantly, however, the richness

of these new data structures suggest that

we are more demanding of the data. Ina

simple univariate IID setting we primarily

are concerned with variability of a single

random variable and questions related to

this variability. In a more complex data

set, however, it is natural to ask more

involved questions while simultaneously

having less a priori insight into the struc-

ture of the data. When more variables are

available, we would certainly ask about

the functional relationship among them.

We have used the phrase, structural in-

ference, for methodologies aimed at de-

scribing such relationships, deliberately

contrasting this phrase with the phrase,

statistical inference, which has tradition-

ally been about determining variability

(i.e. probability distributions). With a

more complex structure, we are open to

ask more of the data than just simple de-

cisions. We may want to ask forecasting

questions, e.g. about weather, economic

projections, medical diagnosis, university

admissions and tax audits, or questions

about automated pattern recognition, e.g.

printed or hand-written characters, speech

recognition and robotic vision, or ques-

tions about system optimization, e.g.,

process and quality control, drug ef-

fectiveness, chemical yields and physical

design.

The contrast between traditional statis-

Computational Statistics

Large to Very Large Sample size

Nonhomogeneous Data Sets

High Dimensional

Computationally Intensive

Numerically Tractable

Imprecise Questions

Weak or No Assumptions relationships

(nonlinearity) error structures

(distribution free)

Structural Inference

Iterative Algorithms Possible

Statistical Robustness

tics and the new statistics is marked and

strong. We summarize in Table 1. We think

that the implications of the computer re-

volution on statistics are sufficient to war-

rant new terminology, specifically com-

putational statistics. This terminology not

only provides the linkage of statistical sci-

ence with computing science, but also puts

the focus on statistics rather than on com-

puting.

3. Some Examples

In this section we should like to illus-

trate these notions of computational sta-

tistics with three examples of approaches

to data that flow from thinking about sta-

tistics in light of contemporary compu-

tation. It goes without saying that such

techniques as bootstrapping, cross vali-

dation and high interaction graphics are

clear well-known examples of what we call

computational statistics. We wish to de-

scribe some less well known ideas: 1. high

dimensional graphical representation, 2.

functional inference, and 3. data set map-

ping.

3.1 Example: High Dimensional

Graphical Representation

Large, high dimensional data sets often

have a complex, non-linear structure. For

314 EDWARD J.

this reason, exploratory analysis is even

more important for such data sets than it

is in more traditional well-structured data

sets. Visualization of data structures in

higher dimensions is, however, even more

difficult than in low dimensional cases

since geometric representation of data

with cartesian coordinates is impossible in

dimensions higher than three.

One interesting approach, the parallel

coordinate representation, has been pur-

sued by Inselberg (1985)? and Wegman

(1986).° A point in n-dimensional space

is represented in Figure 3.1. A parallel

coordinate representation consists of n

parallel axes, each axis meant to represent

one dimension of the n-dimensional vec-

tor. A point in n-space is plotted by mark-

ing x, on the 7th axis and joining x, through

x, by a broken line segment. Thus a point

WEGMAN

in Euclidean n-space is mapped into a

broken line segment in the parallel rep-

resentation. Figure 3.1 represents two

points coinciding in the 4th coordinate.

Figure 3.2 represents a more complex but

artificially contrived data set. While we

will not try to develop intuition for the

parallel coordinate representation in this

paper, our experience has been that with

a very modest amount of training, people

rapidly become adept at interpreting these

diagrams. Figure 3.2 has several features

of interest including a normal marginal

density in dimension one, a negative chi-

square of dimension two, a three dimen-

sional cluster in dimensions 3 to 5, a five

dimensional mode as well as linear and

nonlinear functional relationships.

The mathematical structure of parallel

coordinate diagrams turns out to be ex-

Fig. 3.1. Two points in n-dimensional space plotted in parallel coordinates. These points agree in the

4th coordinate.

COMPUTATIONAL STATISTICS: A NEW AGENDA

\ gs

- Vv >

315

Fig. 3.2. Illustration of five dimensional data set represented in parallel coordinates.

tremely interesting. Focusing on the first

two dimensions of Figure 3.1 for a mo-

ment, one observes that a point in ordi-

nary cartesian coordinates maps into a line

(segment) in parallel coordinates. This

point-line mapping is suggestive of the

duality found in projective geometry. In-

deed, projective geometry plays a key role

in the development of the parallel coor-

dinate representation. If both the carte-

sian plane and two dimensional parallel

coordinate plane are augmented with the

appropriate ideal points so that they are

both projective planes, the transforma-

tion from the cartesian coordinates to the

parallel coordinates becomes a projective

transformation or projectivity. A projec-

tivity can be represented as a matrix trans-

formation on the so-called natural ho-

mogeneous coordinates. The particular

cartesian-to-parallel-coordinates transfor-

mation induces a number of interesting

dualities.

Not only do points map into lines, but

lines map into points as well. Conics map

into conics, rotations map into transla-

tions, translations into rotations and in-

terestingly enough points of inflection map

into cusps and vice versa. There are sev-

eral interesting implications of these facts

beyond just the graphic display value of

parallel coordinates. For one thing, since

316 EDWARD J.

translations are relatively easy to compute

while rotations are relatively harder, there

is a computational advantage to a parallel

coodinate representation when heavy use

of rotations is expected. It is also clear

that points of inflection are relatively dif-

ficult to detect while cusps are relatively

easy. We believe that the parallel coor-

dinate representation will be an advan-

tageous one for computational geometry

as well as statistical data analysis.

The parallel coordinate diagram serves

as a hyperdimensional analogue to the

traditional scatter diagram and thus may

be used as a fundamental tool for high

dimensional exploratory data analysis.

Several notions have already been ex-

plored, but these are certainly prelimi-

nary. It is known, for example, that the

number of crossings of line segments be-

tween adjacent pairs of parallel axes is

invariant with scale transformation. Such

invariance suggests that features of the

parallel coordinate axes depend only on

ranks and thus may hve robustness fea-

tures common to rank-based statistical

methods. Yet another question of signif-

icant interest relates to dimensionality

reduction. Is it possible, for example, to

find a simple graphical algorithm for di-

mensionality reduction based on rota-

tions, translations and nonlinear scaling?

If such a procedure were available either

automatically or with heuristic guidance,

it would be a fundamental tool in model

building.

3.2 Example: Functional Inference

Our fundamental premise is that we are

interested in the structural relationship

among a set of random variates. We for-

mulate this as follows. Given the random

variables X,, X,,... ,X,, which are func-

tionally related byanequation, f(X;,...,

X,) = €, determine f. This is a general-

ization of the problem of finding the pre-

diction equation in the standard regres-

sion problem, Y — xf = e, but in a

nonparametric, nonlinear setting. We

suggest the following notion. Let M =

WEGMAN

{6s sin.itt ye 5 Mp > E IX, ». hee ee

in general is an algebraic variety and un-

der reasonable regularity conditions a

manifold. Thus, there is a fundamental

equivalency between estimating the geo-

metric manifold M and estimating the

function f.

By turning our attention to the mani-

fold M, we make the problem a geometric

One, one whose structure is easier to vis-

ualize using computer graphics. For this

reason we believe there is an intimate

connection between the structural esti-

mation problem and the visualization of

high dimensional manifolds. While graph-

ical methods for looking at point clouds

have proven stimulating to the imagina-

tion, it is extremely difficult to understand

true hyperdimensional structure, partic-

ularly when rotating about an invisible

axis. We believe that a solid structure as

opposed to a point cloud would provide

the visual continuity to alleviate much of

this problem. This solid structure is what

we identify with the manifold M. To get

a handle on the procedure for estimating

a manifold we note a d-ridge is the extre-

mal d-dimensional feature on a hyper-

space structure of dimension greater than

d. The 0-ridge corresponds to the usual

mode. For some d, we contend that a rea-

sonable estimate of M is the d-ridge of

the n-dimensional density function of (X;,

..., X,). This in effect is estimating the

d-dimensional summary manifold with a

mode-like estimator. In essence what we

are suggesting to skeletonize hyperdi-

mensional structures. This type of process

has been done in the image processing

context with good computational effi-

ciency.

The inference technique then is to es-

timate M nonparametrically. This reduces

the scatter diagram to a geometrically de-

scribed hyperdimensional solid. This can

then be explored geometrically using

computer graphics. Features can then be

parametrized and a composite parametric

model constructed. The inference can be

completed by a confirmatory analysis on

the (perhaps nonlinear) parametric model.

COMPUTATIONAL STATISTICS: A NEW AGENDA 317

Techniques presently in use often assume

linearity or special forms of nonlinearity,

e.g. polynomial or spline fits, and often

assume additivity a low dimensional sub-

components, e.g. projection pursuit. We

would not like to take this perspective a

priori. While this methodology may con-

sequently seem complex, the premise is

that geometric-based structural analysis

will offer tools superior to traditional

purely analytic methods for building high

dimensional functional models.

The key to this development is to ap-

preciate the role of ridges in describing

relationships between random variables.

A simple two-dimensional example is il-

lustrated in Figure 3.3. Note that the con-

tours represent the density and the 1-ridge

represents the functional relationship be-

tween x and y in a traditional linear

regression. Since densities are key, a fast,

efficient multidimensional density esti-

mation technique is important.

The slowness of the traditional kernel

estimators in a high dimensional setting

arises from the fact that they are essen-

tially point estimators. That is to say, to

compute f(x) one needs to do smoothing

in a neighborhood of x. For a satisfying

visual representation, the x’s must be cho-

sen reasonably dense. Moreover, tradi-

tional kernels are frequently nonlinear

functions and thus the computation in-

volves the repeated evaluation of a non-

linear function at each of the observations

of a potentially large data set on a dense

Fig. 3.3. Two dimensional scatter diagram with the contours of the two dimensional density function

and the 1-ridge summary line.

318

set of points in the domain. Furthermore,

as dimension increases, exponentially

more domain points are required to main-

tain a constant number of points per unit

hypervolume. Traditional kernel estima-

tors become essentially useless for even

relatively low dimensions.

The traditional histogram provides an

alternative strategy. The histogram is a

two-step procedure. The first step is a tes-

selation of the line. The second step is an

assignment of each observation to a tile

of that tesselation. The computation of

the actual density estimator amounts to a

simple rescaling of tile- (cell-) count. The

histogram is a global estimator since the

function is constant on the tiles which are

finite in number and, indeed, relatively

few in number compared with the dense-

ness of points required for the kernel es-

timator. The traditional histogram, of

course, operates with fixed equally spaced

uniform tiles. There is no reason why the

tiles must be fixed or uniform. Wegman

(1975)’ suggests a data-dependent tesse-

lation in the one dimensional setting and

shows that, if the number of tiles is al-

lowed to grow at an appropriate rate with

the increase of sample size, then asymp-

totic consistency can be achieved.

The ingenious papers by Scott (1985,

1986)°° introduces the notion of the av-

erage shifted histogram, ASH. Scott rec-

Ognizes the computational speed of a

global estimator such as the histogram.

His algorithm computes the histogram for

a variety of tesselations and then averages

these together to obtain smoothing proper-

ties. In this paper we are suggesting a

combination of these two ideas. We pro-

pose a data-driven tesselation of the fol-

lowing sort. Take an a% (10%) subsam-

ple of the sample. Use these points to

form a Dirichlet tesselation of n-space. A

two dimensional example is given in Fig-

ure 3.4. The tiles of the Dirichlet tesse-

lation form the data-dependent convex

regions upon which to base the density

estimator. One pass through the data will

be sufficient to classify each point ac-

cording to tile and thence a simple res-

EDWARD J.

WEGMAN

caling to compute the estimator. Re-

peated subsampling will yield additional

estimators which can then be averaged in

the manner of Scott’s ASH. The details

of this algorithm need to are being ex-

plored, but the following conjectures are

made. Asymptotic properties similar to

those found in Wegman (1975)’ hold.

Maximum likelihood and nearest neigh-

bor properties will hold. Computational

efficiency will be substantially better than

with kernal methods. Because of the re-

peated sampling, bootstrap-type behavior

will hold.

It should be clear that the notions we

are suggesting rely heavily on the gener-

alization of present geometric algorithms

to higher dimensional space. The Diri-

chlet tesselation, for example, has useful

algorithms in 2 and 3 dimensions (see

Bowyer, 1981, Green and Gibson, 1978).'?

but the analogues in higher dimensions

are poorly developed (see Preparata and

Shamos, 1986).* Thus a fundamental ex-

ploration of algorithms for these tessela-

tions in hyperspace must still be done.

Interestingly enough, the computation of

tasselations in hyperspace is closely re-

lated to the computation of convex hulls

(again see Preparata and Shamos, 1986,

p. 246).*

The construction of the n-dimensional

Dirichlet tesselation (Voronoi diagram) is

a key element of the density estimation

technique we suggest. A related issue is

the assignment problem, that is, given the

tiles, what is the best algorithm for de-

termining to which of the tiles a given

observation belongs. In part the 2-dimen-

sional Voronoi diagrams were con-

structed to answer nearest-neighbor-type

questions. That is, given n points, what is

the best algorithm (minimum compute

time) for finding the nearest neighbor. In

general, the answer is known to be O(nd)

where d is the dimension of the space.

There is some reasonable expectation

that, since the construction of the tesse-

lation and the assignment problem are

closely linked, there is an efficient one-

step algorithm for sorting the observa-

COMPUTATIONAL STATISTICS: A NEW AGENDA

319

Fig. 3.4. Dirichlet tesselation (dashed lines) and Delauney triangulation (solid lines) of the plane

based on 13 points.

tions in convex regions about certain

nearest neighbors. If this could be done

in linear, near linear or even polynomial

time, the density estimation technique we

are suggesting may be computationally

feasible for relatively high-dimensional

cases. In any case, the sorting, clustering

and classification results which form the

core of computational geometry also form

the core of this approach to higher di-

mensional data structures.

We hope that this example makes clear

the mathematical complexity inherent

in computational statistics. It is our view

that there is an extremely important

role for mathematical statistics under

the general rubric of computational

Statistics.

3.3 Example: Data Set Mapping

A traditional way of thinking about the

model building process is that we begin

with a fixed data set and apply a number

of exploratory procedures to it in search

of structure within the data set. The data

set is regarded as fixed and the analysis

procedures as variable. Of course, the

model is iteratively refined by checking

the residual structure until a suitable

model reduces the residuals to a unstruc-

tured set of “random numbers.” We sug-

gest an alternative way of thinking.

Normal Mode of Analysis:

Data Set Fixed < Try Different

Techniques on It

320

Alternative Mode of Analysis:

Techniques Set Fixed < Try Differ-

ent Data on It

We have in mind the following. With the

cost or availability of computational re-

sources essentially not a significant con-

sideration in the analysis procedure (i.e.,

they are essentially a free good), we can

afford to standardize on say a dozen or

‘more techniques which are always com-

puted no matter what data are presented.

Others, of course, would still be option-

ally available. Such standard techniques

might include for example standard de-

scriptive statistics, smoothers, spectral es-

timators, probability density estimators

and graphical displays including 3-D pro-

jections, scatter diagram matrices, par-

allel coordinate plots, grand tours, O-O

plots, variable aspect ratio plots and so

on. Each of these might be implemented

on a different node of a parallel comput-

ing device and displayed in a window of

a high resolution graphics workstation,

analogous to having a set of papers on our

desk through which we might shuffle at

will, the difference being that each sheet

of paper would, in effect, contain a dy-

namic, possibly multidimensional display

with which the analyst might interact. We

have in mind viewing each of these data

representations as an attribute of the data

set (object orientation) so that if we mod-

ify the data set representation in one win-

dow, the fundamental data set is modified

and consequently its representations in

all of the windows are modified simulta-

neously.

With the set of techniques fixed, a data

analysis proceeds through an iterative

mapping of the data set, i.e. the data set

is iteratively re-expressed. This is done

by a series of techniques. A discriminant

procedure or a graphical brushing pro-

cedure allows us to transform one data

set into a number of more homogeneous

data subsets. Data transformations, re-

scaling either linear or nonlinear, clus-

tering, removing outliers, transforming to

ranks, bootstrapping, spline fitting and

EDWARD J.

WEGMAN

model building are all techniques for

mapping an old data set into one or more

new ones. Notice that we treat model

building as a simple data map. It is our

perspective that a model fit is just a trans-

formation of one data set to another (spe-

cifically the residuals) similar to any of

the others mentioned.

Two points of interest can be made.

First, the analysis of a data set can be

viewed as the development of a data tree

structure—each node is a data set and

each edge is a transformation or re-

expression of that data set to a new data

set. The data tree structure preserves the

record of the data analysis, indeed, the

data tree is the data analysis. At the bot-

tom of the data tree presumably we will

have data sets with no remaining structure

for, if not, then another iteration of our

analysis and another edge in the data tree

are required. The second point to be made

is that thinking in the terms just described

helps clarify our thinking by conceptually

separating the representational methods

(e.g. graphics, desciptive statistics) from

the re-expression methods (transforma-

tions, brushing, outlier removal, model

building). These are really two separate

functions of our statistical methodology

which are not commonly distinguished,

but when distinguished, aid in clearer

thinking. We particularly think it is help-

ful to understand, for example, that a

square-root data transformation and a

ARMA-model fitting are really quite

similar operations each resulting in a new

data set save that in the latter case we usu-

ally call the new data set the set of resid-

uals. Indeed, when the data analysis is

completely laid out as a data tree, the

full model is really accumulated by start-

ing at the root node (original data set) and

following the edges all the way to the end-

ing node (unstructure residual data set).

4. Curriculum Implications

First of all, it is important to recognize

that operating from the perspective of

COMPUTATIONAL STATISTICS: A NEW AGENDA

computational statistics does not imply

that traditional statistical methodologies

are obsolete. While some automated data

sets will have the characteristics described

earlier, many will not. In addition there

will, no doubt, continue to be many care-

fully designed experiments in which each

data point is costly to acquire, and, hence,

traditional methods will continue to be

used. Nowhere is this probably more true

than in the case of bio-medical clinical

trials. We believe there are certain shifts

in emphasis, however, that may be useful

to recognize.

In terms of mathematical preparation,

real and complex analysis and measure

theory are frequently emphasized as ele-

ments of a graduate curriculum. These are

tied to probability theory and the more-

or-less standard IID parametric assump-

tions. To the extent that the questions we

ask of data are less structured, much of

the need for the standard frameworks and

probability models is lessened. In their

place we will tend to have a more geo-

metric analysis and a more function-ori-

ented, nonparametric framework. The

first and second examples were deliber-

ately chosen to illustrate elements of pro-

jective geometry, differential geometry

and computational geometry. In addition,

there ts a strong element of nonpara-

metric functional inference in example

3.2 suggesting a heavier reliance on func-

tional analysis. We believe therefore that

functional analysis and geometric anal-

321

ysis should become part of the mathe-

matical precursors to a statistics curricu-

lum.

That computation will play a role is ob-

vious, exactly what form it will take is not

so obvious. Certain elements of comput-

ing science would appear to be candi-

dates. Computational literacy means

more than FORTRAN or C programming

or familiarity with the statistical pack-

ages. Clearly such concepts as object-ori-

ented programming, parallel architec-

tures, computer graphics and numerical

methods will play a significant role in

future curricula.

In terms of the statistical core material

itself, I believe the obsession with the

parametric framework (be it classical or

Bayesian) must end. It is important to

recognize that we are often dealing with

opportunistically collected data and that

classical formulations are too rigid. More-

over, as indicated earlier, we are asking

more of our data than simply distribu-

tional questions. Indeed the more inter-

esting questions are the structural ques-

tions (i.e., in the face of uncertainty, how

are two or more random variables related

to each other?). Thus, it would seem that

there should be some de-emphasis of tra-

ditional mathematical statistics (testing

and estimation) and more emphasis on

exploratory and structural inference. A

contrast between a traditional first year

curriculum and a revised curriculum is

laid out in Figure 4.1.

Ist Mathematical Applied Complex Measure

sem Statistics I Variables Theory

2nd Mathematical Design of pplied Probability

sem Statistics I] Experiments Statistics Theory

Fig. 4.1.a. A straw-man traditional first year curriculum for a Ph.D. Program in Statistics. Linkages

between courses are indicated by directed edges.

322

EDWARD J. WEGMAN

Ist Statistical Measure and Geometric Analytic and

sem Inference I Probability Methods Numerical

in Statistics Methods

el cel es

ee oe

2nd Statistical Functional Data Analysis Structural

sem Inference II Analysis for and Graphics Inference

Statistics

Fig. 4.1.6. A straw-man first year graduate curriculum in Computational Statistics. Additional course

work should include data structures and programming, and computing architectures

Acknowledgements

This paper has benefitted from several

conversations with Jerry Friedman. I

would like to thank him for not only these

discussions, but also his enthusiasm for

the computational statistics. This research

was supported by the Air Force Office of

Scientific Research under Grant AFOSR-

87-0179 and by the Army Research Office

under Grant DAAL03-87-G-0070.

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selations,’ Computer J. 24, 164-166.

2. Green, P. J. and Gibson, R. (1978), “Computing

Dirichlet Tesselations in the Plane,” Computer

J. 21, 168-173.

Inselberg, A. (1985), ‘““The Plane with Parallel

Coordinates,” The Visual Computer 1, 69-91.

Preparata, F. P. and Shamos, M. L. (1986), Com-

putational Geometry: An Introduction, New

York: Springer-Verlag, Inc.

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grams: Effective Nonparametric Density Esti-

mators in Several Dimensions,” Ann. Statist. 13,

1024-1040.

. Scott, D. W. (1986), ““Data Analysis in 3 and 4

dimensions with Nonparametric Density Esti-

mation,” in Statistical Image Processing and

Graphics, (Wegman, E. and DePriest, D. eds.)

New York: Marcel Dekker, Inc.

. Wegman, E. J. (1975), ““Maximum Likelihood

Estimation of a Probability Density, Sankhya ( *)

37, 211-224.

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Analysis Using Parallel Coordinates,’ Technical

Report 1, Center for Computational Statistics and

Probability, George Mason University, Fair-

fax, VA, July 1986.

Journal of the Washington Academy of Sciences,

Volume 78, Number 4, Pages 323-332, December 1988

Statistical Analysis of Experiments

to Measure Ignition of Cigarettes

Keith R. Eberhardt

Statistical Engineering Division

Center for Computing and Applied Mathematics

National Institute of Standards and Technology

Administration Building, Room A337

Gaithersburg, Maryland 20899

ABSTRACT

Under the Cigarette Safety Act of 1984, NIST was given the task of studying several

types of commercial and experimental cigarettes to determine their relative propensities

to ignite soft furnishings. The analysis of the data came under close scrutiny by the

Technical Study Group appointed to oversee the research. In one experiment where the

usual chi-squared test could not be readiliy justified, an extension of Fisher’s Exact Test

to 2 xX 12 contingency tables was adopted. In another experiment, a modification of the

angular transformation for count data was used along with normal probability plots of

the effects to analyze a 2° factorial experiment.

Key Words: angular transformation, chi-squared test, contingency table, factorial exper-

iment, Fisher’s exact test, normal probability plot, statistical analysis

1. Introduction

This report describes some statistical

data analysis aspects of two related re-

search projects'” concerned with the pro-

pensity of commercial and experimental

cigarettes to ignite upholstered furniture.

These projects were conducted in the

Center for Fire Research at the National

Institute of Standards and Technology

(NIST, formerly the National Bureau of

Standards) during 1986 and 1987.

Cigarette ignition of furniture is by far

the leading cause of fire deaths and in-

juries in the United States. While the ig-

nition resistance of manufactured furnish-

323

ings has been greatly improved over the

last decade, fire casualties could be fur-

ther reduced if cigarettes were manufac-

tured to cause fewer ignitions. In response

to this situation, Public Law 98-567, the

“Cigarette Safety Act of 1984,” estab-

lished a Technical Study Group on Cig-

arette and Little Cigar Fire Safety com-

posed of representatives of the tobacco

industry, the furniture industry, the fire

service, the public health advocacy, and

concerned Federal agencies. As part of

their charge to design and oversee a re-

search program on cigarette ignition pro-

pensity, the Technical Study Group en-

gaged NIST to conduct the laboratory

experiments described here.

324 KEITH R. EBERHARDT

The following two sections describe ex-

periments designed to compare the per-

formance of various types of commercial

and experimental cigarettes under a va-

riety of test conditions. To measure the

ignition propensity of cigarettes, test

mockups were constructed to simulate

conditions corresponding to what hap-

pens when a lighted cigarette is dropped

on an upholstered chair. The mockups

were constructed using a variety of up-

holstery fabrics and padding types which

were chosen to represent a range of sub-

strates (i.e. fabric and padding combi-

nations) that can ignite with commercial

cigarettes. For each test condition, four

or five cigarettes were lighted and placed

on mockups, and the number of cigarettes

that ignited the substrate was recorded.

Thus, the basic data in these experiments

consist of counts of the number of igni-

tions in a given number of trials. A com-

mon probability model, the binomial dis-

tribution, applies to the data for both cases

to be described, but different statistical

methods were required due to differences

in the questions asked and in the exper-

iment designs used.

2. Differences among

Commercial Cigarettes

An important part of the first NIST

project for the Technical Study Group was

an experiment to determine whether there

are measurable differences in the ignition

propensities of different types of com-

mercial cigarettes. To study this question,

a test protocol was developed under which

12 types of commercial cigarettes were

tested on 18 different mockup configu-

rations. The experiment results are dis-

played in Table 1..The 18 mockup con-

figurations, which are described fully in

[1], differ in type ofsubstrate used, whether

or not the cigarette was placed in a crev-

ice, and whether or not the cigarette un-

der test was covered with a piece of cotton

sheeting.

Inspection of Table 1 reveals that many

of the substrates were either too ignition

prone (columns 1-3), or too resistant

(columns 12-18), to show any differences

among the cigarettes tested. This was dis-

appointing to the experimenters because

the fabric and padding combinations used

for the mockups had been pretested and

were chosen carefully to represent cases

where differences could occur. However,

the pretest samples came from different

lots of material than the larger quantities

which were procured for construction of

the mockups, and although both were

nominally the same, their behavior in cig-

arette ignition tests was quite different.

When the test data of Table 1 were pre-

sented to the Technical Study Group, a

wide variety of statistical analyses—with

contradictory intepretations—were pro-

posed. The reader can readily imagine how

the vested interests of the organizations

represented on the Technical Study Group

would lead some members to favor anal-

yses with conclusions opposite to those

preferred by other members. When the

collection of competing statistical anal-

yses was presented to this author for his

opinion, it was clear that whatever anal-

ysis he proposed would be carefully, and

perhaps critically, reviewed by at least half

of the members of the Technical Study

Group. Thus careful attention was given

to choosing statistical methods based on

assumptions and mathematical approxi-

mations that would be readily accepted.

Some of the proposed analyses of Table

1 treated pairwise comparisons between

cigarettes, within a given test configura-

tion, as constituting a 2 x 2 contingency

table with four trials for each of two cig-

arettes. The most extreme difference in

such a table has 4 ignitions for one ciga-

rette and 0 for the other. Applying the

chi-squared test to a cigarette pair show-

ing a 4 vs. 0 difference in ignitions yields

a significance level of 0.005, which would

indicate strong evidence of a true differ-

ence. Use of the chi-squared test for this

situation was criticized because the sam-

ple sizes (4 cigarettes of each type tested)

STATISTICAL ANALYSIS OF CIGARETTE IGNITION PROPERTIES

325

Table 1.—Comparison of Ignition Propensities for Commercial Cigarettes: Numbers of Ignitions in

4 Trials

Cigarette

Number?

1-3 4-5 6 7

2 4 3 + 1

7 4 4 1 4

1 4 4 4 4

~ ~ + = 3

12 4 4 4 4

11 4 4 4 4

3 a 4 4 4

5 ~ 4 4 4

9 4 4 “4 4

10 - 4 + 4

8 * - 4 4

6 ~ ~ + 4

TOTAL 48 47 45 44

AHHH HWKWOr CO oo

Test Configuration*

9 10

—

12-18 TOTAL

BRNWNNN WR ONrR

anwNnoo°oq°c”c$”roqodrqoqodnrocqcodqd

pe CS Go) QB CorGe) Gama co

j=) ja (>) (o> (=>) (=>) (a>) >) (>) (a) (=)

*The 18 test configurations represented here are fully described in reference [1].

TThe 12 cigarette types represent 12 different commercial cigarette packings which are distinguished by

name, length, sometimes diameter, whether menthol or non-methol, whether filter or non-filter, and by

package type (e.g. soft pack.)

are too small to justify the approximation

implied by use of chi-squared tables. To

properly accommodate the small sample

sizes, use of Fisher’s Exact Test had also

been suggested. By this criterion, a 4 vs.

0 difference in ignitions corresponds to a

significance level of only p = 0.029 —

still less than the often-used figure of 0.05,

but substantially larger than 0.005. While

a result with p = 0.029 might be consid-

eredstatistically significant were there only

one pair of cigarettes under considera-

tion, the fact that there are 66 possible

pairs among the 12 cigarette types further

diminishes the strength of evidence im-

plied by obtaining one, or a few, p-values

less than 0.05. One commenter pointed

out that one should expect to obtain an

average of 3.3 “‘significant differences” by

chance when the 0.05 level is used for 66

comparisons.

Another proposed analysis was based

on the “TOTAL” column of Table 1. In

this analysis, the chi-squared test was used

to test the global hypothesis that all cig-

arettes have equal probabilities of igni-

tion. The result is x? = 9.7 on 11 degrees

of freedom, a value that does not ap-

proach significance. A fault with this ap-

proach is that the row totals from the table

do not satisfy the conditions required for

validity of the chi-squared test. A prac-

tical indication of the problem can be seen

by noting that the computed value of x?

would change by a large amount if col-

umns 1-3 and 12-18 were not included in

the row totals. Alternately, if a suffi-

ciently large number of “‘flat’’ columns

like 1-3 and 12-18 were appended to the

table, the computed value of x? for the

TOTAL column could be made to ap-

proach zero. [Probabilistically, the situ-

ation can be characterized by noting that

the row totals do not have binomial dis-

tributions, as is assumed by use of x*, even

though the individual entries within the

rows are binomial. The large differences

in ignition behavior across the 18 test con-

figurations imply that the row totals are

distributed like sums of binomial vari-

ables, but with different probabilities of

ignition for each term in the sum. Such a

sum is not binomial. ]

The approach finally adopted for Table

1 performs a separate analysis for each

column (test configuration) of the table.

326

Lewontinand Felsenstein’ have shown that

the chi-squared test for 2 x WN contin-

gency tables is valid when the expected

frequencies exceed 1.0 in all cells. Since

the data for configurations 8 and 9 (only)

satisfy this condition, the chi-squared test

was used to analyze each of these columns

as a2 X 12 contingency table. Configu-

ration 8 shows highly significant differ-

ences between cigarettes (x* = 36.6, p <

0.001) while no significant differences are

indicated for configuration 9 (x? = 12.9,

p = 0.30). These two tests can be com-

bined by adding the respective x* values

to obtain x* = 49.6 on 22 degrees of free-

dom, indicating highly significant differ-

ences for the combined tests (p < 0.001).

What about the remainder of the table?

Clearly, no differences between cigarettes

are indicated for configurations 1—3, where

all cigarettes ignited, or 12-18, where none

ignited. The remaining columns, 4—7, 10

and 11, can be evaluated for significant

differences in the numbers of ignitions by

an exact calculation, analogous to Fisher’s

Exact Test for a2 x 2 contingency table.

This procedure is based on the conditional

probability distribution of the data given

the total number of ignitions,’ and it re-

quires enumeration of essentially all pos-

sible patterns of ignitions and non-igni-

tions that are consistent with the marginal

totals of the observed data. Applying this

exact test to columns like 8 and 9, which

have relatively large numbers of both ig-

nitions and non-ignitions, would have been

a very tedious process. Fortunately the

chi-squared test could be used in those

cases, and it is known that the two pro-

cedures give practically identical results

in situations where use of y? is valid.

Of these remaining configurations, col-

umns 6 (p = 0.003) and 7 (p = 0.011)

show significant differences between the

cigarettes tested. None of the other con-

figurations show differences that ap-

proach statistical signifiance.

Overall, the table shows some signs of

interaction between test configurations

and cigarette types. But to conclude that

these data do not provide evidence that

KEITH R. EBERHARDT

commercial cigarettes differ in ignition

propensity would seem unreasonable.

3. A Factorial Experiment

To identify characteristics of cigarettes

that could lead to a reduction in ignition

propensity, a second experiment was de-

signed using cigarettes of well-charac-

terized composition and construction

supplied by the cigarette industry. The

experimental cigarettes were custom-

made to differ on five design character-

istics, each at two levels: tobacco packing

density (low and high), cigarette circum-

ference (21 mm and 25 mm), paper

permeability (low and high), paper citrate

concentration (0.0 and 0.8%), and to-

bacco type (burley and flue-cured). Small

lots of cigarettes were produced corre-

sponding to each of the 2? = 32 possible

combinations of the five design factors,

and five cigarettes of each type were tested

for ignition propensity on upholstered

furniture mockups, as described above.

Four test configurations were used for the

experiments; these were chosen, based on

the experience gained from testing com-

mercial cigarettes, to be conditions where

differences between cigarettes could be

shown. The data resulting from the tests,

shown in Table 2, constitute a complete

2° factorial experiment for each of the test

configurations.

The standard statistical technique for

analyzing data from a factorial design is

the analysis of variance (ANOVA). How-

ever, the hypothesis tests and estimation

procedures of ANOVA produce valid sta-

tistical inferences only if the data for each

cell of the table (defined by the cigarette

design and test configuration) come from

populations that are at least approxi-

mately normal with equal variances. In

fact, the datain Table 2 are binomial count

data, and thus not well-modelled by equal

variance normal distributions: the binom-

ial distribution is asymmetric and the vari-

ance depends strongly on the mean. To

STATISTICAL ANALYSIS OF CIGARETTE IGNITION PROPERTIES 327

Table 2.—Ignition Propensity Results for Experimental Cigarettes

Number of Ignitions

Cigarette Design* Test Configuration

Packing Permea- Circum- Citrate Tobacco

Density bility ference Conc. Type 1 2 3 =

E IL 21 N B 0 1 0 0

E ie 21 N F 1 3 0 0

E le on C B 0 3 3 0

E IE 21 C F 0 5 1 0

E 1G, 25 N B 3 2 2 0

EE L 25 N K 3 1 0 0

5 ie 25 c B 5 5 = 0

E ily 25 € F 5 3 2 0

E H 21 N B 3 os 0 0

E H 21 N F 4 5 3 0

12) H 21 Cc B 4 5 2 0

E H 21 C FE 4 5 5 0

E H 25 N B 5 3 5 0

E H 25 N IE 5 5 2 0

E H 25 C B 5 5 5 0

1 H 25 C FE 5 5 5 0

N Ie 21 N B 2 5 5 0

N L pA N F 5 5 5 1

N sy 21 C B 3 5 5 0

N L 21 C FE 5 5 5 0

N L 25 N B 5 5 5 3

N L 25 N |e 5 5 5 2

N L 25 € B 5 5 5 3

N 1B, 75) c F 5 3 3 3

N H 21 N B 5 5 5 -

N H 21 N IF 5 5 5 5

N H 21 c B 3 5 5 2

N H 21 6 F 5 5 5 =

N H 25 N B 5 5 5 5

N H 25 N 5 5 5 5 5

N H 25 C B 5 2 5 5

N H 25 (S 18 5 5 5 5

*Design Factors:

Packing Density: E = low (expanded tobacco),

N = high (non-expanded tobacco)

Permeability: L = low, H = high

Circumference: 21 = 21-mm, 25 = 25 mm

Citrate Concentration: N = 0.0%, C = 0.8%

Tobacco Type: B = Burley, F = Flue-cured

7Test configurations are described in reference 2.

address this situation, the basic data were nearly constant variance. The formula for

transformed using the Freeman-Tukey obtaining the transformed response vari-

modification of the commonly used an- able is

gular transformation.’ This transforma- "

tion produces a response variable having Y = (0.5RARCSIN[SQRT(4/6) ]

amore nearly symmetric distribution with + ARCSIN[SORT((X + 1)/6) | },

328 KEITH R. EBERHARDT

Table 3.—Significance Probabilities (in Percent) of Design Factors for Experimental Cigarettes

(Experimental error was estimated from 4- and 5-way interactions.)

Test Configuration*

Design Factors 1 2 3 4

D (Packing Density) 0.05% 0.10% 0.01% 0.01%

P (Permeability) 0.08 0.23 0.69 0.01

R (Circumference) 0.03 85 Del 0.01

C (Citrate Conc.) 25 2.0 0.69 7.6

T (Tobacco Type) 8.9 52 56 7.6

Factor Interactions

D x P W555) 0.23 0.69 0.01

DxR 0.45 85 Pl 0.01

Dix C 43 2.0 0.69 7.6

Dix oT 45 52 56 7.6

Pipa 0.93 52 39 Se)

Pix € 45 6.6 85 DI

PIXE i 85 7.4 2)

RxC 29 85 62 22

Rx T 8.9 328 2.8 22

CxXul 45 52 62 81

*Test configurations are described in reference 2.

0.4

ORS

On? 99%

O 95%

LJ 0.1

(ue

funds

Oo 0

= =f 4

a 95%

-0.2 99%

-0.3

vay

-0.4

-3 -2 -1 0 | 2 5

NORMAL ORDER STATISTIC MEDIANS

Fig. 1. Normal probability plot of estimated effects from a 2° factorial analysis of variance for the

data in Table 2 for test configuration 1. The factors are coded as: 1 = Citrate concentration, 2 = Paper

permeability, 3 = Packing density, 4 = Tobacco type (burley or flue-cured), 5 = Circumference (21

mm vs. 25 mm). Multiple factor labels represent corresponding interaction effects. The indicated 95%

and 99% limits on the plot were computed using the 4- and 5-way interaction terms to estimate

experimental error.

STATISTICAL ANALYSIS OF CIGARETTE IGNITION PROPERTIES 329

99%

bt 95%

(a)

—

a 95%

99%

=0'.2

3 2 aa

0 1 2 3

NORMAL ORDER STATISTIC MEDIANS

Fig. 2. Normal probability plot of estimated effects from a 2° factorial analysis of variance for the

data in Table 2 for test configuration 2. The factors are coded as: 1 = Citrate concentration, 2 = Paper

permeability, 3 = Packing density, 4 = Tobacco type (burley or flue-cured), 5 = Circumference (21

mm vs. 25 mm). Multiple factor labels represent corresponding interaction effects. The indicated 95%

and 99% limits on the plot were computed using the 4- and 5-way interaction terms to estimate

experimental error.

where X denotes the number of ignitions

(out of 5 trials).

After transformation, the data were

analyzed by standard ANOVA methods.°

The results of the ANOVA are summa-

rized numerically in Table 3. While this

summary is adequate to convey the main

conclusions of the analysis, the graphical

summary of the same results given in Fig-

ures 1-4 was much more effective for

communicating with the members of the

Technical Study Group.

Figures 1—4 present normal probability

plots of the estimated factorial effects from

the 2° factorial analysis of variance for the

data of Table 2. Under the null hypothesis

that none of the design factors affects ig-

nition propensity, the estimated effects

would constitute (approximately*) a ran-

dom sample from a normal distribution,

and so the plotted points would be ex-

pected to cluster about a single straight

line on the normal probability plot. The

indicated 95% and 99% limits on Figures

1—4 were computed using the 4- and 5-

way interaction terms in the ANOVA to

estimate experimental error. These limits

correspond, respectively, to 5% and 1%

tests of the hypothesis that the factorial

effects are zero.

In addition to providing an effective

means of presentation, the normal prob-

ability plot analysis has the advantage that

it automatically encourages consideration

**“Approximately” here relates to the degree of

success achieved by the Freeman-Tukey transfor-

mation in achieving approximate normality for the

distribution of the response variable Y. For exactly

normal data, the estimated effects would follow an

exact normal distribution. The figures suggest that

normality was more nearly achieved in some cases

(e.g. Figure 1) than others (e.g. Figure 2.)

330

ESUIMATED EeRE Crs

=3 = =|

KEITH R. EBERHARDT

0 1 2 S

NORMAL ORDER STATISTIC MEDIANS

Fig. 3. Normal probability plot of estimated effects from a 2° factorial analysis of variance for the

data in Table 2 for test configuration 3. The factors are coded as: 1 = Citrate concentration, 2 = Paper

permeability, 3 = Packing density, 4 = Tobacco type (burley or flue-cured), 5 = Circumference (21

mm vs. 25 mm). Multiple factor labels represent corresponding interaction effects. The indicated 95%

and 99% limits on the plot were computed using the 4- and 5-way interaction terms to estimate

experimental error.

of the simultaneous inference aspects of

the analysis.’ This relates to the well-

known phenomenon that if, say, 20 hy-

potheses are simultaneously tested at the

5% significance level, one of the hy-

potheses will be rejected, on the average,

even if all 20 are true. In the present case,

the normal probability plots compare the

magnitudes of 31 estimated factorial ef-

fects. Setting aside the 4- and 5-way in-

teraction effects that were used to esti-

mate experimental error, there are 25 null

hypotheses that could be tested (5 main

effects, 10 two-factor interactions, and 10

three-factor interactions.) Even if none of

the factors or interactions were active (i.e.

all 25 null hypotheses were true), the ex-

pected number of rejections at the 5%

significance level would be 1.25 (5% of

25) simply by chance. However, the prob-

ability plot analysis accounts for this phe-

nomenon by drawing attention to only

those effects that appear as outliers on the

plot, whether or not they lie outside the

95% or 99% bands. For example, in Fig-

ure 4., the 1.x 3), 5,and 31a eS

interaction effects lie very close to the

99% bands, corresponding to p-values

near 1%. However, the fact that those

effects do not appear as outliers on the

normal probability plot indicates that

those p-values should not be interpreted

as strong evidence of active effects.

To summarize the results of this exper-

iment, Figures 1-4 and Table 3 show that

two factors, namely, packing density and

paper permeability, were consistently

highly significant across all four test con-

figurations. Two additional factors, cir-

cumference and citrate concentration,

showed clear significance in two of the

test configurations. The factor for tobacco

STATISTICAL ANALYSIS OF CIGARETTE IGNITION PROPERTIES 331

2°53 <2e

ORM EDs bit Fie s

-3 =/) =

0 1 2 5

NORMAL ORDER STATISTIC MEDIANS

Fig. 4. Normal probability plot of estimated effects from a 2° factorial analysis of variance for the

data in Table 2 for test configuration 4. The factors are coded as: 1 = Citrate concentration, 2 = Paper

permeability, 3 = Packing density, 4 = Tobacco type (burley or flue-cured), 5 = Circumference (21

mm vs. 25 mm). Multiple factor labels represent corresponding interaction effects. The indicated 95%

and 99% limits on the plot were computed using the 4- and S5-way interaction terms to estimate

experimental error.

type (i.e., burley vs. flue-cured) did not

show a significant effect on number of

ignitions in any of the cases.

The interactions among these factors

were frequently significant whenever the

main effects were. Significant interactions

indicate that the magnitude of the effect

on ignition propensity for a given factor

is not constant across the levels of the

interacting factor. For example, on test

configuration number 1, the significant in-

teraction between Packing Density and

Circumference indicates that the effect of

Packing Density on ignition propensity is

different in magnitude for the smaller cir-

cumference cigarettes than for the larger

circumference cigarettes in the experi-

ment. Detailed study of the data suggests

that many of the significant interactions

can be explained by the single fact that

the maximum number of ignitions per test

condition could not exceed five in this ex-

periment, thus limiting the possible mag-

nitudes of the estimated effects.

In practical terms, the relation between

the cigarette design parameters studied

and ignition propensity can be summa-

rized as follows: The most significant fac-

tor was low packing density, achieved in

this case by using expanded, large particle

size tobacco. Low packing density appar-

ently lowers ignitions because the avail-

able fuel per unit length is reduced. An-

other very influential factor is the use of

low permeability paper, which reduces

ventilation to the tobacco column. Ciga-

rettes with a 21 mm circumference showed

evidence of reducing ignitions in three of

the four test configurations. Again, this

may be due to the reduction in fuel (less

tobacco and paper) per unit length. The

effect of citrate, which is added to ciga-

332 KEITH R. EBERHARDT

rette paper to regulate the paper burn rate

and to obtain ash of the desired appear-

ance, did not show a consistent effect on

ignition propensity. And tobacco type

consistently showed no effect on igni-

tions.

4. Acknowledgements

The author is grateful to Ms. Susannah

Schiller and Dr. Richard Gann, of the

National Institute of Standards and Tech-

nology for their careful reading of, and

comments on, this manuscript.

References Cited

1. Krasny, J. F. and Gann, R. G. 1986. Relative

propensity of selected commercial cigarettes to

ignite soft furnishings mockups. NBSIR 86-3421,

[U.S.] National Bureau of Standards.

. Gann, R. G., Harris, R. H., Jr., Krasny, J. F.,

Levine, R. S., Mitler, H. E., and Ohlemiller, T.

J. 1988. The effect of cigarette characteristics

on the ignition of soft furnishings. NBS Techni-

cal Note 1241, [U.S.] National Bureau of Stan-

dards.

. Lewontin, R. C. and Felsenstein, J. 1965. The

robustness of homogeneity tests in 2 x N tables.

Biometrics, 21: 19-33.

. Plackett, R. L. 1981. The Analysis of Categorical

Data, 2nd edition. Macmillan, New York. Sec-

tion 6.3.

. Freeman, M. F., and Tukey, J. W. 1950. Trans-

formations related to the angular and the square

root. Annals of Mathematical Statistics, 21: 607-

611.

. Box, G. E. P., Hunter, W. G., and Hunter, J.

S. 1978. Statistics for Experimenters. John Wiley

and Sons, New York. Chapter 10.

. Daniel, C. 1959. Use of the half-normal plot in

interpreting factorial two-level experiments.

Technometrics 1: 311-341.

Journal of the Washington Academy of Sciences,

Volume 78, Number 4, Pages 333-338, December 1988

Environmental Statistics

N. Phillip Ross and Gilah Langner

ABSTRACT

Centralized environmental statistics are needed to provide credible answers to complex

environmental issues. Environmental hazards arise from multiple sources, transcending

geopolitical boundaries, and challenging our limited understanding of how ecosystems

operate. Meanwhile, environmental data are scattered across a number of federal agencies.

To deal coherently with the complex environmental issues, there must be sustained, ~

planned, long-term data collection and analysis efforts.

Environmental issues are becoming an

increasingly vital concern of our society.

Polls taken early in last year’s presidential

campaign showed that high percentages

of the American population consider the

quality of the environment to be a na-

tional priority. More and more, Ameri-

cans are recognizing the interdependence

of their quality’of life with the quality of

the environment in which they live.

However, if one were to ask a repre-

sentative group of American citizens

whether (and in what ways) the state of

the environment had improved or dete-

riorated in recent years, most of the an-

swers received would likely fall in the

“Don’t Know” category. Common sense

and intuition can no longer be relied on

to provide an accurate indicator of the

quality of any individual environmental

Correspondence should be sent to: Dr. N. Phillip

Ross, Chief, Statistical Policy Branch, Office of Pol-

icy, Planning and Evaluation, PM232, U.S. EPA,

401 M. Street S.W., Washington, D.C. 20460

Dr. Ross is Chief of the Statistical Policy Branch

Office of Policy, Planning and Evaluation, U.S.

EPA, Washington, D.C.

Ms. Langner is President of Stretton Associates,

a Washington-based consulting firm specializing in

policy analysis and communications.

resource, let alone of the state of the en-

vironment as a whole. One cannot step

outside and sniff the air to get an accurate

feel for air quality in major cities; indoors,

one cannot rely on one’s senses to deter-

mine whether a house is contaminated by

radon, a radioactive gas that cannot be

seen, smelled, or tasted.

Nor would the experts do much better

than the layperson in answering the same

question. Many old environmental prob-

lems have been addressed, but new ones

have sprung up to take their place. On

balance, it is hard to determine how well

we are doing in keeping our environment

safe and healthy and whether there has

been a net improvement in recent years.

Need for Centralized

Environmental Statistics

One major reason that it is so difficult

to come up with credible answers is that

we are not collecting and integrating the

type of quality-controlled, scientifically-

rigorous data that are necessary in order

to develop a coherent picture of environ-

mental trends. The Environmental Pro-

333

334

tection Agency (EPA) alone has an in-

formation collection budget of over 120

million hours and spends half a billion

dollars annually on data collection. A va-

riety of other federal agencies are actively

involved in different aspects of environ-

mental data collection as well. However,

within the federal government, there is

no dedicated bureau or agency with re-

sponsibility for the collection, integra-

tion, and analysis of the environmental

data necessary for setting priorities and

determining directions on a national

scale.

Statistical agencies or bureaus are com-

monplaces in almost every major federal

department. Such agencies include: the

Bureau of Economic Analysis and the Bu-

reau of the Census at the Department of

Commerce; the Bureau of Justice Statis-

tics at the Justice Department; the Bureau

of Labor Statistics at the Labor Depart-

ment; the National Center for Education

Statistics in the Department of Educa-

tion; the National Agricultural Statistics

Service and the Economic Research Ser-

vice in the Department of Agriculture;

the Statistics of Income Division of the

Internal Revenue Service; the National

Center for Health Statistics in the De-

partment of Health and Human Services;

the Social Security Administration’s Of-

fice of Research and Statistics; the Energy

Information Administration in the De-

partment of Energy; and the Division of

Housing and Demographic Analysis in the

Department of Housing and Urban De-

velopment.

As Paul Portney pointed out in a recent

article,!

While no one would argue that our cur-

rent measures of population or eco-

nomic activity are exact, it is impossible

to imagine modern government oper-

ating in their absence. Indeed, these

measures drive important federal grant

and entitlement programs; they also

help trigger, and then measure the suc-

cess of, major tax and spending pro-

grams, monetary policies, and even for-

N. PHILLIP ROSS AND GILAH LANGNER

eign policy decisions. . . Simply put, we

have not a single data series for the en-

vironment that goes back as far as even

the most recently established of the ec-

onomic and demographic series. . . nor

one that is subject to the same quality

control, careful measurement proto-

cols, or subsequent thorough analyses.

The absence of an active, centralized

focus for environmental statistics in this

country is felt on an international scale as

well. The United States is one of the few

developed nations that lack a centralized

governmental agency responsible for col-

lecting and integrating environmental data

and for producing a base of quantitative

information to support an annual State of

the Environment Report. The time has

come for environmental statistics to

emerge as the next major focus of federal

statistical data collection.

Defining Environmental Statistics

What do we mean by environmental

statistics? Beyond the simple tabulation

of environmental data, the environmental

statistics process we are speaking of is

much broader. It concerns itself with eval-

uating the state of the biosphere (envi-

ronmental media and the fauna and flora

that inhabit media) and its changes over

time. Environmental statistics thus in-

volves identifying information needs, de-

signing appropriate data collection activ-

ities (such as ambient monitoring and

population surveys), ensuring the quality

of the data, and conducting statistical

analysis and interpretation of data in or-

der to produce meaningful indicators of

the state of the environment.

According to the Statistical Office of

the United Nations, environmental sta-

tistics:

(a) cover natural phenomena, human ac-

tivities that exert impacts on the en-

vironment, and the impacts them-

ENVIRONMENTAL STATISTICS 335

selves on the environment and on

human living conditions;

(b) refer to the media of the natural en-

vironment, 1.e., air, water, land/soil,

and to the man-made environment

which includes housing, working con-

ditions, and other aspects of human

settlements;

areas and statistical sources to facil-

itate integrated socio-economic and

environmental planning and poli-

cies.

In examining the current roster of en-

vironmental issues, we can identify three

primary reasons why an enhanced capa-

bility to produce environmental statistics

will be an indispensable aid to environ-

mental decision-making in the coming

years.

(1) Increased Complexity of

Environmental Problems and

Solutions

Environmental problems of the 1980’s

have taken on a subtlety and complexity

that did not characterize the air and water

pollution problems of previous decades.

To be sure, there is still no lack of acute

emergencies—chemical fires, toxic waste

dumps lacking security, and trucks car-

rying hazardous materials overturning on

the highway. However, many of our most

pressing environmental problems involve

us in new and uncertain terrain.

For example, setting standards for

chemicals is an increasingly complex pro-

cess, involving the assessment of the ef-

fects of long-term exposure to pollutants

at levels in the parts per billion and tril-

lion. There are vastly greater numbers of

chemicals in production than were ever

contemplated when much of our original

environmental legislation was put in place.

It is becoming clear that human activities

are influencing and changing the environ-

ment—the balance of ecological systems;

the availability of resources, the climate,

the ozone levels. As each day goes by we

are confronted with more and more po-

tentially serious problems.

The questions facing environmental de-

cision-makers are: which of these prob-

lems are most important; which ones

should receive attention and resources;

which ones require immediate action and

which can wait; how do we educate and

motivate the population to change its

mode of interacting with the environ-

ment; howdoweconveyinformation about

real health risks, without scaring the pop-

ulation and without encouraging compla-

cency?

As environmental problems become

less visible to our senses, the need arises

for sophisticated approaches to the de-

tection and monitoring of pollutants on

human health and the environment. The

physical and engineering sciences have

rapidly progressed to meet the require-

ment of sophisticated detection and mon-

itoring. However, the data collection and

statistical methods needed to appropri-

ately assess the impacts of newly discov-

ered environmental problems have not

kept pace. The costs of collecting ade-

quate environmental data to determine

health effects and to intelligently manage

natural resources are becoming astro-

nomical. Statistical approaches to data

collection and interpretation are the only

solution.

A major difficulty in looking to the fu-

ture is that we have so little information

available from the past. If we started to-

day to coordinate our environmental data

collection activities across the federal gov-

ernment, it would still be ten or more

years before we could start to examine

trends and to use those trends in the de-

cision process.

Certain sources of environmental data

already exist that have the potential to

provide insights into a number of envi-

ronmental processes. Unfortunately,

these sources often represent “‘encoun-

tered data” that cannot be considered a

random sample from the original popu-

lation.’ A variety of situations can give

rise to encountered data—instances where

336

the only feasible sampling procedure gives

unequal chances to the population units

or where the only data available are his-

torical data sets from diverse sources.

While a great deal of work has been done

on how to use encountered data in the

context of animal sightings and monitor-

ing of marine resources, this work must

now be extended to a broader array of

environmental modeling and monitoring

situations.

Finally, many of the environmental is-

sues now facing us transcend geopolitical

boundaries—acid rain, the greenhouse

effect, sea-level rise, ozone depletion, and

the continued loss of species on the planet,

to name a few. From an international per-

spective, it is time for the United States

to join its Western neighbors in devel-

oping a comprehensive long-term base of

environmental information. Although the

United States has taken the lead in de-

veloping research programs in some of

these areas, we have not yet committed

ourselves to the type of statistically de-

signed monitoring programs that are

needed to support hard decisions on sub-

jects involving national and global envi-

ronmental effects.

(2) Need for Integration

A second compelling reason for giving

more attention to environmental statistics

arises out of a perceptible change in the

prevailing image of the environment.

From viewing the world as a warehouse

of resources available for our benefit, we

are starting to recognize the exhaustible

nature of certain resources, such as oil

and wood, and even certain living species.

What once appeared as “‘infinite”’ is now

clearly finite, and in some cases is quickly

being depleted. There is growing talk of

the interrelationships among organisms

that sustain life, and even of the life-sus-

taining nature of the planet itself.

The logical corollary of such an ap-

proach is the need to develop an inte-

grated view of environmental media. We

can no longer deal separately with each

N. PHILLIP ROSS AND GILAH LANGNER

environmental medium—air, water, and

soil—and ignore the ‘‘environmental

merry-go-round” effect of shifting pollu-

tants from one medium to another. En-

vironmental data bases need to reflect this

recognition and allow us to examine and

control for ‘“‘cross-over”’ effects.

Here, part of the problem is that in-

formation and responsibilities for various

segments of the environment are diffused

throughout the Federal Government.

While EPA deals with problems resulting

from pollution of the environmental me-

dia, the stewardship of our environmental

resources is in other hands. Thus, the De-

partment of the Interior maintains pri-

mary responsibility for public lands, min-

erals, national parks, and endangered

species; the Department of Agriculture

handles forestry, soil, and conservation;

and the Department of Commerce is in-

volved in oceanic and atmospheric mon-

itoring and research.

As a result, environmental media are

very often addressed separately from the

environmental resources they support.

There remains a serious need for high

quality data suitable for conducting long-

term evaluations of the state of the en-

vironment, considered as a whole. Our

ability to evaluate environmental prog-

ress in the past and set priorities for the

future is compromised by a lack of ap-

propriate, integrated trend indicators.

Within EPA itself, there are limitations

in what we can do because many of the

Agency’s data bases are primarily ori-

ented towards furthering EPA’s compli-

ance monitoring responsibilities. Com-

pliance data do not necessarily lend

themselves to analyses of long-term trends

in the environment. Take, for example,

the issue of waste reduction. Although

EPA maintains numerous data bases with

facility reports on environmental dis-

charges, at the present time there is no

single data base that can be used to mea-

sure waste reduction efforts. Even if it

were possible to “‘cross-walk” from the

facilities in one data base to those in an-

other (which it generally is not), the data

ENVIRONMENTAL STATISTICS 337

bases are designed to measure different

things in different units. Measurement of

concentrations of hazardous chemicals in

waste streams cannot provide useful data

on waste generation.

On a wider ecological level, we need to

collect new environmental data in con-

junction with our environmental and eco-

logical models. Using these models, we

are beginning to develop an understand-

ing of how ecosystems work. We need

better ways of recognizing what consti-

tutes a healthy ecosystem and better mon-

itoring skills that will provide early warn-

ing signs of damage or injury to an

ecosystem.

(3) The Public’s Right and Need

to Know

A third need for improved environ-

mental statistics is the public’s right to

know more about the environment. This

goes well beyond the legislated “right to

know” provisions in Title III of the Su-

perfund Amendments and Reauthoriza-

tion Act of 1986. EPA has a clear re-

sponsibility to make a wide range of

environmental statistics available to the

public both to fulfill the mandate of dem-

ocratic government and to establish the

credibility of its decision-making on en-

vironmental issues.

The public’s need for environmental in-

formation is significant in numerous sec-

tors of society. Accurate and up-to-date

environmental information is important

for public decision-making at the state,

county, and local levels. It is equally im-

portant for eliciting responsible natural

resource management decisions from in-

dustry. Increasingly, we are relying on in-

dustry to voluntarily cooperate in con-

serving environmental resources and to

make farsighted management decisions.

These decisions must be based on an ad-

equate information base. A 1984 report

by the World Wildlife Fund,’ for example,

identifies 11 corporate decisions that re-

quire the use of resource information, in-

cluding strategic direction, market re-

search, resource acquisition, production

capacity, plant siting, plant design, en-

vironmental compliance, production and

materials purchasing, research and de-

velopment, bank lending, and investment

recommendations.

Members of the public also need a re-

liable, quality-controlled, credible source

of environmental information to help them

evaluate the plethora of health risks that

appear almost daily in the news, and to

help them make judicious personal deci-

sions, whether that involves testing ahome

for radon or installing water treatment

devices. A related need is for clear and

usable explanations of environmental

statistics. Given the complexity of our en-

vironment, the advanced scientific tools

being used, and the probability concepts

in which much of our risk information is

couched, the development and publica-

tion of environmental statistics alone will

not necessarily mean that the public

has ‘‘access” to the information. Com-

munication of the significance and con-

text of the information is essential to

satisfying the public’s right and need to

know.

The increasing complexity of environ-

mental problems, the need for integrated

environmental approaches, and the need

to provide more environmental informa-

tion to the public, all point to the impor-

tance of giving serious attention to envi-

ronmental statistics. One way of solving

the problems and deficiencies outlined in

this article may be to create a federal En-

vironmental Statistics Agency or Bureau.

Recent months have seen a renewed in-

terest in this idea, with proposals and rec-

ommendations coming from a variety of

sources. At the Environmental Protection

Agency, a Science Advisory Board panel

chaired by Alvin Alm recently recom-

mended the creation of a new ecological

research institute as part of a renewed

EPA commitment to long-term environ-

mental research. The institute would have

responsibilities for ecological research,

environmental monitoring, and statistics.

Whatever the approach, it is apparent that

338 R. CLIFTON BAILEY

an enhanced environmental statistics ca-

pability will be vitally important to the

conduct of environmental protection in

this country andin the international sphere

in the coming decade.

References Cited

1. Paul R. Portney, “Needed: a Bureau of Envi-

ronmental Statistics,” in Resources, Resources

for the Future, Winter 1988.

2. Bartelmus, Peter, ‘“‘Environmental Statistics:

Journal of the Washington Academy of Sciences,

Volume 78, Number 4, Pages 339-353, December 1988

Systems, Frameworks and International Ap-

proaches” in Society of American Foresters/et

al, Intl Renewable Resource Inventories for

Monitoring Conf, Corvallis, OR, Aug. 15-19,

1983, pp. 524(5).

. Hennemuth, R. C., G. P. Patil, and N. P. Ross,

“Encountered Data Analysis and Interpretation

in Ecological and Environmental Work: Opening

Remarks.” Presented at the annual ASA meet-

ing, San Francisco, 1987.

. Corporate Use of Information Regarding Natural

Resources and Environmental Quality, prepared

by Train, Russell E., World Wildlife Fund for

the Council on Environmental Quality, 1984.

Some Uses of a Modified

Makeham Model to Evaluate

Medical Practice

R. Clifton Bailey*

Health Standards and Quality Bureau

Health Care Financing Administration

ABSTRACT

The modified Makeham survival model describes the time course of a medical inter-

vention or illness in many cases. A precise understanding of the time course may be used

to evaluate the follow-up time for special studies, to know when the available follow-up

is not adequate, and to balance follow-up time against the number of cases. Also a

knowledge of the time course may be used to evaluate long-term and short-term risk

factors. Long-term and short-term risk factors are studied separately using the widely

available Cox proportional hazards model. This is compared with a fully integrated model

in which the modified Makeham is used with concomitant variables in each of three

structural parameters. The examples rely on data collected by the Health Care Financing

Administration to evaluate the effectiveness of medical interventions on the course of

illness.

*The opinions expressed in this paper are those

of the author and do not necessarily reflect the opin-

ions or policies of the Health Care Financing

Administration.

Correspondence should be sent to: R. Clifton Bai-

ley, Health Standards and Quality Bureau, Health

Care Financing Administration, 2-D-2 Meadows

East, 6325 Security Blvd., Baltimore, MD 21207.

USES OF MODIFIED MAKEHAM MODEL TO EVALUATE MEDICAL PRACTICE 339

Introduction

The value of data in making decisions

and understanding medical practice is a

long standing tradition in medicine. This

article describes some statistical tools

which can be used to advance our under-

standing of medical practice. The main

focus is on a modified Makeham survival

model. This basic model describes the time

course of a medical intervention or illness

in many cases. A precise understanding

of the time course may be used to evaluate

the follow-up time for special studies and

to know when the available follow-up is

not adequate. Examples of the compu-

tations demonstrate the balancing of fol-

low-up time and number of cases. Addi-

tional examples demonstrate how a

knowledge of the time course may be used

to isolate long-term and short-term risk

factors. Two approaches are described.

First, the long-term and short-term risk

factors are studied separately using the

widely used Cox proportional hazards

model. This approach is compared with a

fully integrated modified Makeham

model with concomitant variables in each

of three structural parameters. The ex-

amples in this paper rely on data collected

as part of an effort by the Health Care

Financing Administration to evaluate the

effectiveness of medical interventions on

the course of illness.

Recognition of Statistical Methods in

Extracting Information of Value

from Data

Before beginning a technical descrip-

tion of the Makeham model promised

above, it is worth setting the stage with a

few reminders about the role of statistics

in extracting information from data.

In his presidential address before the

First Indian Statistical Conference, 1938,

R. A. Fisher’ reminded his colleagues that

“in the original sense of the word, ‘Sta-

tistics’ was the science of Statecraft.’’ He

points out that the task of providing pub-

lic information as a function of official

Statistics ““. . . enables the public, if it will,

to size up its own problems. The Socratic

dictum ‘know thyself’ is applicable even

more to peoples than to individuals.”’ Also

he notes that with the development of a

theory of estimation and an understand-

ing of the magnitude and the nature of

the sampling errors, ““The whole tone of

the subject has been altered. The Statis-

tician is no longer an alchemist expected

to produce gold from any worthless ma-

terial offered him. He is more like a chem-

ist capable of assaying exactly how much

of value it contains, and capable also of

extracting this amount, and no more. In

these circumstances it would be foolish to

commend a statistician because his results

are precise, or to reprove because they

are not. If he is competent in his craft,

the value of the result follows solely from

the value of the material given him. It

containsso much information andnomore.

His job is only to produce what it con-

tains.”’ ““To consult the statistician after

an experiment is finished is often merely

to ask him to conduct a post mortem ex-

amination. He can perhaps say what the

experiment died of.”’

There are many notable examples of

the need to extract useful information

from data. For example, Walter Shewhart?

recognized the value of information gen-

erated by industrial processes and de-

veloped methods to chart measurements

sequentially—the control chart. An ex-

ample closer to the subject of this paper

is found in the medical arena. Florence

Nightingale* noted inconsistency in re-

cording the number of deaths at military

hospitals during the Crimean War. At

home she also found that English hospital

records followed no common nomencla-

ture or standard. She worked with Dr.

Farr, of the Registrar-General’s Office to

prepare standard lists for classes and or-

ders of diseases and model Hospital Sta-

tistical Forms to “‘enable us to ascertain

the relative mortality in different hospi-

tals, as well as of different diseases and

340

injuries at the same and at different ages,

the relative frequency of different dis-

eases and injuries among the classes which

enter hospitals in different countries, and

in different districts of the same coun-

tries.”” Furthermore, use of the proposed

forms “‘could enable the mortality in hos-

pitals, and also the mortality from partic-

ular diseases and injuries, and operations

to be ascertained with accuracy; and these

facts, together with the duration of cases,

would enable the value of particular

methods of treatment and of special op-

erations to be brought to statistical proof.”

For her efforts as a “passionate statisti-

cian,’ Florence Nightingale was made

Honorary Member of the American Sta-

tistical Association.*

Outcomes in Medical Statistics

In evaluating medical practices and in-

terventions, an evaluation of chances of

death seems to be an ultimate concern.

The history of the life table and of medical

statistics to a large degree centers around

techniques for statistical summary of mor-

tality.” Actually the techniques developed

for mortality statistics have broad appli-

cation. For example, in engineering, fail-

ure time is often used as a measure of

outcome when we want to know long we

can expect a car, a light bulb, or a per-

sonal computer to last. In all of these

problems, classification of the failure point

and items under test are crucial to the

utility ofthe studies being conducted. Many

problems in applying statistical methods

to medical data revolve around classifying

and recording conditions present, proce-

dures and interventions used, and the out-

comes. The outcomes of interest in health

care can be classified as mortality, mor-

bidity, disability, and ¢xpenditure. In this

paper, the focus is on mortality. How-

ever, methods for mortality analysis have

a role whenever we measure an outcome

by the time or duration for an occurrence

R. CLIFTON BAILEY

such as a readmission, relapse or failure

of a medical intervention or procedure.

The Modified Makeham Model for

Survival Analysis

A modification of the Makeham model

was proposed by Bailey et al. to evaluate

kidney graft survival.®’ The modified

Makeham model has a decreasing hazard

or risk function of the form

r(t) = a exp(—yt) + 8

where a is the initial excess risk, 5 is a

long-term risk and y determines the rate

for the decay of the initial excess risk. The

risk function for the Makeham model as

it is commonly found in the actuarial lit-

erature (Jordan, 1967)° has the form

r(t) = ap’ + 5.

In actuarial applications to human mor-

tality data, p is greater than 1 and the risk

function is increasing with time, ¢. This

corresponds to an increased risk of death

with older age over a lifetime.

When a constant 6 is added to a Gom-

pertz force of mortality to obtain the form

shown above the model is referred to as

Makeham’s modification of the Gom-

pertz even though Kurtz (1930) attri-

butes the idea for the use of the additive

constant 6 to Gompertz himself. In our

modified form of the Makeham, p is less

than 1, since p = exp(—vy). The decreas-

ing risk form of the Makeham works well

when there is a high risk intervention fol-

lowed by a period of recovery during which

the excess risk of the intervention dimin-

ishes with time.

The risk function is also known as the

hazard function or the force of mortality.

The risk curve shows us at what rate fail-

ures occur relative to the number of sur-

vivors at any time, ¢. The corresponding

expression for the proportion surviving at

time ¢ is

USES OF MODIFIED MAKEHAM MODEL TO EVALUATE MEDICAL PRACTICE 341

ope { = | ele ar}

S(t)

= exp{—{8r + (a/y)[1 — exp(—ye)]}}.

The modified Makeham model also in-

cludes concomitant variables in each of

its positive parameters as follows:

Q = exp(a + a,x, + °°

fe, Key PC) CE NOYAX,)

Be seXD (Boy habit 3.73:

+ Bix; +o + Baxy)

VWisresP Oo A Wyse

rey tt YEE)

This survival model has great utility for

evaluation of survival data following some

high risk event such as surgery. The fol-

lowing description of this and related tools

will be applied to examples using Medi-

care data to evaluate the effectiveness of

medical interventions.

Time Course of the Makeham Model:

Its Role in Statistical Studies

The time course of the Makeham model

is important for two important statistical

activities: the design of follow-up studies,

the evaluation of factors affecting long-

term and short-term risk.

The following sections will attempt to

isolate the long-term from the short-term

components of the modified Makeham

model. In evaluating the design for fol-

low-up studies, we focus our design ef-

forts on getting the information to eval-

uate the long-term risk components. This

approach is in the spirit conveyed in pres-

idential address cited above! when Pro-

fessor Fisher recalls that his teacher Pro-

fessor Whitehead of Cambridge used to

say: ‘“The essence of applied mathematics

is to know what to ignore.”’ With suffi-

cient lapse of time we can ignore the short-

term components. Then an evaluation of

the follow-up time required for a study is

reduced to a simpler problem in which the

risk function is a constant once the short-

term risk has become negligible. As you

will see, we don’t really ignore the short

term components. Instead we use our best

estimates of these components to recast a

complicated problem in terms of a simpler

problem.

The second aspect of isolating the long-

term from the short-term is to evaluate

complex data on medical intervention. An

estimate of the time for the short-term

hazard to become negligible relative to its

initial value allows us to use the popular

Cox proportional hazards model to better

understand the role of important risk fac-

tors. As before the estimates are based

on estimates for the parameters of a mod-

ified Makeham model with no concomi-

tant variables. The full Makeham model

with concomitant variables provides the

more satisfying approach when we have

a high risk intervention followed by a pe-

riod of recovery or return to stable or

constant risk. The full Makeham model

provides in one frame work a means to

jointly evaluate the proper balance of var-

ious risk factors. The result is a more com-

plex, comprehensive summary of com-

plex data.

Design of Survival Studies When the

Makeham Model is the Appropriate

Survival Model

To determine an appropriate follow-up

time for a study, there must be sufficient

time to estimate the long-term risk com-

ponent 6 when the Makeham model is the

appropriate survival model. Basically in-

formation on 6 is not available until the

short-term risk, a exp(—yt), has become

negligible. A reasonable approach is to

342 R. CLIFTON BAILEY

find the short-term time, 7,, such that the

hazard

r(t) = a exp(—yt) + 6

is equal to a value close to the long-term

risk itself. For this example, we use the

value r(t) = 1.16. That is, the short-term

effect is diminished to within 10% of 5.

This means that

a exp(—yt) + 6 = 1.18

or equivalently,

a exp(—yTs) = 0.1 8.

The solution for the time at which this

risk is achieved gives

Ts = —(1/y)In(0.1 8/a).

Note that 7; is negative when a is less

than 0.1 5. In this case simply use T; =

0. Now, as an approximation, we have the

constant risk form

r(AT) = 6

and the information on 6 begins accu-

mulating at time, 7; according to the

expression for the information

(6, AT) = 1 — exp(—6 AT)

where AT is the time lapse after time Ts.

When AT is zero, the above equation im-

plies there is no information about 6. As

AT approaches infinity, or symbolically

AT —— ~,

the information on 6 approaches 1 or

100%. Not only is /(6, AT) the infor-

mation on 6, but also it is related to the

survival function for the constant hazard

function where

[Gg ADia tl 1S¥ (AP)

where S;(AT) is the survival curve for

those cases not failed at 7;. This means

that information on the long-term risk ac-

cumulates as failures occur after time Ts.

To get an idea of how this works, see

Figure 1. For purposes of illustration,

consider a value of 6 = 0.2 per year. Then

to get 50% of the potential information

on 6 would require a study to extend

AT = —(1/8)In(0.5)

0.693/8

years beyond 7; or 3.5 years when 6 =

0.2 per year. A period of one year beyond

T; would provide 18% of the information

on 6. The idea is to design a study based

on getting the more difficult, long-term

information for the parameter 6. In taking

this approach, we rely on the very simple,

pragmatic notion, that it is more difficult

to obtain reliable long-term information.

By focusing the problem on the long-term

risk parameter, 5, we simplify a complex

problem and insure an adequate design

for a full evaluation of long- and short-

term risk factors. On this basis we eval-

uate sample sizes for follow-up study and

illustrate the balance between the number

of cases and the follow-up time.

Sample Size for a Follow-up Study

To plan a follow-up study, we must

evaluate a sample size or number of cases

to be included in our study. To do this we

reduce the complex modified Makeham

model to the simpler model with a con-

stant risk function by first estimating the

time for our model to be reduced to this

simpler form. This adaptation permits us

to borrow techniques already established

for the simpler problem. Essentially we

must find the sample size required to es-

timate 5. For example, this can be com-

puted from an approximate formula in

Gross and Clark (1975)! for the confi-

dence limits on 8. Use the formula for the

100(1 — a)% confidence limits on 6

USES OF MODIFIED MAKEHAM MODEL TO EVALUATE MEDICAL PRACTICE 343

Information on Longterm Risk

0.8

0.6

0.4

Information on Longterm Risk

0.2

0 2 4 6

ra) (risk/year)

Time (years) Additional Follow-up

Fig. 1. Information accumulates on the long-term risk, 5, as the follow-up time increases. The time

shown in the figure must be added to the time required for the short-term risk to become negligible.

)1- 2028] <¢

A Jb

ZR eee a

be ie

to find the number of cases m needed to

obtain an estimate within 100k% of 3.

The result

is the number of cases, assuming infinite

follow-up time and full information on 8.

Then we adjust the sample size to account

for the expected follow-up time. If m’ is

the actual sample size at time Ts, the ef-

fective sample size for a total follow-up

time of AT + Tz, is

m.— jm (le exp( —0.A 7).

To adjust the sample size m for this

follow-up time, first compute m then

m' = m/(1 — exp(—6 AT)).

This formula allows us to evaluate op-

tions to use more cases or a longer follow-

up time in survival studies. An additional

adjustment to the sample size accounts for

the expected number of cases lost before

T;. The adjusted sample size is

m" = m'/S(Ts)

where

S(Ts) = exp{—{8Ts

+ (a/y)[1 — exp(—yTs)}}

is the Makeham survival curve.

For example, one year of follow up from

T; with 95% confidence would yield a

sample size of

m = (1.96/0.1)? = 384

would provide an estimate of 6 within 10%

of 8(k = 0.1).

344 R. CLIFTON BAILEY

Witha = 10.6, y = 39.1 and6 = 0.183,

(parameter estimates from the time course

of medicare heart attack data),

Ts = —(1/y)In(0.18/a)

= —(1/39.1)In((0.1)(0.183/10.6))

= 0.16 years,

Using the m above, we find that one year

of follow-up from the 0.16 years or a total

follow-up of 1.16 years, gives

m' = m/0.167 = 2,299

and

m” = m’'/0.741 = 3,103 cases.

The calculations for two years of fol-

low-up beyond 0.16 years for a total fol-

low-up of 2.16 years gives

m' = m/0.306 = 1,255

and

m" = m'/0.741 = 1,694 cases.

In contrast, the time course of heart

failure with a = 2.37, y = 10.77 and 6

= 0.377, has T; = 0.38 years.

Then for 1 year of follow-up beyond

0.38 years or 1:38 years

m' = 384/0.314 = 1223

and

m'" = 1223/0.698 = 1752 cases,

and for two years of follow-up beyond

0.38 years for a total of 2.38 years

gives |

nv 1 384)0.580)— 725

and

m” = 725/0.698 = 1039 cases.

These calculations clearly illustrate the

trade offs between follow-up time and

sample size that can be used in designing

studies. These computations are impor-

tant even in retrospective studies based

on administrative data because they pro-

vide insight into the number of years of

back records that will be needed for a

study. A careful evaluation of the re-

quired sample size for a study must in-

clude other factors, such as the expected

recruitment rate and an allowance for

cases lost to follow up. A fuller discussion

of these issues can be found in Meinert."!

Application of The Makeham Model in

the Evaluation of Data for the

Effectiveness and Use of Medical

Interventions—Long-Term Versus

Short-Term Risk Factors

As part of a project developed in late

1985 and early 1986, the Health Care Fi-

nancing Administration (HCFA) and the

Peer Review Organizations (PROs) un-

dertook a project to develop data on the

patterns of use and the effectiveness of

medical interventions. This project is part

of a comprehensive effort undertaken by

HCFA to assess and stimulate improve-

ment in the quality of medical care ren-

dered to Medicare beneficiaries. The ef-

fort is in four segments:

1. Monitoring of trends over time in use

and outcome of medical interventions.

2. Analysis of variation in use and out-

come over geographic areas and pro-

viders of care.

3. Detailed investigation of the patterns

of medical practice that underlie the

time trends and variations in outcomes

among localities.

4. Feedback and education to exchange

and improve information.

The examples which follow are derived

from the third segment in which detailed

investigations are being conducted for

cardiovascular problems. For this inves-

USES OF MODIFIED MAKEHAM MODEL TO EVALUATE MEDICAL PRACTICE 345

Table 1.—Maximum likelihood Estimates for the

Structural Parameters of the Makeham Model

Heart Heart

Attack Failure

Number of cases B52 3274

a (per year) 10.6 237

y (per year) 39.1 10.77

8 (per year) 0.183 03377

T,, (days) 22 78

tigation, a sample of just over 3100 cases

for each condition is available for analy-

sis. As a first step in understanding the

short- and long-term course of patient

survival following a medical intervention,

it is useful to fit the Makeham model with

decreasing hazard to the data. The result

of this fit can be used to graph the hazard

Over time, estimate the time course of the

risk following intervention, and engage in

a more thorough examination of the role

of key risk factors over the time.

To demonstrate these ideas, maximum

likelihood estimates were obtained for the

Makeham model for two data sets. One

has 3152 heart attack cases and the other

3274 cases with heart failure. The results

of this fit are shown in Table 1.

The risk curves are shown in Figure 2

and the corresponding survival probabil-

ities are shown in Figure 3.

Where do the Survival Curves Cross?

One important property of the Make-

ham modelis that survival curves can cross

Risk for Heart Failure and Heart Attack

Risk/y

120

Heart Attack

o— 10.6; y—39:1 0 —0483

Heart Failure

= 2.57, ¥—10577, 0= 01377

180 240 300

t (days)

Fig. 2. The modified Makeham risk functions for the heart attack and heat failure data. Note the

crossing of the hazard (risk) functions at 0.04832 year or 17.6 days.

346 R. CLIFTON BAILEY

Survival Probability

0.64

Heart Attack

0.4

120

Survival Probability

Heart Failure

180 240 300

t (days)

Fig. 3. The Survival Probability for the Modified Makeham Model for the Heart Attack and Heart

Failure Data. Note the crossing of the survival functions at a time later than that shown for the risk

functions shown in Figure 2.

when different sets of parameters are used.

For example, when we compare two sur-

vival curves with parameters a, y, 6 and

a’, y’, 5’ graphical solution of this prob-

lem will be apparent in many cases (see

Figure 3). An algebraic solution. of the

nonlinear equation for the cross over time

is not generally available. However, if the

graphical display of several survival curves

does not show a cross over, we know that

if a cross over occurs, it will occur for a

large value of time. In this case we can

equate the expressions for survival curves

and assume yf, and y’t, are large. Then

approximate cross over time is

Oe 0%

Once the approximate cross over time

is known, more precise estimates of the

cross Over time can be easily found from

the graph or by iterative search. Note that

a negative cross over time means the curves

don’t cross. For the survival curves shown

in Figure 3, the cross over time from this

approximation is 96 days. Also observe

that the crossing of the risk functions

shown in Figure 2 occurs before the cros-

sing of the survival functions.

The Heart Attack Data for Separating

the Short- and Long-Term Risk Factors:

A Methodological Example

In this section, we explore the heart

attack data described above. There are

many possible variables to consider and

USES OF MODIFIED MAKEHAM MODEL TO EVALUATE MEDICAL PRACTICE 347

we wish to evaluate the risk factors that

play initially and long-term.

In considering these variables, we used

the time 7; where

T, = —(1/y)In(0.1)

to make separate evaluations of the short-

and long-term risk factors. This formu-

lation uses the time 7; for the initial ex-

cess hazard to diminish to 10% of the

initial value of the excess risk, a, so

a exp(—yT7,) = 0.1a.

This formula for separating long and

short term risks uses a criterion which dif-

fers from that for T; used for sample size

calculations. In our examples, the values

Ts used in the sample size calculations are

longer than the corresponding values of

T,. The use of a longer time for the sam-

ple design problem is more conservative.

In the estimation problem, there is the

additional consideration that a longer pe-

riod leaves fewer cases for the evaluation

of the long-term risk factors. Obviously

either approach for separating long-term

and short-term components of risk could

be used. With either approach, the first

step is to obtain parameter estimates for

the simple form of the Makeham with no

concomitant variables in the model. The

values shown in Table 1 provide a time

course which can be use to partially iso-

late the long-term from the initial or

short-term risk factors.

Once the time 7; has been determined,

two applications of the Cox proportional

hazards model were made to evaluate the

long-term and the short-term risk factors.

The SAS” procedure, PROC PHGL’M,

provides a handy tool for evaluating a

number of concomitant variables in the

Cox proportional hazards model. One

handy feature of the SAS implementation

is the option for stepwise model building

in which variables are tried systematically

in succession to assess their contribution

to the model. The initial risk factors were

evaluated using the data with no modifi-

cation. Significant risk factors are found

using the stepwise feature of the SAS

PROC PHGLM. The analysis is then re-

peated on the same data with the survival

time shifted from zero to T,. In the case

of the heart attack data, 7; = 22 days.

Consequently, the value 22 days is sub-

tracted from each survival time in the in-

itial data set. Negative values are assigned

a missing value and deleted from the long-

term survival analysis. The results of these

analyses are shown in Tables 2 and 3.

Table 2 shows the parameter estimates

for 24 risk factors which were significant

(P < 0.05) predictors of patient survival

in the Cox proportional hazards model.

When the survival time was modified by

subtracting 7; = 22 days from each sur-

vival time, 702 of the 3152 survival times

became less than zero and had to be ex-

cluded from the long-term analysis shown

in Table 3. Consequently, the number of *

cases used in the long-term model was

reduced from the 3152 cases used in the

initial risk evaluation to 2450 cases for the

long-term risk evaluation. At the same

time the number of censored survival times

is reduced from 1311 to 609. Censored

cases are those with a death or actual fail-

ure not yet observed during the period of

observation. Note that of the 24 variables

found to be significant predictors in the

initial risk model, only 14 remained sig-

nificant in the long-term model.

We consider this approach a handy

kludge for dealing with a complex prob-

lem. However, with the results of the

modified Makeham shown in Table 4, we

estimated simultaneously the components

of risk for all 24 variables shown in Table

2. In Table 4 an asterisk (*) was inserted

by the parameter estimates for each of the

delta components which were excluded

from the long-term model shown in Table

3. There are the 10 variables in Table 2

which are excluded from Table 3. If the

10 delta components with asterisks in Ta-

ble 4 are judged against their standard

errors, these components are not statis-

tically different from zero.

Furthermore the parameter estimates

348 R. CLIFTON BAILEY

Table 2.—Parameter Estimates for the Cox Proportional Hazards Model for Unmodified Survival Time

for 3152 Cases of Heart Attack

The parameters estimates were obtained from 3152 cases of heart failure of whom 1311 died during the

period observed. The MODEL CHI-SQUARE = 801.90 WITH 24 D.F. (—2 LOG L.R.) P = 0.0 The

output is from SAS® PROC PHGLM.

PARAMETER ESTIMATES

STEPWISE PROPORTIONAL HAZARDS GENERAL LINEAR MODEL PROCEDURE

3152 OBSERVATIONS

1311 UNCENSORED OBSERVATIONS

0 OBSERVATIONS DELETED DUE TO MISSING VALUES

—2 LOG LIKELIHOOD FOR MODEL CONTAINING NO VARIABLES = 20381.20

MODEL CHI-SQUARE = 1141.74 WITH 24 D.F.

MAX ABSOLUTE DERIVATIVE = 0.1537D-09. —2 LOG L = 19579.30.

MODEL CHI-SQUARE = 801.90 WITH 24 D.F. (—2 LOG L.R.) P = 0.0

FINAL PARAMETER ESTIMATES

VARIABLE CODE* BETA STD. ERROR CHI-SQUARE P

Corr ERAGE 0.051 0.006 69.23 0.0000

Leukocytosis HVWBC 0.012 0.003 14.54 0.0001

Low Value LVK 0.172 0.072 5.64 0.0176

Potassium

High Value HVPH 2G 0.635 Teds) 0.0066**

Readmitted F122 0.291 0.115 6.40 0.0114**

<30da

Disoriented F293000 0.403 0.160 6.36 0.0116**

Ischemia F411800 — 0.176 0.065 7.44 0.0064**

MI Age not F412000 —0.157 0.065 5.80 0.0160**

determined

Glucose V425 0.000989 0.000229 18.53 0.0000**

Dissociation F426890 1.004 0.171 34.32 0.000

Congestive F428000 0.418 0.064 42.17 0.0000

Heart Failure

BUN V430 0.00526 0.00153 11.87 0.0006

PO, V461 — 0.00723 0.00183 15:56 0.0001**

Coma/Stupor F780005 0.906 0.128 50.27 0.0000

Pseudonomias V785000 0.00185 0.00054 11.47 0.0007

Murmur F785201 0.381 0.102 14.05 0.0002**

Systolic V785501 — 0.00997 0.00148 45.16 0.0000

Blood Pressure

Respirations V786010 0.0120 0.0034 12.18 0.0005

Stroke/TIA F826 0.367 0.088 17.36 0.0000

History

Coronary Heart F832 0.261 0.075 11.99 0.0005

Failure History

Myocardial ~ F876 0.143 0.064 4.96 0.0259

Infarction History

Cancer CA 0.632 0.147 18.44 0.0000

Chronic Renal RN 0.323 0.145 4.99 0.0254**

Disease

Diabetic DB —0.219 0.103 4.52 0.0336**

*Codes which begin with the letter F are indicator variables and codes that begin with V are values.

**Indicates variables not significant long-term as shown in Table 3.

USES OF MODIFIED MAKEHAM MODEL TO EVALUATE MEDICAL PRACTICE 349

Table 3.— Parameter Estimates for the Cox Proportional Hazards Model for a Modified Survival Time

for 2450 Cases of Heart Attack

For this analysis the survival time was modified by subtracting 22 days. Negatives values were deleted from

the analysis. The parameters estimates were obtained from the remaining cases of heart failure using SAS®

PROC PHGLM. The estimate of a 22 day period for the long-term risk to dominate was based on the

Makeham fit of the time course of the survival data. The estimates shown are for the variables shown in

Table 1 which were identified as significant in the stepwise proportional hazards general linear model

procedure with the default settings (P < 0.05).

609 UNCENSORED OBSERVATIONS

702 OBSERVATIONS DELETED DUE TO MISSING VALUES

FINAL PARAMETER ESTIMATES

Variables CODES* BETA

‘AGE ERAGE 0.0691

Leukocytosis HVWBC 0.0122

Potassium LVK 0.277

Dissociation F426890 0.896

A-V

Congestive Heart F428000 0.555

Failure

BUN V430 0.0155

Coma/Stupor F780005 0.691

Pseudonomias V785000 0.00321

Murmur F785201 0.378

Respirations V786010 0.0228

Stroke/TIA History F826 0.552

Coronary Heart F832 0.374

Failure History

Myocardial Infarc- F876 0.254

tion History

Cancer CA 0.939

STD. ERROR CHI-SQUARE P

0.0093 55.42 0.0000

0.0058 4.46 0.0347

0.112 6.09 0.0136

0.338 7.02 0.0080

0.090 37.64 0.000

0.0022 48.33 0.0000

0.311 4.92 0.0266

0.00081 15.80 0.0001

0.148 6.50 0.0108

0.0053 18.63 0.0000

0.123 20.24 0.0000

0.109 11.74 0.0006

0.091 7.85 0.0051

0.199 22.31 0.0000

*Codes which begin with the letter F are indicator variables and codes that begin with V are values.

for the modified Makeham model provide

the raw material to evaluate specific in-

dividual situations. With a specific case at

hand, the component parameters can be

used to estimate the structural parameters

a, y, and 6. With these estimates, both

the predicted survival curve and the pre-

dicted risk function can be evaluated and

plotted to provide a comprehensive fore-

cast for the situation. When the model is

used with a treatment or procedure that

can be administered as appropriate, the

results of the model prediction summarize

the experience of thousands of observa-

tions to succinctly predict the course of

survival for each option for the specific

individual case. This means that a simple

answer that one approach is preferred over

another must be replaced by the more

elaborate evaluation specific to the case.

And the choices are more complex in that

the survival curves may cross just as they

did in the comparision of the heart at-

tack and the heart failure data. In such

cases, the choice is a trade-off between the

short-term outcome and the long-term

outcome. The result is an elaborate

quantitative assessment of the expected

outcome that is custom fit to cover a com-

plex mix of individual situations. Clearly

such analyses provide a resource for sum-

marizing experience that awaits further

exploration and exploitation.

The appeal of the proportional hazards

model rests largely on the fact that the

conclusions derived from comparisons

based on this model remain simple, even

though complex adjustments are made.

The comparisons are simple because the

proportional hazards model does not re-

350

R. CLIFTON BAILEY

Table 4.—Estimates of the Makeham Parameters for the Heart Attack Data Set

Maximum likelihood estimates are shown along with approximate standard error for the estimate (S.E.).

Variables are identified with the code shown in Table 2 and a suffix designates alpha (a), gamma (y) or

delta (6) components.

MAXIMUM OF THE LOG LIKELIHOOD = —8209.242

PARAMETER

ESTIMATE

S.E.

PARAMETER

ESTIMATE

S.E.

PARAMETER

ESTIMATE

SAEP

PARAMETER

ESTIMATE

S.E.

PARAMETER

ESTIMATE

S.E.

PARAMETER

ESTIMATE

S.E.

PARAMETER

ESTIMATE

S.E:

PARAMETER

ESTIMATE

S.E.

PARAMETER

ESTIMATE

S.E.

PARAMETER

ESTIMATE

S.E.

PARAMETER

ESTIMATE

S.E.

PARAMETER

ESTIMATE

Salas

PARAMETER

ESTIMATE

SE.

F293000_a

0.874

0.267

F412000_«

—0.442

0.138

F426890_a

1.03

0.286

V430_a

— 3.72E-04

2.96E-03

F780005_c

0.764

0.175

F785201_a

3.21E-02

0.223

V786010_«

—3.28E-03

6.21E-03

F832_a

0.147

1.174

CA_a

— 0.231

0.296

DB a

— 0.376

0.218

F29300_+y

0.201

0.274

F412000_y

— 0.305

0.154

F426890_+>

0.155

0.402

V430_y

—3.43E-03

3.98E-03

F780005_y

— 0.495

0.221

F785201_y

— 0.388

0.260

V786010_y

~5.64E-03

6.65E-03

F832_y

0.157

0.212

CA_y

— 0.837

0.352

DB_y

6.54E-02

0.216

Sell

HVWBC 8

1.00E-02

F29300_8

0.127"

0.343

F412000_8

~0.141*

0.116

F426890_ 6

atl

0.397

V430_8

1.62E-02

3.09E-03

F780005_56

— 0.560

O22

F785201_8

0.387

0.199

V786010 8

3.11E-02

6.53E-03

F832_8

0.484

0.130

CA 8

0.803

0.280

DB 8

7.89E-02*

0.161

ERAGE a

3.41E-02

1.54E-02

LVK_a

~2.93E-03

0.135

F122_a

0.449

0.223

F411800_a

— 0.292

0.135

V425 a

1.69E-03

4.12E-04

F428000_a

0.180

0.122

V46l_a

— 6.26E-03

3.23E-03

V785000_c

3.15E-04

1.03E-03

V785501_a

—2.47E-02

2.37E-03

F826_«

0.205

0.195

F876_«

—3.71E-02

0.136

RN_a

= (0.297

0.268

ERAGE_y

— 1.64E-02

2.35E-02

LVK_y

— 0.240

0.140

F122_y

0.198

0.231

F411800_y

~0.113

0.140

V425_y

5.25E-04

4.48E-04

F428000_+y

— 0.264

OFZ

V461_y

4.07E-03

3.68E-03

V785000_y

~9.72E-04

1.16E-03

V785501_y

~1.11E-02

2.59E-03

F826_y

—5.54E-02

0.240

F876_¥

—2.63E-02

0.152

RN_y

tle

0.395

ERAGE 8

F411800_8

Satin”

0.110 -

V425 8

1.53E-04*

4.61E-04

F428000_8

0.461

0.117

V461_8

~1.37E-03*

3.77E-03

V785000_8

3.44E-03

9.96E-04

V785501_8

5.35E-03*

3.55E-03

F826 8

0.581

0.152

F876_8

0.338

0.107

RN 8

—0.468*

0.464

“Estimated delta components which correspond to values not found significant in the Cox proportional

hazards model as shown in Table 3.

USES OF MODIFIED MAKEHAM MODEL TO EVALUATE MEDICAL PRACTICE 351

sult in survival curves that cross. The

modeling approach illustrated by the

modified Makeham places the focus on

estimation of complex outcomes rather

than the artificial reduction of complex

outcomes to simplistic conclusions that

came from formulating issues in terms of

simplistic statistical hypotheses.

Conclusion

The examples of the use of the modified

Makeham model to evaluate medical in-

terventions are promising. The compu-

tational cost associated with fitting this

complex model to large data sets may be

a limitation. If computational resources

become a problem, then an appropriate

statistical answer is to use a sample. The

computational limitations are more likely

to come from the need to include many

complex adjustments in our models. To

deal with these problems in an economical

fashion will be a challenge. In this paper,

it has been shown that simpler models,

such as the Cox proportional hazards

model, can be used with the simple struc-

tural form of the Makeham model to gain

useful insights. A related example by

Olshen etal.'* describes the Cox model and

other powerful statistical methodology

such as classification trees. We anticipate

the need to build models in which it is

necessary to examine many variables in

many combinations. To do this efficiently,

we must being various statistical and com-

puting resources into play. For example,

in medicine it is often the case that many

variables may carry very similar infor-

mation to the problem. When this is the

case, there are numerous alternative

models that are essentially indistinguish-

able. In such cases, external information

can be very useful in the final selection of

a model for a particular purpose. The ex-

ternal information may be in the form of

costs, convenience, or reliability or risk

to the patient of a clinical measure. The

external information may include a real-

ization that a variable has been miscoded

or that the information is nci coded con-

sistently. The biggest challenge to using

complex models for evaluating medical

procedures and practices from the infor-

mation contained in large data bases comes

from the problems inherent in such large

collections of data. On the other hand,

the challenge is to have the courage to

make the best of what is available. The

very probing of the data to glean valuable

insights regarding current medical prac-

tice will stimulate new questions and the

very use of the data in this productive

fashion will encourage those responsible

for providing and maintaining these data

to do a better job. Without use, the in-

formation is lost and the process of learn-

ing from experience is far more parochial

than it need be. Many things are being

tried. We need to study the really good

practices and the really bad practices to

learn what works and when it works. We

need only look at the conventional gath-

ering of medical knowledge to realize that

clinical trials are conducted on very select

populations, each practitioner has at most

limited experience, information in jour-

nals is often based on studies at a single

institution, and the current thinking in-

stilled in medical school graduates changes

slowly with experience. With models which

focus on effective use of data to jointly

evaluate short- and long-term risk factors,

there is a challenge to fully investigate

major data resources in order that we may

better understand medical practice.

Acknowledgement

The author wishes to express his grat-

itude to Henry Krakauer and Miles Davis

of the Health Care Financing Adminis-

tration for their encouragement and com-

ments on this paper.

References Cited

1. Bennett, J. H. 1974. Collected Papers of R. A.

Fisher, Volume IV 1937-1947, The University

352

R. CLIFTON BAILEY

of Adelaide, Australia. Paper 159, pages 160-

163.

. Shewhart, Walter. 1931. Economic Control of

Quality of Manufactured Product, New York,

D. Van Nostrand Co., Inc.

. Cook, Edward. 1914. The Life of Florence

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DELEGATES TO THE WASHINGTON ACADEMY OF SCIENCES,

REPRESENTING THE LOCAL AFFILIATED SOCIETIES

7 CLEATS GTEC) IES) 011 0) 1 ga le Barbara F. Howell

Pere stical SOCICtY Of WaShiMetOn . <i 5 ics oc. oe te tele ee ee teense ee eet Edward J. Lehman

PI MECICICDY. Ol WASHINGTON: = 2/1. 05 cic nceletsi stein cose 0 \s elepe coe ois tage ed ae eg eisie ge ees Austin B. Williams

TEMES EV COL NV ASPALITXEQ)IN 552) nea ciate ches «a lane Qe a a. cldediv’e im g)Sccnie cs winNy. « Ce we Jo-Anne A. Jackson

IMIPIEIE ARN SOCICEY Ol VWASMIN GLO. 2.05505 000655 6 acs boo Sic nos oes ee nave ce SIS rele eyes Manya B. Stoetzel

SNEMEMAP MOT ANIC SOCICUW Os eae tie cic: onda lcisforen aig sia ele souk Fels Sane Sel atEe Ow see bas Gilbert Grosvenor

PERCHES OCICLVAOM VV ASHE O LON) 105 15118 oo a thei n aoe Siena neice a eecieele gi eo Lee ap wes James V. O’Connor

emeenncreicty OF the District of Columbia .: 2... 2.02.0... 0c0c cece eee eee ne eee Charles E. Townsend

IBLF OLICAIASOCICLY 26 2s ne See nln sb ake Gites ce eicusisiaie mn ecatse oterdi ave aie 3'e-oa Be ayauelae Paul H. Oehser

MMAEMCCICE SOI V\WASHINIOLOM:. s3r\ccc settee anes 2 aictae Dees ale ce cma ee eadesiauess Conrad B. Link

mmo ainctican Foresters, Washington Section ....... 20... 26 e eke cee ence ences Mark Rey

PEE AOCIC LYK Oly ENGINE CES. .0 elo loctse legs see isis eiaielased sein o Wie sel atuiid eee eiaeee na George Abraham

Institute of Electrical and Electronics Engineers, Washington Section................. George Abraham

American Society of Mechanical Engineers, Washington Section...................0-0000- Michael Chi

PET CAl SOCICLY OF WaSHIN PCO .260. 6 co ka ete e lois ope eRe ob Cee ees eee Robert S. Isenstein

Seaestean society for Microbiology, Washington Branch......... 2.0... 2... .jc0cjee eee es eee ea Vacant

Society of American Military Engineers, Washington Post....................--. Charles A. Burroughs

fmeemeanoocicty of Civil Engineers, National Capital Section... .... 00.0002 0.0... 0 ne eeses Carl Gaum

Society for Experimental Biology and Medicine, DC Section ...................... Cyrus R. Creveling

ema society tor Metals, Washington Chapter... 0.2.6... fo 03 ee ese Fae ee ee oes James R. Ward

American Association of Dental Research, Washington Section.....................-.-. Eloise Ullman

American Institute of Aeronautics and Astronautics, National Capital Section............... Paul Keller

maeeanenictcorolorical Society, DC Chapter .. 0. 2. eb Dannie ce is ee wees be os A. James Wagner

Insecticide Society of Washington PEP oy eeEM ete Na er asin lacclls Soden oe Atte eh Rae ae Oe Albert B. DeMilo

Seemswea society of America, Washington Chapter. ..............-0: 0.005 ee ecee cee Richard K. Cook

Pe Meameucicar Society, Washington Section: 2.5.0 2.0.06 ccc eee eet ete bee e seat se Paul Theiss

mastitute of Food Technologists, Washington Section ....................222+ eee Melvin R. Johnston

American Ceramic Society, Baltimore-Washington Section........................ Joseph H. Simmons

SuREnaIP RE Ne LIES OCICL VE Se ila caldera ales ome hoe als oD b ialee One eleped Meum teieveene Alayne A. Adams

Eee MELTISCORYAOl SCONCE! CUD... i. a5. be joteceat vies sys wie iv slave Ges Libis sa veleloih ce eve thale Albert Gluckman

American Association of Physics Teachers, Chesapeake Section ...................... Peggy A. Dixon

Smeaesociety of America, National Capital Section... ........2- 0.20. 5226- eee William R. Graver

American Society of Plant Physiologists, Washington Area Section............... Walter Shropshire, Jr.

Washington Operations Research/Management Science Council ...................... Doug Samuelson

Bammer society of America, Washington Section.: .........02 52. sete cee ese ce tens onl Carl Zeller

American Institute of Mining, Metallurgical

sasectrolcum Engineers, Washington Section... 2... 52... 6. ce cnie eines een te Ronald Munson

See MIO AMI EAIPAS(TOHOMICNS 2 ,>) 5 ac.2)4 2-02 creas sakla ds sais sue es nes nis de eye eee Robert H. McCracken

Mathematics Association of America, MD-DC-VA Section................0..0eeeeee Alfred B. Willcox

SBA STALE CHCA CO HEMIISES S50. ici os ocacne se Se dw asic ao) ed CO eee Miloslav Rechcigl, Jr.

SEE NONG PIC ale ASSOCIATION 5505.05 2 aha neni oe ie Ls Sine aha oh artic oie ela) Sodeeimin die aeesn ewe a Bert T. King

American Phytopathological Society, Potomac Division..................-.00000e00e Roger H. Lawson

Society for General Systems Research, Metropolitan Washington Chapter ..... Ronald W. Manderscheid

Pemiatm Actors Society, Eotomac Chapter... .2i; 0562s <i eons yee ele fee Ue ee ee wots Stanley Deutsch

PemcbGanhishieries. society, Potomac Chapter: .. 0-25... .....cce0sseeseneecccnenenals Robert J. Sousa

mavaciaon for Science, Lechnology and Innovation.............<:-.-c.sesserceeere ree Ralph I. Cole

BR PRLEMESHCIOlaSICAl SOCIELY fe) 08. 06. eae ee ss as Kotte ee cade yond etlns Ronald W. Manderscheid

Institute of Electrical and Electronics Engineers, Northern Virginia Section.............. Ralph I. Cole

Association for Computing Machinery, Washington Chapter..............-..0-00005 James J. Pottmyer

BT aRIE OES EACSHCAIISOCIELY Is <5 ses eee oo a vie won ens geo sidim inte nin yale R. Clifton Bailey

Delegates continue in office until new selections are made by the representative societies.