MULTIVARIATE ANALYSISSTATISTICAL INFERENCE)

CONSULTING, STATISTICAL

DEFINITION

Statistical consulting means quite differentthings to different people. In this article itwill be used in a very broad sense: one ormore statisticians working together with oneor more persons who need statistical assis-tance to help solve some problem of interest.As an example, we would include in ourdefinition the efforts of a statistician whoworked for years with a chemical engineerplanning experiments and analyzing data toimprove the yield of a chemical process. Wewould also include the response of a statisti-cian to a telephone query on how to com-pute a standard deviation.

Our definition of statistical consulting isby no means universally accepted. Some ar-gue strongly that a consultant must take fullresponsibility for all statistical aspects of acooperative venture before the effort canproperly be termed consulting. Others takeprecisely the opposite view-that a joint en-terprise in which the statistician takes a ma-jor role is by definition a collaborative rela-tionship, not a consulting one. To this group,a consulting relationship is a more shallowendeavor, something undertaken ratherlightly and without great responsibility. Wemention these differences because there israther strong disagreement in thg professionand the reader is likely to encounter theseand other views.

Our position is that both extremes are"consulting", that the difference is one ofquality.In-depth "total involvement" is goodconsulting, whereas giving quick answers tocasual inquiries or "sprinkling the holy waterof statistical significance" on weak analysesis poor consuiting. However, using the tele-phone to enhance continued communicationis often a valuable component of a goodconsulting relationship.

CONSULTING, STATISTICAL 141

WHAT CONSULTANTS DO

Two excellent descriptions of what goodconsultants do are given by Marquardt [2]and Deming [7]. In Marquardt's words,good statisticians become "totally involved"in the projects on which they are working.They learn about the subject matter, whothe key people are, how the data are col-lected, what the goals of the project are, andwhat the constraints are in terms of time andresources. They then help formulate a planof action that tries to ensure that good datawill be collected and that proper analysesare carried out on the data collected. Theyhelp document the conclusions reached bythe investigation. Consultants cannot reallyclaim success until the lessons learned fromthe study have been accepted and put intoaction.

The ways in which consultants work seemendlessly varied. Here are several examples.

Example 1. Jane is the only statistician in astate agency and provides much needed sta-tistical expertise on a wide variety of pro-jects. One of her projects concerns the WhiteRive5.

This river is heavily industrialized andmany of the industries discharge wastewaterinto the river. Recent federal legislation hasforced all of them to improve the quality ofthe water discharged but there is still a prob-lem when the river is low and the watertemperature is high. On such days the dis-solved oxygen content of the river falls be-low the minimum level considered safe foraquatic life. The statistical task is to examinehistorical data on flow rate and temperatureand seek to develop a reasonable approxi-mation to how these two factors vary to-gether. Data are available for the previous45 years but the problem is complicated inseveral ways: the flow measurement processhas been recalibrated twice; the water sam-pling method for temperature measurementswas changed at two different times; somedata are "obviously" wrong and many othervalues appear quite unlikely; there are anumber of missing values; and the manage-

148 CONSULTING. STATISTICAL

ment practices for the dams that regulateflow have been changed at various times,some of which can only be guessed.

The analysis of the White River data hasthus, not unexpectedly, evolved from a sim-ple tabulation and smoothing operation intoa more complicated process involving a fairamount of detective work. Key steps haveincluded phone calls, letters, and visits to theArmy Corps of Engineers (which regulatesthe river), officials in the city of St. Claire(where the early tempefature measurementswere made), and Black's Paper Mill (whichtook some of the later temperatures). Theprocess has been made more difficult by thefact that some of the people who made theearly measurements have died or movedaway. Jane has worked closely throughoutwith state pollution* specialists and key per-sonnel from other agencies. She is in theprocess of completing her report, which willbe used as the basis for decisions involvingmillions of dollars of new antipollution mea-sures. Jane finds it exhilarating to be in-volved in projects of such importance, but itis also a bit scary. She often wishes therewere some other statistician in her groupwith whom she could double-check herwork.

Example 2. Fred works for a manufacturerof ceramic materials. Several months ago hewas given responsibility for building a largedata base to help solve some major problemsin the manufacturing of an important newproduct. So far his work on this project hasinvolved:

1. Gaining familiarity with complex ma--- 'chinery and manufacturing processes so

that he can help define measurementsand other data that need to be taken.

2. Designing sampling plans to measurecharacteristics of a two-dimensional sur-face, such as surface smoothness.

3. Doing exploratory analysis of pilot data.

4. Designing forms to be used in data col-lection.

5. Helping specify the algorithms necessaryfor computerized data reduction andanalysis.

6. Working with computer experts to de-sign efficient procedures for storing andaccessing the data.

7. Beginning the development of a suitablereport system.

Other key steps still remaining include: ana-lyzing the data, checking results, communi-cating results, making recommendations forchange, and following up to see that appro-priate changes are made. Fred knows thatthis is a tough assignment; one in whichmuch money will be invested and one inwhich, if he is not very careful, little usefulinformation will be gained. However, if hesucceeds, as he expects to do, his work willhave been extremely useful to his company.

Example 3. Al works for a governmentphysical sciences research laboratory and isthe leader of a group of three statisticiansand two computer specialists. An importantaspect of Al's approach to consulting is theemphasis he puts on in-house teaching. Hetries to keep the scientists in his lab abreastof both old and new statistical developmentswhich are relevant to their problems. As aresult of his lectures, scientists in his"classes" are continually bringing him newproblems. He works on each problem untilhe feels he understands it, then has the"student" scientist solve it with his guidance.This way both he and the scientist learn alot.

Much of the work in his laboratory seemsto fall in the areas of nonlinear* modelfitting and nonstandard time-series* analy-sis. He has found that existing computerprograms often are not satisfactory for hisneeds, so his group spends a substantialamount of effort developing new computerprograms for analyzing data. Al and hisgroup also do the more conventional typesof consulting.

These few examples by no means exhaustthe rich variety of working styles and envi-ronments experienced by statistical consul-tants. Some work alone, others in teams.They work in government, in industry, inuniversities, in banks, in other types of orga-

nizations, and as private consultants. Appli-cation areas include engineering, agriculture,medicine, biology, sociology, marketing, pol-itics, law, economics, physical sciences, de-mography, meteorology, and indeed everyarea that attempts to learn from data. Theinterested reader might want to see the bibli-ography on consulting by Woodward andSchucany [17] and the collection cif interest-ing examples of applications of statistics byTanur et al. [6], as well as the works byCameron [5] and Daniel [6].

HISTORICAL PERSPESTIVE

Modern'statistical methods, together withthe mathematical statistical theory that helpsunify them, have largely been developed inresponse to the needs of consultants andothers who sought to learn from data. Manyof the early pioneers in statistical theory andmethods were themselves scientists. For ex-ample, Francis Galton* first devised the cor-rejiation coefficient* to quantify the amountof inheritance of continuous variables inman. He later sought the assistance of ayoung mathematician named Karl Pearson*,who became interested in statistics and sub-sequently made many important contribu-tions to statistics while consulting with Gal-ton and others. W. S. Gosset* ("Student"), achemist at the Guinness Brewery, similarlysaw that he needed better tools to evaluatethe results of his experiments and went on todevelop the very widely used Student's /-test*.

R. A. Fisher*, by far the most importantcontributor to modern statistics, became in-terested in the field as an evolutionary biolo-gist. His early mathematical training andoriginality enabled him to make consider-able advances in statistical understandingand to an appointment at age 29 as thestatistician at Rothamsted Experimental Sta-tion in England. His greatest contributionsresulted from serving as statisticial consul-tant to the diverse staff at Rothamsted.While there he served as consultant to scien-tists in chemistry, bacteriology, entomology,soil science, plant physiology, botany, and

CONSULTING, STATISTICAL r49

agriculture. Fisher later wrote in the prefaceto his path-breaking Statistical Methods forResearch Workers: "Daily contact with thestatistical problems which present them-selves to the laboratory worker has stimu-lated the purely mathematical researchesupon which are based the methods here pre-sented." Then, as now, there..was strong in-terplay between good st4tistical theory andapplication. (See also Box [3].)

In the United States, Iowa State Univer-sity was the first to develop a college-levelprogram in statistics. There in 1924, HenryA. Wallace (later to become U.S. Secretaryof Agriculture and Vice-President) led agroup of 20 scientists in a study of correla-tion and regression. This soon led to theestablishment of a statistical consulting cen-ter at Iowa State with George W. Snedecor*and A. E. Brandt in charge. This center wasthe wellspring of much of the early statisticsin the United States and in the 1930s hostedextended visits from many famous statisti-c ians, inc luding R. A. F isher* , JohnWishart, Frank Yates*, and Jerzy Neyman*.Key faculty members included GertrudeCox, W. G. Cochran, and Charles P. Win-sor. The early learning programs at IowaState had a strong consulting flavor. Forexample, when Fisher visited, local research-ers took turns at presenting at seminarssome of their own experimental data andassociated statistical analyses. Afterward,Fisher and the others present were invited tocomment on the speaker's interpretation:whether the question the experiment andanalysis attempted to answer was the onethe experimenter intended to ask, what addi-tional inferences might have been drawn,and so on.

The early interests at Rothamsted andIowa State centered on agriculture, andsome of the tools developed for agriculturewere readily adaptable for use in industry.But different sorts of procedures were alsoneeded. In agriculture, time ordering withinsmall sets of supposedly homogeneous mea-surements had not been a problem becausemeasurements were not ordinarily made inclose time order. But in data from the physi-cal sciences and industry, physicist Walter

I5O CONSULTING. STATISTICAL

A. Shewhart found that the data sets helooked at, even those from very good labora-tory scientists, almost invariably containedpeculiarities when looked at with respect totime order. In his studies of small sets ofdata from supposedly stable laboratory pro-cesses, Shewhart found trends, shifts in level,and other patterns. The control chart* tech-niques he introduced in response were sim-ple and effective, and soon became a vitalmeans of monitoring manufacturing pro-CCSSES.

During World War II, the need to employstatistical and other quantitative methods inproblem solving became apparent in agreatly expanded range of fields. The Britishorganized operations research* teams in thearmed services, and the United Statesquickly followed suit by employing statisti-cians such as A. E. Brandt of Iowa State andW. J. Youden*, originally an industrialchemist. At the same time, Harold F. Dodgeand Harry G. Romig of Bell Laboratoriesand Hugo Hamaker of Philips (Eindhoven)were developing acceptance sampl ingplans*. These plans helped ensure thatcartridges would fit in the rifles for whichthey were intended without having to belaboriously inspected one by one. Statisticalanalysis of survival data showed that thenumber of ships sunk in trans-Atlantic cross-ings was roughly independent of the numberof ships in the convoy, thus implying thatsmaller percentages would be sunk in largerconvoys. Other statistical analyses helpedimprove the accuracy of aerial gunnery. Im-proved test plans and analyses helped iden-tify the median detonating power of bombs.

Soon after the end of the war, W. Ed-wards Deming began a series of 18 trips toJapan to teach statistical quality control* toindustry. These visits and the action of Japa-nese management have changed the qualityof Japanese goods from poor to excellent.

These and other developments meant thatsoon after the war there was great demandfrom a wide variety of sources for statisticaladvice. Demand rose from industry, govern-ment, agriculture, medicine, biology, educa-tion, sociology, psychology, and many other

areas. Rapid growth in the demand for sta-tistical consulting had begun. It has notabated some 35 years hence.

SKILLS NEEDED BY A CONSULTANT

A statistical consultant, to be fully effective,should have many diverse skills. Ideally, heor she should:

Have a genuine desire to solve realproblems and help others to solve prob-lems.

Be able to help investigators formulatetheir problem in quantifiable terms.

Be able to listen carefullv and to askprobing questions.

Have a broad knowledge and t rueunderstanding of statistical and scientificmethods.

Be able to adapt existing statisticalprocedures to novel errvironments.

Be able to locate or develop goodstatistical procedures in a timely fashion.

Be able to keep abreast of developmentsin statistics.

Be willing to meet deadlines, even if itrequires substantial extra effort.

Be able to understand something aboutthe clients' subject matter and speak a bitof the clients' language.

Be a good teacher-much success inconsulting depends on being able to helpothers understand statistical tools, andtheir strengths and weaknesses.

Be wil l ing to settle for a reasonablycorrect approximate solution, then go onto the next problem.

Be able to identify important problems(and thus avoid spending too much timeon projects of little significance).

Have the confidence to use as simple aprocedure as will get the job done, be itdesign or analysis.

Be able to convince others of the validityof a solid solution and see to it that properaction is taken.

Be able to use computers effectively anddirect others in their use.

Be a good problem solver.

Be wi l l ing to meet c l ients regular lyon their home ground, and take theresponsibility to meet and communicatewith all members of the working team.

Be diplomatic and know when to bend,when to stand firm, and how to helpsmooth over conflicts amons other teammembers.

Be willing to get some experience in theactual collection of the data.

Be willing to take the time to check andd.ouble-check procedures and results.

Be able to communicate effectively inwrit ing as well as orally (this oftenincludes helping clients write their reportsas well).

Be able to make a good estimate of howmuch effort will be required to solve theproblem without actually having to solvethe problem itself.

CONSULTING AND COMMUNICATION

Statistical consulting by its very definitionimplies collaboration between individuals-moreover, between individuals in differentfields. Good communication is vital to suc-cessful consulting. Failures in communica-tion are frequent and can lead to any num-ber of undesirable consequences. Probablythe most prevalent is what Kimball I l]termed an error of the third kind: providinga good solution to the wrong problem. Goodconsultants try to resist the ternptation togive a quick answer. They try to make surethat they have a good understanding of thesituation and that the goals of the projectare clear before they make any specific pro-posals. Frequent continued interaction isalso usually required, lest the statistician orthe subject-matter specialists (or both) beginto head off in the wrong direction.

Since good communication is key to beinga successful consultant, it is important thatcommunication skil ls be continuously stud-

CONSULTING, STATTSTICAL l5r

ied. The articles by Boen and Fryd [] andZahn and Isenberg [18] provide a good start,but since communication in statistics is inessence little different from other communi-cation, many of the popular general-purposetreatments are also relevant. Several of theseare mentioned in the Boen and Fryd refer-ences.

The critical importance to consultants ofgood writing skills is also emphasized bySalsburg [3] and in the important report bySnee et al. [5].

COMPUTERS AND CONSULTANTS

By far the most important development ofthe mid-twentieth century for statistical con-sultants is the widespread availability of rel-atively inexpensive electronic computers*and the programs that make them easy touse. With computers one can afford to try awide variety of models and not be limited tomodels that are simple to compute. One cantry models with nonstandard assumptions,including models whose solutions involvecomplicated iteration schemes (see, e.g.,Efron [9]).

Probably even more important is the com-puter's ability to handle very large and com-plex data bases. In many cases computerscan be used as intimate parts of the data-gathering process. For example, computerscan be used to monitor household energyconsumpt ion, envi ronmental pol lu t ion,weather, and laboratory experiments. Databases of millions of numbers can be readilyaccumulated. Analyzing data sets of this sizerequires new ways of thinking about data.However, computers have made the analysisof data sets having 10,000 cases on 50 ormore variables relatively common.

With the larger sizes come data bases ofincreasingly complex structures, where eventhe statistical procedures remain unclear.For example, one might record familial in-teraction patterns, digitizing for each familymember each verbal or nonverbal cue andtoward whom it was directed. This might bedone at different t imes of the dav. on week-

152 CONSULTING. STATISTICAL

days and weekends, in different seasons, andat different ages. Some families might begiven some "treatment" designed to improvetheir communication pattern. The researchquestion might be: What does the treatmentdo to communication patterns? The datarnight all be available on a computer, but byand large, appropriate tools for analysis stillneed to be developed.

One of the rnost important benefits of thecomputer for statistical consultants is theability to plot* the data in many differentways with minimal effort. Plots often proveto be enormously useful in understandingwhat is really going on in a data set.

But computers also introduce new prob-lems. Data that are "in the computer," butnot readily accessible in a useful fashion,might almost just as well not exist. Similarly,if the only contribution of the computer is toprovide stacks of tabular output, the com-puter and the data are likely to be of littlevalue. An additional problem with largedata bases is that of "computer error"; mi-nor slips in programs can introduce subtleerrors in results that are very difficult todetect and can lead to erroneous conclu-sions.

KEEPING UP WITH STATISTICS

The ideal consultant has a good generalknowledge of a great many aspects of statis-tics. Keeping this knowledge up to date andbeing prepared to develop sufficient depth ina new area on a timely basis requires ongo-ing effort. To help in this regard, most con-sultants belong to one or more professionalorganizations, including regional, national,or international statistical societies and tech-nical societies with a strong statistical com-ponent. Most of these societies have periodicmeetings wherein members can learn of newdevelopments in the field and mingle withcolleagues who have similar interests. Manyconsultants also try to attend short courses,professional meetings on special topics, andin-house seminars and colloquiums.

The printed literature of statistics, likethat in most professions, is growing at arapid pace. Important developments are of-ten summarized in new books or in enqyclo-pedias such as this Encyclopedia of StatisticalSciences or the International Encyclopedia ofStatistics (Macmillan Publishing Co., NewYork). The Current Index to Statistics*(CIS): Applications, Methods and Theory ispublished annually by the American Statisti-cal Association* and the Institute of Mathe-matical Statistics*. This index providesauthor and subject indexes and aspires torelatively complete coverage of the field ofstatistics. Each volume includes a list of re-lated indexes and information retrieval svs-tems.

ETHICS

"There are three kinds of lies: lies, damn liesand statistics" (Disraeli). "Statistics canprove anything." Sentiments like these repre-sent only part of the ethical problem facedby statistical consultants. Ethical problemsseem to arise more frequently for consultingstatisticians than for many other profession-als partly because consultants tend to workon problems where the outcome is importantyet somewhat in doubt, and where the con-clusions may be contrary to the immediateinterests of the client who funded the consul-tation. Further, in most cases there may notbe a single besr mode of statistical analysis.Add to all these factors a sprinkling of hu-man nature and some honest disagreementsof opinion and it is not surprising that ethi-cal dilemmas arise. Here are some examples.

Example 1. Salaries are being comparedbetween two historically distinct componentsof a university. One group alleges that it isunderpaid; central administration agreesthat this group's pay is lower but attributes itto differences in experience, scholarly pro-ductivity,. academic credentials, and relatedfactors. Both groups agree that a regressionanalysis of salaries, adjusting for such fac-

tors as years of experience, publications, andso on, would be informative. Central admin-istration commissions a study, but when un-favorable results begin to emerge, puts pres-sure on the statisticians to use the modelthat makes the salaries appear to be themost nearly equitable. The statisticians feelthis would be unethical and insist on report-ing several sets of results, explaining thestrengths and weaknesses of each. They tryto be very diplomatic, but realize that theirsincerity may cost them future funding andsupport.

Example 2. In a study of a new medicationa company statistician notices a strong sug-gestion of a possibly serious side effect. Theresult is not Quite statistically significant andto check it would require considerable extraexpense and study. Her employer points outthere is no legal requirement for them tocheck further and company pharmacologistsbelieve that the result is chemically unlikely.The statistician is not quite sure what to do:she knows that events with spurious statisti-cal significance do occur all the time. Shefinally decides to wait and see, keeping awatchful eye on similar situations for anyhint of a recurrent event.

Example 3. An analysis is done for a statedepartment of transportation to check theeffectiveness of its "driver improvement pro-gram" for problem drivers. The study showsthe program has no beneficial effect whatso-ever. A report is written and given to theproject sponsors, who quietly file it awaywhile keeping their multimillion-dollar pro-gram going. Should the statisticians call inthe press? Tell the governor? Or trust thattruth will win out in the long run? Theydecide to work up through channels hopingthat some level of management will recog-nize the potential cost savings available fromabolition of the program.

Examples like these are by no means every-day events, but they do occur often enoughto be a legitimate concern for many consul-

CONSULTING. STATISTICAL I53

tants. For further discussion, see Deming

[7,8], Bross l4l, Science.[14], and the refer-ences contained in these articles.

TEACHING CONSULTING

Many students who obtain degrees in statis-tics go on to become statistical consultants.Yet rarely are departments of statistics pre-

.pared to offer them a program that helpsease the transition between the classroomand the firing line of live consulting. Themost eloquent statement of the problem maywell be that of Box [2]:

Swimming could be taught by lecturing thestudent swimmers in the classroom threetimes a week on the various kinds of strokesand the principles of buoyancy and soforth. Some might believe that on complet-ing such a course of study, the graduateswould all eagerly run down to the pool,jump in, and swim at once. But I think it'smuch more likely that they would want tostay in the classroom to teach a fresh lot ofstudents all that they had learned.

What is thus needed is a means wherebystudents can work actively with good consul-tants and gain experience in being consul-tants under the watchful eye of someonewho can help them see how to do it betterbefore bad habits are developed. Being en-couraged to do some consulting before leav-ing the academic environment also meansthat those who go on to teach statistics willat least have some appreciation of the actualuses of statistics. Many who have studied theproblem believe that statisticians need anintern program such as that of doctors.Some schools offer these, but more areneeded.

Components of a good educational pro-gram for consultants would include ways toimprove interpersonal communication, howto use and keep up with statistical literature,how to analyze data, how to gather gooddata and recognize bad data, how to writegood reports, how to use the computer, and

154 CONSULTING. STATISTICAL

how to develop techniques for nonstandardsituations. The program should overlay allthis with a heavy dose of actual analysis,design, report writing, and consulting.

A very important ingredient of such aprogram would be the actual conduct of aproject involving data gathering and analy-sis. The famous consultant W. E. Demingwrites: "I never lose a chance to get experi-ence with the data; I enumerated a districtin the Census of 1940; I've been out oninterviews at least 40 different times on Cen-sus work, labor force, social surveys, marketresearch; I've used the telephone; I've col-lected data on hundreds of physical andchemical trials and on reliability and testingand inspection in plants; to me this experi-ence is extremely important." Hunter [0]has illustrated the usefulness of a data-gathering project in teaching even beginningstudents the importance of detail and thereal difficulty associated with gathering gooddata. All consultants, and indeed all whoseek to learn from data, need to be aware ofthe fact that many and perhaps most datasets have important errors of the sort thatnegate the effectiveness of any analysis thatdoes not identify them. For example, indus-trial plant data often have startup effects,experiments on mice have cage-related ef-fects, large data bases have computer pro-cessing errors, flowerpots get interchanged,and human beings make recording errors.

REWARDS OF CONSULTING

Most consultants gain enormous satisfactionfrom their work. Even young consultantshave an opportunity to play a large andoften decisive role in major decisions. Theyare asked to help plan the data gatheringthat will be used in making important de-cisions-then they are asked to analyze thedata and help make decisions.

Statistical consultants are continuallylearning about new fields-from the micro-biology of DNA to the relative accidentrates of twin-bed to single-bed trailer trucks.Much of statistics is like detective work.

Consultants search for hidden clues in thedata or the theory behind the data to findout what might have happened. Then aftermuch hard digging, there is the joy of under-standing, followed by the challenge of howto make the results clear to others.

References

tl l Boen, J. and Fryd, D. (1978). Amer. Statist.,32,58-60.

[2] Box, G. E. P. (1979). J. Amer. Statist. Ass.,74,l-4.

t31 Box, J. F. (1978). R. A. Fisher, The Life of aScientist. Wiley, New York.

141 Bross, I. D. J. (1974). Amer. Statist.,28, 126-127.

[5] Cameron, J. M. (1969). Technometrics, ll, 24'I-254.

t6l Daniel, C. (1969). Technometrics, ll,24l-245.

I7) Deming, W. E. (1965). Ann. Math. Stat ist. ,36,1883-1900. (A very careful and detailed state-ment of the statistician's and the client's responsi-bilities. Highly recommended for study. See alsoits references.)

t81 Deming, W. E. (1972). Int. Statist. Rev., 40,215-219. (A leading private consultant's code of eth-ics.)

[9] Efron, B. (1979). SIAM Rev., 21, 460-480.

UOl Hunter, W. G. (1977). Amer. Stat ist. ,3l, 12-17.(A convincing demonstration that students cangain considerable benefit from actually doing ex-periments.)

I l ] Kimball , A. W. (1957). J. Amer. Stat ist. Ass.,57,133-142.

[2] Marquardt, D. W. (1979). Amer. Stat ist. ,33, 102-107- (An excellent summary of the exciting role ofa "totally involved" consultant.)

[3] Salsburg, D. S. (1973). Amer. Statist.,27, 152-154.

ll4l Science (1977). 198, 677-705. (A series of articleson the ethics of medical experimentation, includ-ing statistical aspects.)

[5] Snee, R. D., Boardman, T. J., Hahn, G. J., Hill,W. J., Hocking, R. R., Hunter, W. G., Lawton,W. H., Ott, R. L. and Strawderman, W. 8.,(1980). A mer. Statist., 34, 65-75. (Recommenda-tion for graduate training of consultants.)

[6] Tanur, J. M., Mosteller, F., Kruskal, W. H., Link,R. F., Pieters, R. S., and.Rising, G. R. (1978).,Srdrrs/r'c.r: A Guide to the Unknown, 2nd ed. Hol-den-Day, San Francisco. (Fireside reading of ex-citing statistical applications.)

[7] Woodward, W. A., and Schucany, W. R. (1977).Biometrics,33, 564-565. (A nearly complete bibli-ography on the s_ubject through 1977.)

[8] Zahn, D. A., and Isenberg, D. J. (1980). 1979

Proceedings oI lhe Section on Statistical Education,

American Statistical Association, Washington, D.

C., pp. 6'1-72. .

Acknowledgments

In writing this article I have benefited enormously from

the detailed and helpful comments of many. I would

particularly like to thank T. A. Bancroft, Joan Fisher

Box, W. Edwards Deming, Dennis Friday, Bert Gunter,

Gerald J. Hahn, Ellis R. Ott, Ronald D. Snee, Douglas

Zahn, and especially Alison K. Pollack.Others who made important contributions include

James R. Boen, George E. P. Box, Cathy Campbell,

John Crowley, William G. Hunter, Kevin Little, Peter

M. Piet, Gerald van Belle, Donald Watts, and virtually

all members of the Wisconsin Statistical Laboratory.

The patient and skillful typing and retyping by Debbie

Dickson was also critical.None of these people agrees completely with every-

thing I have said.This work was in part done at the UW Mathematics

Research Center and thus was supported in part by the

U. S. Army under Contract DAAG29-75-C-ffi24.

(BTOSTATISTTCSCLINICAL TRIALSCOLLECTION OF DATACOMPUTERS AND STATISTICSDEMOGRAPHYECOLOGICAL STATISTICSENGINEERING STATISTICSEXPLORATORY DATA ANALYSISGEOSTATISTICSGRAPHICAL REPRESENTATION

OF DATAPRINCIPLES OF PROFESSIONAL

STATISTICAL PRACTICESTATISTICAL EDUCATIONSTATISTICS IN (various fields))

BrueN L. JorNnn

CONSUMER PRICE INDEX

The Consumer Price Index (CPI) is a mea-sure of the changes in prices paid by urbanconsumers for the goods and services theypurchase. Essentially, it measures the pur-chasing power of consumers' dollars by com-paring what a sample "market basket" ofgoods and services costs today with what thesame market basket would have cost at an

CONSUMER PRICE INDEX 155

earlier date. The CPI is compiled and re-leased monthly by the Bureau of Labor Sta-tistics (BLS).

UNIVERSE AND CLASSIFICATION

In 1978, the BLS began publishing two sepa-rate CPIs: (l) a new CPI for All UrbanConsumers (CPI-U), which covers about807o of the total civilian noninstitutionalpopulation, and (2) a revised CPI for UrbanWage Earners and Clerical Workers (CPI-W), which represents about half of the popu-lation covered by the CPI-U.

The CPI is based on prices of food, cloth-ing, shelter, fuels, transportation fares,charges for doctors' services, drugs, andother goods and services that people buy forday-to-day living. Individual indexes arepublished for over 300 different expenditureclasses. Separate indexes are also publishedfor 28 local areas. Area indexes do not mea-sure differences in the level of prices amongcities; they measure only the average changein prices for each area since the base period.

THE INDEX

The Consumer Price Index is calculated us-ing a modified Laspeyres index of the gen-eral form

, . - (2 ,P , , ,20 . , ) " ,00 ,

' t - \ ; rn ,Qo, ,J . " - - '

where

1r : index for period I

P1.i, Ps.;: prices for item i in periods I and 0,

respectively

Qe,, : quantity of item i sold in period 0

(the base period)

These indexes may be viewed as measuringthe price change of a constant set of con-sumption through time. Item weights arebased on the Consumer Expenditure Survey(most recently for 1972-1973).