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WILLIAM GEMMELL COCHRAN
July 15, 1 909-March 29, 1980
BY MORRIS HANSEN AND FREDERICK MOSTELLER
WILLIAM GEMMELL COCHRAN was born into modest
circumstances on July 15, 1909, in Rutherglen, Scot-
land. His father, Thomas, the eldest of seven children, had
begun his lifetime employment with the railroad at the age
of thirteen. The family, consisting of Thomas, his wife ican-
nie, and sons Oliver and William, moved to Gourock, a hol
iciay resort town on the Firth of Clyde, when William was six,
and to Glasgow ten years later.
Oliver has colorful recollections of their childhood. At age
five, Willie (pronounced Wully), as he was known to family
and friends, was hospitalizecI for a burst appendix, and his
life hung in the balance for a day. But soon he was home,
wearying his family with snatches of German taught him by
a German patient in his nursing-home warcI. Willie hacI a
knack for hearing or reacting something and remembering
it. Oliver recalls that throughout his life, Willie wouIcl walk
or sit around reciting poems, speeches, advertisements, mu-
sic hall songs, and in later life oratorios anc! choral works he
was learning.
Until Willie was sixteen, the family livect in an apartment
known in ScotIand as a "two room and kitchen" a parIor-
cum-ctining room (usect on posh occasions, about twelve
times a year), a bedroom usect by the parents, and a kitchen.
.
.
61
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BIOGRAPHICAL MEMOIRS
In the kitchen foot! was prepared, cooked, served, and eaten;
dishes were washed, laundry done, friends entertained, anct
homework accomplishecI. It was also the boys' bedroom in
the form of an alcove-with-bed known as "the-hole-in-the-
wall." The boys had a happy chilc~hoocI, with mile-Ion" walks
to and from public school twice a clay (lunch was eaten at
home) anc! play at the oceanside.
Willie was a great achiever in school, usually coming in
first. Oliver feels he hac! an irresistible urge to be first, often
calculating closely just how much he would have to do to gain
that enct. Oliver recalls being worrier! about passing a profes-
sional exam and having Willie say to him: "l don't know what
on earth you're worrying about; you only have to pass, ~ have
to be first." He was referring to the Bursary Competition,
open to all scholars in Scotland. And he was first, winning
his fees to Glasgow University. Later he was in an even larger
competition for the George A. Clark Scholarship, which pro-
videcI support for four years and paid his Cambridge fees.
Without winning these competitions, he almost assuredly
wouIcl not have been able to attend either Glasgow or Cam-
bridge.
Willie tract no absorbing hobbies as a boy, although he
dabble(1 in many things. Cycling, hiking, ant! walking in the
hills were his chief physical activities. Later, studying and
reading became primary. His scholastic prowess won him
many books as prizes and created an extensive home library.
Cochran graduated with the M.A. from Glasgow in 1931
with first class honors in mathematics and natural philosophy
(physics) and shared the Logan Medal for the most distin-
guishe(1 graduate in the Arts Faculty. That same year he en-
terec] St. John's College, Cambridge, anct stuclied for the
mathematics tripos (mathematics major) as a prelude to be-
coming a research student. As an elective, he chose a new
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WILLIAM GEMMELL COCHRAN
63
course, Mathematical Statistics, taught by John Wishart. A
fellow student believes that the Great Depression had inter-
estect him in the work of a Dr. Mess, who advocated thorough
mathematical investigation of economic problems. He was
doubtless also influenced by R. A. Fisher's work at this time.
By now he hac} dropped the use of Willie, and among his
colleagues he was known as Bill.
Bill was persuaclect by Frank Yates to leave Cambridge
without his doctorate to accept a position, a rare opportunity
in the depression year of 1934, to do practical research at
Rothamstec] Experimental Station. Cochran never die! re-
ceive an earned doctorate, although he received honorary
degrees from The University of Glasgow (1970) ante
Johns Hopkins University (19751.
During his six years at Rothamstect, Cochran pioneered
with Yates in cleveloping techniques for analyzing replicatecl
anc! long-term agricultural experiments and for assessing the
effects of weather patterns on crop yielcis. They also studied
selection effects in non-ranclom sampling.
At RothamstecI, Cochran gainer! a great deal of practical
experience anct became well known in his fielcI. In 1937 he
marries! Betty I. M. Mitchell, a plant pathologist.
After visiting Iowa State College (now University) in Ames
in 1938, Cochran agreed to return there the following year
to teach. The imminence of war in 1939 made him hesitate
to leave Europe, but he felt he must keep his worct. Uncler
George Snedecor, in 1939 {owe State was a center for statis-
tical treatment of experimental work at a time when mocl-
ern applied statistics had little foothold in America. The em-
phasis in applied statistics at Iowa was then on sample surveys
anct experimental design. Cochran lectured on both topics in
his first quarter, and these lecture notes matured over the
next ten years into his two well-known texts on these topics.
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BIOGRAPHICAL MEMOIRS
Two of Cochran's three children were born in Ames, Eliza-
beth in 1940 and Alexander Charles in 1942.
In 1943-44 Cochran took leave to join the Princeton Sta-
tistical Research Group at Princeton University as a research
mathematician. He was to work on Army-Navy research
problems, including naval warfare and a survey of bomb ef-
ficiency, for the Office of Scientific Research and Develop
ment.
At Iowa State, Cochran ant! Gertrude Cox initiated their
collaboration, which culminated in their book Experimental
Design, published in 1950. In 1946, at Cox's instigation, Coch-
ran left Iowa to organize and head the graduate program in
experimental statistics at North Carolina State College at Ra-
leigh. Cox envisioned this program as half of the Institute of
Statistics, the second part consisting of a Department of
Mathematical Statistics at the University of North Carolina at
Chapel Hill, headed by Haroict Hotelling. The Cochran's
third child, Theresa, was born in North Carolina in 1946.
In January 1949 the Cochrans moved to Baltimore, where
Bill became head of the Department of Biostatistics in the
School of Hygiene and Public Health at The Johns Hopkins
University. Here his interest in medical and health problems
increased. Bill published a second book, Sampling Techniques
(19531. His two books along with his 1967 revision, at Sne-
decor's request, of Snedecor's Statistical Methods-became im-
portant reference texts and were widely translatecI. Statistical
Methods is one of the most wiclely cited books in the scientific
literature.
In 1957 the Department of Statistics was organized at
Harvarc! University, and Cochran joined the stab, remaining
nineteen years until he became professor emeritus in 1976.
During his time at Harvarcl, his continual interest in biosta-
tistics was reflected in his interaction with the Department of
Biostatistics in the Harvard School of Public Health.
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WILLIAM GEMMELL COCHRAN
COCHRAN S WORK
65
In discussing Cochran's scientific work, we open with his
most famous theorem, anc! follow with selections of his work
on the design and analysis of comparative investigations, with
both experiments ant! comparative observational studies.
After an overview of his work on counter! ciata, we present
some of his contributions to the theory ancT practice of
sample surveys, follower! by brief mention of other areas of
work. With a few exceptions, we emphasize his advice and
philosophy rather than the details of his technical work.
Cochran's first paper (1934), a mixture of algebra and
analysis, brought into mathematical statistics an extremely
valuable and widely used result, now called Cochran's Theo-
rem: ~ Let Xj, j = ~ ,2, . . . ,p, be inclepenclent stanciarc! normal
ranclom variables with sum of squares Q. Let Q be clecom-
posect into the sum of k quadratic forms Q2, where Qi has
rank ri, i = I,2, . . . ,k. Then if one of the following three
k
conditions hoIcis, so clo the other two: (a) ~ ri = p, (b) each
i = ~
Qi has a chi-squarecl distribution, and (c) each Qi is indepen-
dent of every other.
Cochran (1934) himself exploited this result to show that
analysis of variance can be extenclec] to a variety of situations
requiring adjustment for covariates.
DESIGN AND ANALYSIS OF COMPARATIVE
INVESTIGATIONS
Agriculture. Over the years, sets of Cochran's papers fo
cusecI on methods of value to many applied areas, including
agriculture and biomeclical research. At Rothamstec! he ex
' The form cited is suggested by Maurice G. Kendall and Alan Stuart, The Ad-
vanced Theory of Statistics, 2d ea., vol. 1 (New York: Hafner Publishing Company,
1 963), 360-6 1.
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BIOGRAPHICAL MEMOIRS
posited new clevelopments in lattice designs, attributing the
general method to Frank Yates. These clesigns help breeders
of wheat, soybeans, corn, and small grains by permitting
comparisons of large numbers of varies es (squares being
preferable, such as 49, 64, 8l, 100, ...~. He compares the
performance of these designs with that of others (1941a,
194 1 b, 1 943b).
Along with the descriptions of the methods and their
strengths and weaknesses, Cochran continually emphasized
the computational effort required in the analysis and the im-
portance of being able to communicate the ideas to the in-
vestigator. Why shouIc] the half-day or day of calculation
required for the analysis be of much concern when an agri-
cultural investigation has already required considerable land
for much of a season and several workers to carry it out?
Perhaps Cochran realizect that a computation that took him
half a clay might leave a breeder helpless. He was therefore
eager to reassure the breeder of its feasibility. Indeed, he said
(1941a, p. 355), "Extra complication in the statistical analysis
may be a drawback to the widespread use of a design in other
respects. If the experimenter floes not clearly unclerstand the
assumptions involved in the statistical manipulations, or the
reasons for them, he loses confidence in the final results of
the calculations."
In several papers, Cochran gave substantial reviews in-
tended to guide experimentation in specialized subject mat-
ters. For example, just before leaving the United Kingdom
for the U.S.A., he presented a major review paper (1939a)
on the design and analysis of long-term agricultural experi-
ments that won plaudits during discussion from Sir John
Russell, R. A. Fisher, l. Wishart, F. Yates, M. S. Bartlett, M. G.
Kendall, and H. O. Hartley. Cochran clealt not only with for-
mal design and analysis considerations but also with impor-
tant features of the practical execution of these trials in the
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WILLIAM GEMMELL COCHRAN
67
fielct: size and shape of plots, numbers of replications, choices
of stratification or blocks, heacIlands and guard rows between
plots, ant] the value of a year or two of a uniformity trial
prior to a long-term field experiment, especially for a new
crop. And he warner! the statistician, "It is not sufficient for
him Ethe statistician] to provide the best possible clesign to
suit the size of the experiment; it is also his duty to acivise
whether he thinks the experiment as clesignecI is worth
cloing, or whether it should be postponed until more re-
sources are available" ~ ~ 939a, p. ~ 061.
With Gertrude Cox (1946a), he summarized the principal
sources of variation in greenhouse experimentation (temper-
ature, moisture, and shading gradients) and major designs
~c Luau eo~ for such sometimes nearly overwhelming
variables. Curiously, in 1946 they reported that they had no
information about the possible benefits of moving pots
around, although this is one advantage of the greenhouse
over fielcI conditions.
His article in the International Encyclopedia of Statistics
(197Sb) on experimental design contains an instructive post-
script on the rise of the use of experiments in the social sci-
ences and the encouragement given to this movement by the
Social Science Research Council. That postscript relates more
generally to his stucly (1976) of the history of experimenta-
tion. After introducing us to Arthur Young's total intolerance
for any method but comparative experiments, Cochran notes
(1976, p. 5), "This issue persists today. In reviewing the pres-
ent state of knowledge about the relative merits of two ther-
apies for hospitalizect patients, we may finct a few well-
controlled experiments and a larger number of doctor's
observations on their experiences with one or the other ther-
apy. Young wouIc! seem to suggest that to consider the latter
group is a waste of time."
Cochran used the history article to include a little instruc
,] ~, ~
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BIOGRAPHICAL MEMOIRS
tion on experimental design, as well as to get in a few licks
about some consulting problems he tract su~erecl. He sug-
gested that most consulting statisticians will have had expe-
rience with an investigator who begins "'I want to do an ex-
periment to show that....' He knows the answer." Cochran
user! this remark as a springboard to discuss double-blind
experiments. In a similar aside, Cochran used James John-
ston's book on agricultures to make an aclctitional point. After
describing Tohnston's position that a bad investigation wastes
money and leads to incorrect results in standard! textbooks,
as well as to the neglect of further research, Cochran said
(1976, p. 9), "I have hear(1 this point made recently with re-
gard to medical experiments on seriously ill patients, where
there is often a question for the doctor if it is ethical to con-
duct an experiment, but from the broader view-point fit is]
a question of whether it is ethical not to conduct experi-
ments."
Cochran used history to console the young scholar. Upon
recalling that after Student's t tables had been available for
fourteen years anti practically no one used them, he said,
"Young research workers who feel that the world is very slow
to appreciate their results might be heartened by this ex-
ample. The world is indeec! a little slow at times to realize
how brilliant we are" (1976, pp. 13-141. He sums up the
history of statistics in agriculture by saying that it took a cen-
tury to take two major steps: (~) to begin applying probability
theory (already available in astronomy) to interpret quanti-
tative experiments and (2) to establish efficient practical
methods for the concluct of field experiments.
Bioassay. A sequence of papers (three with Miles Davis:
1963 1964, 1965a; and 1973) reported on Cochran anti Dav
23. F. W. Johnston, Experimental Agriculture, Being the Results of Past and Suggestions
for Future Experiments in Scientific and Practical Agriculture (Edinburgh: W. Blackwood
and Sons, 1849).
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WILLIAM GEMMELL COCHRAN
69
is's studies of bioassay, where the investigator wants to find
the LD50, the dosage that kills 50 percent of the animals or
insects. They stucliect sequential approaches using a grid of
dosages. Animals are tested at an initial close, ant! the out-
come at that dose guides the choice of the next close up or
clown. In one version, if the first close kills, the second close
is one step smaller; if it does not, the next animal gets a close
one step higher. This process continues. They recommendec!
a two-stage approach. The first stage uses few animals with
large steps until it locates a reversal, and the second stage
uses the Robbins-Munro method with smaller steps.
Clinical Trials. His papers on the design of clinical trials
(1961a, 1977b) had a rather general nature. In the first
(1961a), he emphasized heavily the value of precise protocol,
power, blindness, randomization, and design. The biostatis-
tician of the ~ 980s-with special survival analyses, sequential
designs, ant! balancing approaches-might be surprised,
even affronted, to react ~ ~ 96 ~ a, p. 7 ~ ): "The planning and
conduct of a clinical trial cloes not involve any difficult or
esoteric intellectual principles. It is mainly a matter of hare!
work anc! attention to detail."
The second paper (1977b) was a group effort focused on
surgical experiments in cluoclenal ulcer. Although Cochran
hac! suffered a substantial illness, he was essentially recov-
erecI, but he did not want to take on any extra tasks. Conse-
quently he refused to take part in a working group in the
Faculty Seminar on Health and Medicine at the Harvard
School of Public Health. But students and friends pleaded
with him to change his mincI, and in the end he chaired the
Working Group on Protocol Issues. After two years of dis-
cussions in depth of the principal experiments in surgery for
duodenal ulcer, the group proclucect a comprehensive list of
medical and statistical criteria for consideration in further
experiments. Most of the criteria have value for design, anal
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BIOGRAPHICAL MEMOIRS
ysis, anc! reporting of comparative medical investigations
generally, notjust for surgery for cluo(lenal ulcer. Again, care
and precision in protocol were emphasized. The lists cannot
be reproclucect here, but a remark on follow-up to obtain
information on nearly 100 percent of patients treated is
worth quoting (1977b, p. 1911: "A search produced few ref-
erences to available techniques for guarding against follow-
up tosses. There seems to be no substitute for determination."
They reported that at the Mayo Clinic high rates of follow-
up have been "achieved by writing letters ctirectly to patients
and not going through their doctors; if no reply is forth-
coming, the telephone is used. If the patient is not found, a
vigorous search is undertaken, inclucting use of bill-collecting
agencies, who apparently have experience with similar prob-
lems" (1977b, p. 191).
Observational Studies. Program arrangers often asked
Cochran to provide a substantial general paper on the con-
cluct of comparative studies intended to decicle causation. In
discussing the advantages of matching subjects or materials
as compared with the use of covariance adjustment in obser-
vational studies, he first notes! that the methods perform al-
most equally well. "A clifficulty which ~ have occasionally en-
counterec! with covariance is that some scientists have an
inborn suspicion of adjustments to the ciata, and although
the adjustments made in the covariance analysis are entirely
objective, they may finct a rather gruciging acceptance" ~1953,
p. 6871. (Although Cochran correctly stated that, given least
squares, the adjustment itself is objective, the decision to
make it usually is not; when many covariables are available,
many subsets can be selected. The suspicious scientist has a
right to some skepticism because an investigator couIcl adjust
for the subset that gave results most pleasing to him or her.
Nevertheless, when the covariables for adjustment are cho-
sen in advance of the investigation, the method is objective.)
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WILLIAM GEMMELL COCHRAN
79
rules for establishing strata boundaries by comparing them
empirically for several different forms of populations with
varying amounts of skewness. In 1962 he jointly authored,
with J. N. K. Rao and H. O. Hartley, a paper that proposed
a simple procedure for unequal probability sampling without
replacement. This approach hacI the advantages of simplicity
of calculation and the ability to provide unbiased estimates
of the variance of the estimators. This was a topic that re-
ceivec! considerable attention at the time, and a number of
different procedures were proposer! by various authors.
The problem of nonsampling errors in surveys is one that
has received extensive attention, and in 1968 Cochran pre-
parect a review paper and extenclect some of the earlier work
that had been done in this area. He concluded, as clo others,
that errors in measurement can sometimes seriously vitiate
most stanciard statistical techniques anti at other times have
only trivial effects clepencting on the size of the relevant
response variances ant! covariances. He adclec! that what
seems neecled at the present state of development of this area
are many studies that permit the estimation of these vari-
ances and covariances, and that most of these studies should
be embedcled in ongoing surveys. "When an 'errors of mea-
surement' stucly has to be conducted separately, as will some-
times be necessary because of the complexity of such studies,
it is always difficult to reproduce the working conditions of
an actual survey" (1968, p. 665~.
In "Laplace's Ratio Estimator" (1978a), Cochran took an
engaging historical tour. He reviewed the well-known esti-
mate made by Laplace in 1802 of the total population of
France. Laplace took a sample (by purposive sampling pro-
ceclures) of communes in France and persuacled the govern-
ment to have a population census taken in each of these.
Births were registered throughout France, and therefore
were known for each commune as well as the country as a
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BIOGRAPHICAL MEMOIRS
whole. He then estimated the total population of France with
the ratio estimator Y = Xy/x where X is the known total reg-
isterecI births, x is registered births for the sample communes,
and y is the total population for the sample communes. The
estimate was 28.4 million. L~aplace then estimated the stan-
ciard error of this estimate to be 108,000. In computing the
estimated sampling error, Laplace assumed that the birth
rate in each commune (and of course in all of France) was
the consequence of sampling births and population at ran-
dom with equal probability from the same urn, a finite su-
perpopulation.
Cochran reported: "He found the large-sample ctistribu-
tion of his error of estimate to be approximately normal, with
a small bias and a variance that he calculates" (1978a, p. 31.
Cochran then points out that in computing the sampling~er-
ror Laplace failecI to recognize that the birth rates in the
sample and in all of France were not independent, ant! states
in a summary remark:
It is unfortunate that Laplace should have made a mistake in proba-
bility in a book on the theory of probabilities. In his application, however,
the mistake was of little consequence. His working out of the large-sample
distribution of the ratio estimator and his concept of the superpopulation
as a tool in studying estimates from samples are pioneering achievements.
(1978a, p. 10)
Cochran wrote a number of review papers related to
sample-survey topics (1938b, 1947, 1951, 1956) that pro-
vided lucid summaries of the state of the art at the time the
papers were written ant! gave acictitional interpretations. Of
course his textbook, Sampling Techniques, is a substantially
comprehensive summary, with extensions of theory to round
out topics and with reporting of empirical results to provide
better guidance on practical implications of some of the
methods. It is unctoubtedly the most wiclely used textbook in
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WILLIAM GEMMELL COCHRAN
81
teaching sample surveys, as is attested by the printing of sec-
ond and third editions in 1963 and 1977.
COCHRAN S OTHER CONTRIBUTIONS
TO STATISTICS AND TO SOCIETY
Cochran suggested that statisticians might profitably con-
duct a survey to finct out how scientists use statistical tech-
niques and how they are helped by them. He thinks it "might
be very illuminating to statisticians if it couIcT be carried out
despite the obvious difficulties. Statisticians are, ~ think,
rather quick to jump to conclusions about the kinds of prob-
lems which scientists in other fields are supposec! to face, anc!
about their presumer! uses and misuses of statistical methods
and ideas" ( 1952, pp. 334-351. Because he was writing in the
Annals of Mathematical Statistics, he probably felt he was speak
. . . .
sing only to the statisticians.
Having illustratecl Cochran's propensity for returning to
problems repeatecIly, we shall not review all the topics where
he carried on such a program. Instead we merely mention
that these incluclecI: (a) the problem of weighting to combine
results from several comparable experiments (for example,
when the effects in the different experiments did not neces-
sarily have the same true means or previsions and when pre-
cisions neeclec! to be estimated); (b) the problems associates!
with both qualitative ant! quantitative ctiscriminant functions;
(c) the use of covariates in experiments and observational
studies; (cI) the effect of errors of measurement on regres-
sion, analysis of variance, and the analysis of counted ciata;
anti (e) special analyses for detecting outliers, for handling
missing observations, for acIding or removing a variable in
regression, or for comparing scales of measurement.
Cochran was an exceptional teacher, beloved by his stu-
dents. He directed four dissertations at North Carolina,
fifteen at Johns Hopkins, ant! nineteen at Harvard. In acicli
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BIOGRAPHICAL MEMOIRS
tion he greatly influenced a large number of other students.
They recall his clarity, wit, willingness to help, and use of
practical examples culled from his experience. As one said,
Bill "pulled it all together in a way that made it fun to cal-
culate coefficients ant! to invert matrices. We wanted to do it
because Bill would have been clisappointect if we failed."
Bill had a great ability to get to the heart of any statistics
problem with virtually no time lost. He was succinct and clear
in his teaching and writing. He worked with his graduate
students to try to make them understand where the problem
formulation and inductive statistics enclect and the clecluctive
mathematics began. Bill displayer! the great knack for linking
the theoretical and the applied that Americans associate with
statisticians trained in the United Kingdom, and he was able
to explain complicatect statistical information to investiga-
tors in language they could unclerstancl. Consequently he
was a much sought-after consultant anct an excellent com-
mittee member or head. His calm fairness anct down-to
earth attitude assurer! attention to dealing with the core
problem.
Cochran limitecI his committee participation to the
amount of work he could hancIle. He chaired the committee
appointed by the American Statistical Association at the re-
quest of the National Academy of Sciences to review the Kin-
sey, Pomeroy, and Martin stucly of sexual behavior in the hu-
man male, work that resulted in a book (1954a). He served
as chairman of the Pane! of Statistical Consultants, U.S. Bu-
reau of the Census. He server! on the committee to consider
the effect of battery additives on the life of batteries, on the
Academy Committee to the Atomic Bomb Casualty Commis-
sion, and on the Committee on Epidemiology and Biometry
at the National Institutes of Health. The Subcommittee on
National Morbidity Survey of the U.S. National Committee
on Health Statistics, of which he was a member, submitted a
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W I L L I A M G EM M E L L C O C H RA N
83
report to the Surgeon General that was the basis, with little
change, of the National Health Survey Act. A smoker, Bill
was the only statistician on the Surgeon General's Committee
on Smoking and Health.
Bill received many honors. He was at various times pres-
iclent of four major statistical organizations: the Institute of
Mathematical Statistics in 1946, the American Statistical As-
sociation in 1953, the Biometric Society (which he helpecI
found as a member of the organizing committee) in 1954-
55, ant! the International Statistical Institute in 1967-71. He
was elected to the American Academy of Arts and Sciences
in 1971 ant! to the National Academy of Sciences in 1974.
He was a fellow of the American Association for the Acivance
ment of Science; honorary fellow of the Royal Statistical So-
ciety; ant! Guggenheim fellow, 1964-65. He received the
Guy Medal of the Royal Statistical Society in 1936, the S. S.
Wilks Memorial Medal (American Statistical Association) in
1967, and the "Outstanding Statistician" Award (Chicago
Chapter, American Statistical Association) in 1974. He was
editor of the Journal of the American Statistical Association from
1945 to 1950.
Personally, Bill was an unpretentious man with Scottish
wit and humor. He was a believer in the fellowship of man,
and one of the few things sure to elicit his anger was a bigoted
comment. Although he preferred to work by himself rather
than to collaborate with others, he was friencIly to everyone
and liked by all. He and his wife Betty, to the delight of col-
leagues anti students, entertained frequently, and enjoyed
square ciancing, theater, music, and travel. Hundreds of sta-
tisticians from far-flung places attended Bill's retirement clin-
ner in ~ 976.
The last several years of Bill's life were plagued with a
series of medical problems. Nonetheless, after his retirement
anc! his move to his Cape Cod home, he continued to travel,
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BIOGRAPHICAL MEMOIRS
to teach, and to write. He died in OrIeans, Massachusetts, on
March 29, 1980.
WE APPRECIATE THE ADVICE AND SUPPORT of his wife Betty
Cochran and brother Oliver Cochran, and of colleagues Arthur P.
Dempster, John Emerson, Katherine Godfrey, David C. Hoaglin,
Augustine Kong, Erich Lehmann, Lincoln E. Moses, Marjorie O1-
son, Katherine Taylor-Halvorsen, and Cleo Youtz. We have also
benefited from correspondence with Richard L. Anderson and
Geoffrey Watson and from their writings about Cochran cited in
the references.
REFERENCES
Anderson, R. L. William Gemmell Cochran 1909-1980, A Per-
sonal Tribute. Biometrics, 36(19801: 574-78.
Dempster, Arthur P., and Frederick Mosteller. In Memoriam. Wil-
liam Gemmell Cochran 1909-1980. The American Statistician, 35,
no. 1~19811:38.
Dempster, Arthur P., Margaret Drolette, Myron Fiering, Nathan
Keyfitz, David D. Rutstein, and Frederick Mosteller (chairman).
Faculty of Arts and Sciences-Memorial Minute, W. G. Coch-
ran. Harvard Gazette (3 December 19821:4.
Watson, G. S. William Gemmell Cochran 1909-1980. The Annals of
Statistics, 10~1982~: 1-10.
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WILLIAM GEMMELL COCHRAN
SELECTED BIBLIOGRAPHY
1934
85
The distribution of quadratic forms in a normal system, with ap-
plications to the analysis of covariance. Proc. Cambridge Philos.
Soc., 30:178-91. L11
1936
a. The statistical analysis of field counts of diseased plants. i. R.
Stat. Soc., Ser. B (Suppl.), 3:49-67. L4]
b. With D. }. Watson. An experiment on observer's bias in the se-
lection of shoot-heights. Emp. J. Exp. Agric., 4~13~:69-76. F5]
c. The of distribution for the binomial and Poisson series, with
small expectations. Ann. Eugen., 7:207-17. F61
1937
The efficiencies of the binomial series tests of significance of a
mean and a correlation coefficient. l. R. Stat. Soc., Ser. A,
100:69-73. [9]
1938
a. An extension of Gold's method of examining the apparent
persistence of one type of weather. Q. }. R. Meteorol. Soc.,
64:631-34.
b. The information supplied by the sampling results. Ann. Appl.
Biol., 25:383-89. L12]
c. Crop estimation and its relation to agricultural meteorology. I.
R. Stat. Soc., Ser. B (Suppl.), 5:1-45. t151
1939
a. Long-term agricultural experiments. i. R. Stat. Soc., Ser. B
(Suppl.), 6:104-48. L18]
b. The use of the analysis of variance in enumeration by sampling.
}. Am. Stat. Assoc., 24:492-510. F191
1940
a. The analysis of variance when experimental errors follow the
Poisson or binomial laws. Ann. Math. Stat., 11 :335-47. L22]
NOTE: The numbers in brackets at the end of each entry correspond to the number
given that paper in Contributions to Statistics, 1982.
OCR for page 86
86
BIOGRAPHICAL MEMOIRS
b. The estimation of the yields of cereal experiments by sampling
for the ratio of grain to total produce. I. Agric. Sci., 30:262-75.
F23]
1941
a. Lattice designs for wheat variety trials. }. Am. Soc. Agron.,
33:351-60. [24]
b. An examination of the accuracy of lattice and lattice square
experiments on corn. Iowa Agric. Exp. Stn. Bull., 289:397-415.
F27]
1942
a. Sampling theory when the sampling-units are of unequal sizes.
I. Am. Stat. Assoc., 37:199-212. L28]
b. The X~ correction for continuity. Iowa State Coll. I Sci.,16:421
36. L29]
1943
a. Analysis of variance for percentages based on unequal num-
bers. }. Am. Stat. Assoc., 38:287-301. L331
b. Some additional lattice square designs. Iowa Agric. Exp. Stn.
Bull., 318: 729- 48. L34]
1946
a. With Gertrude M. Cox. Designs of greenhouse experiments for
statistical analysis. Soil Sci., 62: 87-98. F361
b. Relative accuracy of systematic and stratified random samples
for a certain class of populations. Ann. Math. Stat., 17: 164-77.
t38]
1947
Recent developments in sampling theory in the United States. Proc.
Int. Stat. Conf., 3:40-66. F401
1950
The comparison of percentages in matched samples. Biometrika,
37:256-66. L43]
1951
Modern methods in the sampling of human populations. Am. I.
Public Health, 41:647-53. F46]
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WILLIAM GEMMELL COCHRAN
1952
The x'2 test of goodness of fit. Ann. Math. Stat., 23:315-45. F491
1953
87
Matching in analytical studies. Am. I. Public Health, 43:684-91.
F52]
1954
a. With Frederick Mosteller and John W. Tukey. Statistical Problems
of the Kinsey Report on Sexual Behavior of the Human Male. Wash-
ington, D.C.: American Statistical Association.
b. Some methods for strengthening the common x2 tests. Biomet-
rics,10:417-51.~591
1956
Design and analysis of sampling. In: Statistical Methods, ed. George
W. Snedecor, pp. 489-523. Ames: Iowa University Press. L631
1957
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With Gertrude M. Cox. Experimental Designs, 2d ed. New York: John
Wiley.
1961
a. Designing clinical trials. In: Evaluation of Drug Therapy, ed. F. M.
Forster, pp.71-77. Madison: University of Wisconsin Press. L701
b. Comparison of methods for determining stratum boundaries.
Bull. Int. Stat. Inst., 38:345-58. t721
1962
With i. N. K. Rao and H. O. Hartley. On a simple procedure of
unequal probability sampling without replacement. J. R. Stat.
Soc., Ser. B. 24:482-91. L75]
1963
With Miles Davis. Sequential experiments for estimating the mean
lethal dose. In: Le Plan d'Experiences, pp. l 81-94. Paris: Editions
du Centre Nationale de la Recherche Scientifique. t781
1964
With Miles Davis. Stochastic approximation to the median effective
dose in bioassay. In: Stochastic Models in Medicine and Biology, ed.
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BIOGRAPHICAL MEMOIRS
John Gurland, pp. 281-300. Madison: University of Wisconsin
Press. L82]
1965
a. With M. Davis. The Robbins-Munro method for estimating the
median lethal dose. I. R. Stat. Soc., Ser. B. 27:28-44. F841
b. The planning of observational studies of human populations.
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1967
Planning and analysis of non-experimental studies. In: Proceedings
of the Twelfth Conference on the Design of Experiments in Army Re-
search and Testing, AItO-D Report 67-2, pp. 319-36. Durham,
N.C.: U.S. Army Research Office. L88]
1968
Errors of measurement in statistics. Technometrics, 10:637-66.
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1972
Observational studies. In: Statistical Papers in Honor of George ~
Snedecor, ed. T. A. Bancroft, pp. 77 - 90. Ames: Iowa State Uni-
versity Press. L971
1973
Experiments for nonlinear functions (R. A. Fisher Memorial Lec-
ture). l. Am. Stat. Assoc., 68:771-81. L991
1976
Early development of techniques in comparative experimentation.
In: On the History of Statistics and Probability, ed. D. B. Owen, pp.
3-25. New York: Marcel Dekker. F1051
1977
a. Sampling Techniques, 3d ed. New York: John Wiley & Sons.
b. With Persi Diaconis, Allan P. Donner, David C. Hoaglin, Nich-
olas E. O'Connor, Osler L. Peterson, and Victor M. Rosenoer.
Experiments in surgical treatment of duodenal ulcer. In: Costs,
Risks, and Benefits of Surgery, ed. ~ohn P. Bunker, Benjamin A.
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WILLIAM GEMMELL COCHRAN
Barnes, and Frederick Mosteller, pp. 176-97. New York: Ox-
ford University Press. F1061
1978
89
a. Laplace's ratio estimator. In: Contributions to Survey Sampling and
Applied Statistics, ed. H. A. David, pp. 3-10. New York: Aca-
demic Press. t1071
b. Experimental design. I. The design of experiments. In: Inter-
national Encyclopedia of Statistics, ed. William H. Kruskal and Ju-
dith M. Tanur, pp. 285-94. New York: The Free Press. t110]
1980
With George W. Snedecor. Statistical Methods, 7th ed. Ames: Iowa
State University Press.
1982
Contributions to Statistics. New York: John Wiley & Sons. (A collection
of the 116 papers published by William G. Cochran.)
1983
Planning and Analysis of Observational Studies, ed. Lincoln E. Moses
and Frederick Mosteller. New York: John Wiley & Sons.
Representative terms from entire chapter:
william gemmell
