Table Of ContentSpringer Series in Statistics
Peter McCullagh
Ten Projects
in Applied Statistics
Springer Series in Statistics
SeriesEditors
PeterBühlmann,SeminarfürStatistik,ETHZürich,Zürich,Switzerland
PeterDiggle,Dept.Mathematics,UniversityLancaster,Lancaster,UK
UrsulaGather,Dortmund,Germany
ScottZeger,Baltimore,MD,USA
SpringerSeriesinStatistics(SSS)isaseriesofmonographsofgeneralinterestthat
discussstatisticaltheoryandapplications.
The series editors are currently Peter Bühlmann, Peter Diggle, Ursula Gather,
andScottZeger.PeterBickel,IngramOlkin,andStephenFienbergwereeditorsof
theseriesformanyyears.
Peter McCullagh
Ten Projects in Applied
Statistics
PeterMcCullagh
DepartmentofStatistics
UniversityofChicago
Chicago,IL,USA
ISSN0172-7397 ISSN2197-568X (electronic)
SpringerSeriesinStatistics
ISBN978-3-031-14274-1 ISBN978-3-031-14275-8 (eBook)
https://doi.org/10.1007/978-3-031-14275-8
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To Rosa
Preface
Goals
Thebookbeginswithtenchapters,eachdevotedtoadetaileddiscussionofaspecific
project. Some of these are projects that arose as part of the statistical consulting
programattheUniversityofChicago;othersaretakenfromrecentpublicationsin
thescientificliterature.Thediscussionspecificallycoversanalysesthatmightseem
superficiallyplausible,butareinfactmisleading.
The areas of application range from medical and biologicalsciences to animal
behavior studies, growth curves, time series, and environmental work. Statistical
techniques are kept as simple as is reasonable to do justice to the scientific
goals. They range from summary tables and graphs to linear models, generalized
linear models, variance-componentmodels, time series, spatial processes, and so
on. Recognition of relationships among the observational units and the need to
accommodatecorrelationsamongresponsesisarecurringtheme.
The second half of the book begins by discussing a range of fundamental
considerationsthatshapemyattitudetoappliedstatistics.Oncetheyarepointedout,
thesemattersappearsosimpleandobviousthatitishardtoexplainwhyadetailed
discussionshouldbeneededinanadvanced-leveltext.Butthesimplefactthatthey
aresofrequentlyoverlookedshowsthatthisattitudeisunhelpful.Mostsuchmatters
are relatedto statistical design,the placementof the baseline,the identificationof
observationalunitsandexperimentalunits,theroleofcovariatesandrelationships,
initialvalues,randomizationandtreatmentassignment,andsoon.Othersarerelated
to the interplaybetween design and modelling:Is the proposedmodelcompatible
with the design? More technicalmatters related to stochastic processes, including
stationarity and isotropy, techniques for constructing spatio-temporal processes,
likelihoodfunctions,and so on are coveredin later chapters.Parametricinference
is important, but it is not a major or primary focus. More important by far is to
estimatetherightthing,howeverinefficiently,thantoestimatethewrongthingwith
maximumefficiently.
vii
viii Preface
The bookis aimed at professionalstatisticians and at studentswho are already
familiar with linear modelsbut who wish to gain experiencein the application of
statistical ideas to scientific research. It is also aimed at scientific researchers in
ecology, biology, or medicine who wish to use appropriate statistical methods in
theirwork.
The primary emphasis is on the translation of experimental concepts and
scientific ideas into stochastic models, and ultimately into statistical analyses and
substantiveconclusions.Althoughnumericalcomputationplays a major role, it is
notadrivingforce.
The aim of the book is not so much to illustrate algorithms or techniques of
computation,buttoillustratetheroleofstatisticalthinkingandstochasticmodelling
in scientific research. Typically, that cannot be accomplished without a detailed
discussion of the scientific objectives, the experimental design, randomization,
treatment assignment, baseline factors, response measurement, and so on. Before
settling on a standard family of stochastic processes, the statistician must first
ask whether the model is adequate as a formulation of the scientific goals. Is it
self-consistent? Is it in conflict with randomization? Does it address adequately
the sexual asymmetry in Drosophila courtship rituals? Is the sampling scheme
adequateforthestatedobjective?AglanceatChaps.1–5showstheextenttowhich
the discussion must be tailored to the specific needs of the application, and the
unfortunateconsequencesof adoptingan off-the-shelfmodelin a routineway.As
D.R.CoxonceremarkedatanISImeetingin1979,“Therearenoroutinestatistical
questions—onlyquestionablestatisticalroutines.”
Everyanalysisandeverystochasticmodelisopentocriticismonthegroundsthat
itisnotagoodmatchfortheapplication.Aperfectmatchisararity,socompromise
is needed in every setting, and a balance must be struck in order to proceed. At
variouspoints, I haveincludedplausibleanalysesthatare deficient,inappropriate,
misleading,orsimplyincorrect.Thehopeisthatstudentsmightlearnnotonlyfrom
theirownmistakesbutfromthemistakesofothers.
Computation
The R package (R Core Team, 2015) is used throughout the book for all plots
and computations. Initial data summaries may use built-in functions such as
apply(...) or tapply(..) for one- and two-way tables of averages, or
plot(...)forplotsofseasonaltrendsorresiduals.Apartfromstandardfunctions
suchaslm(...)forfittinglinearmodels,glm(...)forgeneralizedlinearmod-
els,andfft(...)forthefastFouriertransformation,twoadditionalpackagesare
usedforspecializedpurposes:
1. regress(...) (Clifford and McCullagh, 2006) for fitting linear Gaussian
modelshavingnon-trivialspatialortemporalcorrelations;
Preface ix
2. lmer(...)(Batesetal.,2015)forfittinglinearandgeneralizedlinearrandom-
effectsmodels.
Either package may be used for fitting the models in Chaps.1 and 2; glm() is
adequateformostcomputationsinChaps.3and7;regress()isbettersuitedto
theneedsofChaps.4and5;andlmer()isbettersuitedforChap.9.
Organization
The book is not organized linearly by topic. From a logical standpoint, it might
havebeenintellectuallymoresatisfyingtobeginatthebeginningwithChap.11and
to illustrate the various statistical design concepts with examples drawn from the
literature.Thatoptionwasconsideredandquicklyabandoned.Adeliberatechoice
hasbeenmadetoputasmuchemphasisontheprojectsasonthestatisticalmethods
andtodrawuponwhateverstatisticaltechniquesarerequiredasandwhentheyare
required.For that reason, the projects come first. Thus, a reader who is unsure of
the distinction between covariatesand relationshipsor between observationaland
experimentalunitsortheimplicationsofthosedistinctionsmayconsulttherelevant
portionsofChap.11.
Severaloftheprojectsaretakenfromexperimentsreportedintherecentscientific
literature.Inmostcases,theexperimentaldesignisfairlyeasytounderstandwhen
the structure of the units is properly laid out. The importance of accommodating
correlations arising from temporal or other relationships among the units is a
recurringtheme.Andifthatistheonlylessonlearned,thebookwillhaveserveda
usefulpurpose.
Acknowledgments
My attitude toward applied statistics has been shaped over many years by discus-
sions with colleagues, particularly David Wallace, Mike Stein, Steve Stigler, Mei
Wang, and Colm O’Muircheartaigh. The books on experimental design by Cox
(1958), Mead (1988) and Bailey (2008), and the pair of papers Nelder (1965a,b)
onrandomizedfieldexperimentshavebeenparticularlyinfluential. CoxandSnell
(1981)isatroveofstatisticalwisdomandunteachablecommonsense.
For the past 25years, I have worked closely with my colleague Mei Wang,
encouraginggraduate students and advising research workers on projects brought
tothestatisticalconsultingprogramattheUniversityofChicago.Overthatperiod,
we have given advice on perhaps 500 projects from a wide range of researchers,
from all branches of the Physical and Biological Sciences to the Social Sciences,
PublicPolicy,Law,Humanities,andeventhe DivinitySchool.Allof theattitudes
expressed in these notes are the product of direct experiences with researchers,
x Preface
plus discussions with students and colleagues. Parts of three consulting projects
areincludedinChaps.1,3and10.
Other themes and whole chapters have emerged from an advanced graduate
course taught at the University of Chicago, in which students are encouraged to
work on a substantial applied project taken from the recent scientific literature.
Chapter 5 is based on a course project selected by Wei Kuang in 2020. I have
includeda detailedanalysis ofthis projectbecause it raisesa numberof technical
issuesconcerningfactorialmodelsthatarewellunderstoodbutseldomadequately
emphasizedintheappliedstatisticalliterature.Chapter9isbasedoncourseprojects
byDongyueXie,IrinaCristali,LinGui,andY.Weiin2018–2020.Chapter16was
motivated by a 2020 masters project by Ben Harris on spatio-temporal variation
in summer solar irradiance and its effect on solar power generation in downstate
Illinois.Alloftheattitudesandopinionsexpressedintheseanalysesareminealone.
Overthepastfewyears,severalstudentshavetackledvariousaspectsoftheOut-
of-Africaproject.Some have gonebeyondthe call of duty,includingShaneMiao
forherMastersprojectattheUniversityofOxfordin2016,andJosephineSantoso
forherMastersprojectattheUniversityofChicagoin2022.
I am indebted to students and colleagues, particularly Heather Battey, Laurie
Butler, Emma McCullagh, Mike Stein, Steve Stigler, and Mei Wang, for reading
andcommentingonanearlierdraftofthemanuscript.
Chicago,IL,USA PeterMcCullagh
