Using Statistics in Social Research: A Concise Approach

245 Pages·2013·1.79 MB·English

by  Scott M. Lynch (auth.)

Scott M. Lynch
Using Statistics
in Social
Research
A Concise Approach
Using Statistics in Social Research

Scott M. Lynch
Using Statistics in Social
Research
A Concise Approach
123
ScottM.Lynch
DepartmentofSociology
PrincetonUniversity
Princeton,NewJersey,USA
ISBN978-1-4614-8572-8 ISBN978-1-4614-8573-5(eBook)
DOI10.1007/978-1-4614-8573-5
SpringerNewYorkHeidelbergDordrechtLondon
LibraryofCongressControlNumber:2013945760
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ForMikeandBetsy,myparents

Preface
This book began as a collection of lecture notes and has evolved over the last
several years into its current form. My goal in putting the book together was to
remedy some problems I perceive with extant introductory statistics texts. To that
end, this book has several features that differentiate it from standard texts. First,
typicalintroductorystatisticstextsarenowcommonlyover500pageslong.Tobe
blunt, I don’t believe that students actually read texts when they are so lengthy.
So, although a 500C-page book may be chock-full of examples, illustrations, and
interesting side information, such detail is offset by the fact that students will not
readit.Here,Ihavetriedtoprovidelimited,butsufficient,examplesofconceptsand
tokeeptheactualtextlimitedtoabout200pages.Indoingso,Ihavenotcovereda
numberofstatisticalmethodsthatarenotcommonlyused,likeFisher’sexacttest,
Kruskal’sTau,andtheSpearmancorrelation.Whilethese,andsimilar,methodsare
certainly still used, they have limited application in contemporary social research.
Thus,theycanbeinvestigatedindetailbystudentswhenneededinthefuture(e.g.,
forathesisorotherresearchpaper)viaothersources.
Second, in this book, I integrate statistics into the research process, both
philosophically and practically. From a philosophical perspective, I discuss the
difficultieswithconceptslike“proof”and“causality”inadeductivescientificand
statistical framework. From a practical perspective, I discuss how research papers
areconstructed,includinghowstatisticalmaterialshouldbepresentedintablesand
figures,andhowresultsanddiscussionsectionsshouldbewritten.
Third, I emphasize probability theory and its importance to the process of
inference to a greater extent than many books do. Most books discuss probability
theory, but I feel its relationship with statistics is underdeveloped. In this book,
probabilityispainstakinglyshowntobethebasisforstatisticalreasoning.
Fourth, I have included a number of homework problems at the end of almost
every chapter, along with answers to the first half of them in each chapter
in an appendix. There are several differences between the homework problems
and answers I provide and those found in typical texts. First, I do not provide
as many exercises as is commonly found in texts. In most chapters, there are
approximately10exercises.TheexceptionsareChap.5,with50items,andChap.6,
vii
viii Preface
with 40 items. My rationale for this is that for developing an understanding of
mostconcepts,Idonotbelievestudentsneedtoperformdozensofexercises:once
they have done one or two, especially ones that are word based and involve more
thought in implementation, they understand the process. With problems involving
more complicated (or at least tedious) calculations—like the chi-square test of
independence, ANOVA, correlation, and simple regression—performing repetitive
calculations may even be detrimental, fostering a “losing the forest for the trees”
problem.
Thus,aseconddifferencebetweenmyexercisesandthoseoftenfoundintextsis
thatIhavetriedtoconstructexercisesthatareinteresting,thatoftenmaybesolved
indifferentways,thatarerealisticinthesensethattheyoftenrequirethinkinglikea
full-fledgedresearcherwould,andthatofteninvolveinformationthatcannotsimply
bedroppedintoaformulainarotefashion.Forexample,intheexercisesforone-
way ANOVA modeling, I have three exercises without solutions (and three with
solutions).Inone,therawdataareprovided,andthestudentmustcomputesumsof
squaresandcompletetheANOVAtable.Thisproblemteststhestudent’sabilityto
perform the basic computations. In another, a partial ANOVA table is provided,
and all the student must do is understand the structure of the ANOVA table to
completeit(i.e.,SST D SSB CSSW anddf.T/ D df.B/Cdf.W/)Finally,
in another, the student is provided with group-level statistics like the mean and
varianceandmustrecover(twoof)thesumsofsquaresby“undoing”thevariance
calculationsbeforeconstructingtheANOVAtable.Thisproblemteststhestudent’s
deeperunderstandingoftheconnectionbetweenvariancesandsumsofsquares.
AthirddifferencebetweenmyexercisesandthosefoundinothertextsisthatI
usetheexercisesinsomecasestointroduceadditionalmaterialnotcovereddirectly
in the chapter and as further examples of concepts and methods discussed in the
chapter.Asanexampleoftheformerstrategy,thelastexerciseinChap.6introduces
thebasicideasunderlyingcapture-recapturemethodology.Thedetailedanswersto
exercisesexemplifythelatterstrategy:theanswersaredetailedmuchasasolution
toanexampleproblemwouldbewithinachapterinatypicaltext.Theyareplaced
attheendofthechaptersothattheydonotdisrupttheflowofthetextandsothat
studentscanworktheproblemsandchecktheirthoughtandcomputationprocesses
astheyworkthem.
AfinaldifferencebetweenthistextandothersisthatIroutinelyusesimulatedor
contriveddata,ratherthanrealdata,toillustrateconcepts.Tobesure,Iuserealdata
fromtheGeneralSocialSurveyheavilyinbothexamplesandexercises.However,
whilerealdataareusefulforgivingstudentsconcreteexamples,Ithinksimulated
dataareoftenmoreusefulwhentryingtoillustratedifficultideas,especiallywhen
showinghowunknownscanbeestimated.Inrealdata,theunknownsareunknown!
Also, it is generally the case that real data are messy. It is easier, for example, to
illustrate the notion of row and column percentages in cross-tabs using rounder
numbers than may be found in real data. Perhaps as a better example, it is easier
toillustratetheideaofwithinversusbetweensumsofsquaresinANOVAmodeling
bycreatingcontriveddatainwhichthewithinsumofsquaresis0andcontrastingit
withdatainwhichthebetweensumofsquaresis0.
Preface ix
LayoutforaCourse
Thebookisintendedasatextforasemester-longcourseonintroductorystatistics
for social science students. Princeton semesters are relatively short (12 weeks),
and our courses have one-day-per-week “precepts” in which the large class is
broken into smaller groups (of about 15 students each) that are led by preceptors
(graduateteachingassistantsorthecourseinstructor).Iusethesepreceptstoteach
studentshowtousestatisticalsoftwareandtohelpstudentsworkthroughhomework
problems.Giventheprecepts,therearetwo1-hlecturesperweek.Afterdiscounting
3 days for exams, that leaves 21 lectures. Table 1 shows the organization of the
lecturesandthecorrespondingbookchapters.
As the table shows, I give four exams in my course. The first covers the
basics oftheresearch processand descriptive statistics.Themidtermexam covers
probability theory and one sample inference. The third exam covers various two-
sample statistical tests, like the independent samples t test, and the chi-square test
of independence. The final exam covers ANOVA, the correlation, and regression
modeling.
Lecture Topic Chapter
1 Overviewofresearch 1,2
2 Dataacquisition 3
3 continued
4 Summarizingdata 4
5 continued
* Firstexam none
6 Probabilitytheory 5
7 continued
8 CentralLimitTheorem 6
9 Onesampletests
10 Confidenceintervals
11 Review none
* Mid-termexam
12 Two-sampletests/intervals
13 continued
14 Chi-square 7
15 ANOVA 8
16 Correlation&simpleregression 9
17 continued
* Thirdexam none
18 Multipleregression 10
19 continued
20 continued
21 Tablesandfigures 11
Table1. Typicalcoursestructurebasedonbook