Introduction to Quantitative Data Analysis in the Behavioral and Social Sciences

227 Pages·2017·5.326 MB·English

by  Michael J. Albers

Introductionto
QuantitativeDataAnalysis
intheBehavioraland
SocialSciences

Introduction to
Quantitative Data Analysis
in the Behavioral and
Social Sciences
Michael J. Albers
East Carolina University
Thiseditionfirstpublished2017
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10 9 8 7 6 5 4 3 2 1
v
Contents
Preface ix
AbouttheCompanionWebsite xiii
1 Introduction 1
BasisofHowAllQuantitativeStatisticalBasedResearch 1
DataAnalysis,NotStatisticalAnalysis 3
QuantitativeVersusQualitativeResearch 8
WhattheBookCoversandWhatItDoesNotCover 9
BookStructure 10
References 11
PartI DataAnalysisApproaches 13
2 StatisticsTerminology 15
StatisticallyTestingaHypothesis 15
StatisticalSignificanceandp-Value 19
ConfidenceIntervals 26
EffectSize 27
StatisticalPowerofaTest 31
PracticalSignificanceVersusStatisticalSignificance 34
StatisticalIndependence 34
DegreesofFreedom 36
MeasuresofCentralTendency 37
PercentileandPercentileRank 41
CentralLimitTheorem 42
LawofLargeNumbers 44
References 48
vi Contents
3 AnalysisIssuesandPotentialPitfalls 49
EffectsofVariables 49
OutliersintheDataset 53
RelationshipsBetweenVariables 53
ASingleContradictoryExampleDoesNotInvalidateaStatistical
Relationship 60
References 62
4 GraphicallyRepresentingData 63
DataDistributions 63
BellCurves 64
SkewedCurves 68
BimodalDistributions 71
PoissonDistributions 75
BinomialDistribution 77
Histograms 79
ScatterPlots 80
BoxPlots 81
RangesofValuesandErrorBars 82
References 85
5 StatisticalTests 87
Inter-RaterReliability 87
RegressionModels 92
ParametricTests 93
NonparametricTests 95
One-TailedorTwo-TailedTests 96
TestsMustMakeSense 99
References 103
PartII DataAnalysisExamples 105
6 OverviewofDataAnalysisProcess 107
KnowHowtoAnalyzeItBeforeStartingtheStudy 107
PerformanExploratoryDataAnalysis 108
PerformtheStatisticalAnalysis 109
AnalyzetheResultsandDrawConclusions 110
WritingUptheStudy 111
References 112
Contents vii
7 AnalysisofaStudyonReadingandLightingLevels 113
LightingandReadingComprehension 113
KnowHowtheDataWillBeAnalyzedBeforeStartingthe
Study 113
PerformanExploratoryDataAnalysis 115
PerformanInferentialStatisticalAnalysis 122
Exercises 132
8 AnalysisofUsabilityofanE-CommerceSite 135
UsabilityofanE-CommerceSite 135
StudyOverview 135
KnowHowYouWillAnalyzetheDataBeforeStartingthe
Study 136
PerformanExploratoryDataAnalysis 138
PerformanInferentialStatisticalAnalysis 147
Follow-UpTests 151
PerformingFollow-UpTests 153
Exercises 157
Reference 158
9 AnalysisofEssayGrading 159
AnalysisofEssayGrading 159
ExploratoryDataAnalysis 160
InferentialStatisticalDataAnalysis 165
Exercises 173
Reference 175
10 SpecificAnalysisExamples 177
HandlingOutliersintheData 177
Floor/CeilingEffects 182
OrderEffects 183
DatafromStratifiedSampling 184
MissingData 184
NoisyData 186
TransformtheData 187
References 188
11 OtherTypesofDataAnalysis 189
Time-SeriesExperiment 189
AnalysisforDataClusters 192
Low-ProbabilityEvents 193
MetadataAnalysis 193
Reference 195
viii Contents
A ResearchTerminology 197
Independent,Dependent,andControlledVariables 197
BetweenSubjectsandWithinSubjects 199
ValidityandReliability 200
VariableTypes 201
TypeofData 201
IndependentMeasuresandRepeatedMeasures 203
VariationinDataCollection 205
Probability—What30%ChanceMeans 212
References 214
Index 215
ix
Preface
Thisbookstrivestobeanintroductiontoquantitativedataanalysisforstudents
whohavelittleornoprevioustrainingeitherinstatisticsorindataanalysis.It
does not attempt to cover all types of data analysis situations, but works to
impartthepropermindsetinperformingadataanalysis.Toooftentheproblem
withpoorlyanalyzedstudiesisnotthenumbercrunchingitself,butalackofthe
critical thinking process required to make sense of the statistical results. This
book works to provide some of that training.
Statisticsisatool.Knowinghowtoperformat-testoranANOVAissimilar
toknowinghowtousestylesandpagelayoutinWord.Justbecauseyouknow
howtousestylesdoesnotmakeyouawriter.Itwillnotevenmakeyouagood
layout person if you do not know when and why to apply those styles.
Likewise, statistics is not data analysis. Learning how to use a software
package to perform a t-test is relatively easy and quick for a student. But
knowingwhenandwhytoperformat-testisadifferent,andmorecomplex,
learningoutcome.Ihadastudent,whohadtakentwograduate-levelbusiness
statistics courses, remark when she turned in a statistics heavy report in a
writingclass:“Inthestatclasses,Ionlylearnedenoughtogetmethroughthe
testproblems.Ihavenoideahowtoanalyzethisdata.”Shehadlearnedhow
tocrunchnumbers,butnothowtoanalyzedata.Bluntly,shewastedhertime
and money in those two classes.
Theissueforresearchersinthesocialsciencesisnottolearnstatistics,butlearn
toanalyzedata.Thegoalisnottolearnhowtousethestatisticalteststocrunch
numbers, but to be able use those tests to interpret the data and draw valid
conclusions from it. There is a wide range of statistical tests relevant to data
analysis; some that every researcher should be able to perform and some that
requiretheadvice/helpofastatisticalexpert.Goodquantitativedataanalysisdoes
notrequireacomprehensiveknowledgeofstatistics,but,rather,knowingenough
toknowwhenitistimetoaskforhelpandwhatquestionstoask.
Everyquantitativeresearchstudy(essentiallybydefinition)collectssometype
ofdatathatmustthenbeanalyzedtohelpdrawthestudy’sconclusions.Agreat
study design is useless unless the data is properly analyzed. But teaching that
x Preface
data analysis to students is a difficult task. What I have found is that most
textbooks fall into one of these categories.

Researchmethodtextbooksthatexplainhowtocreateandexecute astudy,
buttypicallyareverylightonhowtoanalyzethedata.Theyareexcellenton
explainingmethodsofsettingupthestudyandcollectingthedata,butnoton
the methods to analyze it after it has been collected.

Statisticstextbooksthatexplainhowtoperformstatisticaltests.Thetestsare
explained in an acontextual manner and in rigorous statistical terms. Stu­
dentslearnhowtoperformatest,but,fromaresearchstandpoint,theequally
importantquestionsofwhenandwhytoperformitgetshortshrift.Asdothe
questionsofhowtointerprettheresultsandhowtoconnectthoseresultsto
the research situation.
Thisbookdiffersfromtextbooksinthesetwocategoriesbecauseitfocuseson
teachinghowtoanalyzedatafromastudy,ratherthanhowtoperformastudy
orhowtoperformindividualstatisticaltests.Noticethatinthefirstsentenceof
apreviousparagraphIsaid“datathatmustthenbeanalyzedtohelpdrawthe
study’s conclusions.” The key word in the sentence is help versus give the
study’sconclusions.Theresultsofstatisticaltestsarenotthefinalconclusions
for research data analysis. The researcher must study the test results, apply
themtothesituationalcontext,andthendrawconclusionsthatmakesense(see
Figure 1.1 in Chapter 1). To support that process, this book works to place
statistical tests within the context of a data analysis problem and provide the
background to connect a specific type of data with the appropriate test. The
work is placed within long examplesand the entire process of data analysis is
coveredinacontextualizedmanner.Itlooksatthedataanalysisfromdifferent
viewpointsandusingdifferentteststoenableastudenttolearnhowandwhen
to apply different analysis methods.
Twomajorgoalsaretoteachwhatquestionstoaskduringallphasesofadata
analysisandhowtojudgetherelevanceofpotentialquestions.Itiseasytorun
statisticaltestsonallcombinationsofthedata,butmostofthosetestshaveno
relevance or validity regardless of the actual research question.
This book strives to explain the when, why, and what for, rather than the
buttonpushinghow-to.Thedataanalysischaptersofmanyresearchtextbooks
are little more than an explanation of various statistical tests. As a result,
studentscomeawaythinkingtheimportantquestionsareprocedural,suchas:
“How do I run a chi-squared test?” “What is the best procedure, a Kruskal–
WallistestorastandardANOVA?”and“Letmetellyouaboutmydata,andyou
cantell mewhat procedureto run.”(Rogers,2010, p.8). These arethewrong
questionstobeaskingatthebeginningofadataanalysis.Rather,studentsneed
to think along the lines of “what relationships do I need to understand?” and
“whataretheimportantpracticalissuesIneedtoworryabout?”Unfortunately,
mostdataanalysistextsgetthemlostisthetreesofindividualtestsandnever
explains where they are within a data analysis forest.