Introductory to statistics for forensic scientists

267 Pages·2005·1.446 MB·English

by  David Lucy

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Introduction to Statistics for
Forensic Scientists
David Lucy
UniversityofEdinburgh,UK

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Introduction to Statistics for
Forensic Scientists

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Introduction to Statistics for
Forensic Scientists
David Lucy
UniversityofEdinburgh,UK

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LibraryofCongressCataloging-in-PublicationData
Lucy,David.
Introductiontostatisticsforforensicscientists/DavidLucy.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN-13978-0-470-02200-0(HB)ISBN-13978-0-470-022019(PB)
ISBN-100-470-02200-0(HB) ISBN-100-470-022019(PB)
1.Forensicsciences–Stat isticalmethods. 2.Forensicstatistics. 3.Evidence(Law)–Statisticalmethods.
I.Title.
HV8073.L832005
519.5024(cid:2)36325 2005028184
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ISBN-13978-0-470-02200-0(HB)ISBN-13978-0-470-022019(PB)
ISBN-100-470-02200-0(HB) ISBN-100-470-022019(PB)
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Contents
Preface ix
Listoffigures xi
Listoftables xiii
1 Ashorthistoryofstatisticsinthelaw 1
1.1 History 1
1.2 Somerecentusesofstatisticsinforensicscience 3
1.3 Whatisprobability? 4
2 Datatypes,locationanddispersion 7
2.1 Typesofdata 7
2.2 Populationsandsamples 9
2.3 Distributions 9
2.4 Location 11
2.5 Dispersion 13
2.6 Hierarchiesofvariation 14

3 Probability 17
3.1 Aleatoryprobability 17
Onethrowofasix-sideddie 17
Asinglethrowwithmorethanoneoutcomeofinterest 18
Twosix-sideddice 19
3.2 Binomialprobability 21
3.3 Poissonprobability 24
3.4 Empiricalprobability 25
Modelledempiricalprobabilities 25
Trulyempiricalprobabilities 27
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vi CONTENTS
4 Thenormaldistribution 29
4.1 Thenormaldistribution 29
4.2 Standarddeviationandstandarderrorofthemean 30
4.3 Percentagepointsofthenormaldistribution 32
4.4 Thet-distributionandthestandarderrorofthemean 34
4.5 t-testingbetweentwoindependentsamples 36
4.6 Testingbetweenpairedobservations 40
4.7 Confidence,significanceandp-values 42
5 Measuresofnominalandordinalassociation 45
5.1 Associationbetweendiscretevariables 45
5.2 χ2testfora2×2table 46
5.3 YulesQ 48
5.4 χ2testsforgreaterthan2×2tables 49
5.5 φ2andCramersV2 50
5.6 Thelimitationsofχ2testing 51
5.7 Interpretationandconclusions 52
6 Correlation 55
6.1 Significancetestsforcorrelationcoefficients 59
6.2 Correlationcoefficientsfornon-lineardata 60
6.3 Thecoefficientofdetermination 63
6.4 Partialcorrelation 63
6.5 Partialcorrelationcontrollingfortwoormorecovariates 69
7 Regressionandcalibration 75
7.1 Linearmodels 75
7.2 Calculationofalinearregressionmodel 78
7.3 Testing‘goodnessoffit’ 80
7.4 Testingcoefficientsaandb 81
7.5 Residuals 83
7.6 Calibration 85
Alinearcalibrationmodel 86
Calculationofaconfidenceintervalforapoint 89
7.7 Pointstoremember 91

8 Evidenceevaluation 95
8.1 Verbalstatementsofevidentialvalue 95
8.2 Evidencetypes 96
8.3 Thevalueofevidence 97
8.4 Significancetestingandevidenceevaluation 102
9 Conditional probabilityandBayes’theorem 105
9.1 Conditionalprobability 105
9.2 Bayes’theorem 108
9.3 Thevalueofevidence 112
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CONTENTS vii
10 Relevanceandtheformulationofpropositions 117
10.1 Relevance 117
10.2 Hierarchyofpropositions 118
10.3 Likelihoodratiosandrelevance 120
10.4 Thelogicofrelevance 122
10.5 Theformulationofpropositions 123
10.6 Whatkindofpropositionscanwenotevaluate? 124
11 Evaluationofevidenceinpractice 129
11.1 Whichdatabasetouse 129
Typeandgeographicfactors 129
DNAanddatabaseselection 131
11.2 Verbalequivalenceofthelikelihoodratio 133
11.3 Somecommoncriticismsofstatisticalapproaches 136
12 Evidenceevaluationexamples 139
12.1 Bloodgroupfrequencies 139
12.2 Trouserfibres 141
12.3 Shoetypes 144
12.4 Airweaponprojectiles 148
12.5 Heightdescriptionfromeyewitness 150
13 Errorsininterpretation 155
13.1 Statisticallybasederrorsofinterpretation 155
Transposedconditional 156
Defender’sfallacy 157
Anothermatcherror 157
Numericalconversionerror 158
13.2 Methodologicalerrorsofinterpretation 159
Differentlevelerror 158
Defendant’sdatabasefallacy 159
Independenceassumption 159
14 DNAI 161
14.1 Lociandalleles 161
14.2 Simplecasegenotypicfrequencies 162
14.3 Hardy-Weinb ergequilibrium 164
14.4 Simplecaseallelicfrequencies 166
14.5 Accountingforsub-populations 168
15 DNAII 171
15.1 Paternity–motherandfatherunrelated 171
15.2 Databasesearchesandvalueofevidence 174
15.3 Discussion 176
16 Samplingandsamplesizeestimation 179
16.1 Estimationofamean 179
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16.2 Samplesizesfort-tests 181
Twosamplet-test 181
Onesamplet-test 183
16.3 Howmanydrugstosample 184
16.4 Concludingcomments 188
17 Epilogue 191
17.1 GraphicalmodelsandBayesianNetworks 192
Graphicalmodels 192
Bayesiannetworks 194
17.2 Kerneldensityestimation 195
17.3 Multivariatecontinuousmatching 196
Appendices
A Workedsolutionstoquestions 199
B Percentagepointsofthestandardnormaldistribution 225
C Percentagepointsoft-distributions 227
D Percentagepointsofχ2-distributions 229
E Percentagepointsofbeta-betadistributions 231
F PercentagepointsofF-distributions 233
G CalculatingpartialcorrelationsusingExcelsoftware 235
H Furtheralgebrausingthe“thirdlaw” 239
References 243

Index 249