Statistics for Social Research PDF
Preview Statistics for Social Research
Statistics for Social Research This book isdedicated to mymother mylate father Alex,Tasos, Effi,Anne,Elli,Mimi, Costa, Anna Erin, Ben, Luke,Sophie, Elli Rose,Jordan Pamela,Ryan,Michelle Timothy, Alana Danielle,Christine,Leanne, Marie Amanda,Lisa Alexandra,Andrea,Christopher Stacey,Chloe, Billie-Marie Alexandra, Katherine, Evelyn andtheones stilltocome Statistics for Social Research George Argyrous School ofSocial Science and Policy The University of New South Wales. Australia © George Argyrous 1997 All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission. No paragraph of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright, Designs and Patents Act 1988, or under the terms of any licence permitting limited copying issued by the Copyright Licensing Agency, 90 Tottenham Court Road, London, W1P 9HE. Any person who does any unauthorised act in relation to this publication may be liable to criminal prosecution and civil claims for damages. First published 1997 by MACMILLAN PRESS LTD Houndmills, Basingstoke, Hampshire RG21 6XS and London Companies and representatives throughout the world ISBN 978-0-333-73023-2 ISBN 978-1-349-14777-9 (eBook) DOI 10.1007/978-1-349-14777-9 A catalogue record for this book is available from the British Library. 10 9 8 7 6 5 4 3 2 1 06 05 04 03 02 01 00 99 98 97 Contents Introduction x Part1 Descriptivestatistics 1 Variables andmeasurement 3 Theconceptualization andoperationalization ofvariables 4 Levelsofmeasurement 7 Discreteandcontinuous variables 11 Summary 12 2 Basictoolsofdescription: Tables 15 Typesofdescriptive statistics 16 Percentages andproportions 17 Frequencydistributions 19 Classintervals 23 3 Graphs 28 Somegeneralprinciples 29 Piegraphs 29 Bargraphs 30 Histograms 33 Frequency polygons 34 Commonproblems andmisusesofgraphs 35 4 Measures ofcentral tendency andmeasures ofdispersion 41 Measures ofcentraltendency 41 Choosingameasureofcentraltendency 47 Measuresofdispersion 50 Summary 57 5 Descriptive statistics onSPSS 60 Assigningvariablelabels:The DefineVariablecommand 62 Definingvalues:TheValueLabelscommand 63 vi Contents Dataentry 67 Savingadatafile 70 Openingadatafile 71 Frequency tablesusingSPSS 72 Validcasesandmissingvalues 73 Measuresofcentral tendencyusingSPSS 75 MeasuresofdispersionusingSPSS 76 Summary 77 6 The normalcurve 79 The normaldistribution 79 z-scores 84 Usingnormalcurves todescribe adistribution 87 NormalcurvesonSPSS 92 Part2 Inferential statistics A Hypothesistesting: The onesamplecase 7 Samplingdistrihutions 103 Randomsamples 105 Thesamplingdistributionofasamplestatistic 107 Thecentrallimittheorem 112 Generating random samplesusingSPSS 113 Summary 117 8 Estimationandconfidence intervals 118 Estimation 119 Changing theconfidencelevel 125 Changingthesamplesize 128 Choosingthesamplesize 131 9 Introductionto hypothesistesting: Thez-test for asingle mean 134 Hypothesis testing:Thegeneral idea 134 Hypothesistestingindetail 140 Whatdoinference tests 'prove'? 150 The significanceofstatisticalsignificance 151 Atwo-tailz-testforasinglemean 152 Aone-tailz-testforasinglemean 155 Summary 158 10 The z-testfor asingle mean 160 TheStudent'st-distribution 160 Degreesoffreedom 163 Theone-samplet-testusingSPSS 169 Contents vii 11 Thez-test for asingleproportion 174 Binomialvariables 174 Thesamplingdistributionofsampleproportions 176 Thez-testforasingleproportion 177 Thez-testforasingleproportion usingSPSS 179 Estimatingapopulation proportion 181 Inferenceusingtheconfidenceintervalforaproportion 182 12 One samplenon-parametrictests 185 Parametricandnon-parametric tests 185 Thechi-squaregoodness-of-fittest 186 Thechi-squaregoodness-of-fittestusingSPSS 190 Thechi-squaregoodness-of-fittestfornormality 193 Anothernon-parametrictest:Therunstestforrandomness 196 TherunstestusingSPSS 201 Part2 Inferentialstatistics B Hypothesistestingfor twoor more independentsamples 13 The r-test for the eqnalityoftwomeans 209 Dependentandindependent variables 210 Thesamplingdistribution ofthedifferencebetweentwomeans 212 Thetwo-samplez-testusingSPSS 217 One-tailandtwo-tail tests 221 Appendix:Thez-testfortwomeans 223 14 Analysis ofvariance 226 Hypothesistesting withmorethantwosamples:Thegeneralidea 226 Theone-wayanalysisofvarianceF-test 231 ANOVAusingSPSS 237 15 Ordinaldata tests for twoor more samples 245 TheWilcoxon ranksumtest 246 TheWilcoxonranksumtestusingSPSS 251 Othernon-parametrictestsfortwoormoresamples 253 Appendix:TheMann-Whitney V-test 254 16 The chi-squaretest for independence 257 Thechi-squaretestandothertestsofsignificance 257 Describingasample:Crosstabulations 258 Crosstabulations usingSPSS 261 Statisticalindependenceandtherelationshipsbetweenvariables 262 Thechi-squaretestforindependence 264 Degreesoffreedom 268 viii Contents Thedistributionofchi-square 269 Thechi-squaretestusingSPSS 272 Problemswithsmallsamples 275 Problemswithlargesamples 276 Appendix:Hypothesistestingfortwoproportions 279 Part2 Inferentialstatistics C Hypothesis testing for twodependentsamples 17 Thez-testfor the mean difference 287 Dependentandindependentsamples 287 Thedependentsamplest-test forthemeandifference 288 Thedependentsamplest-test usingSPSS 291 18 Non-parametrictests for dependentsamples 298 TheMcNemartestforbinomialdistributions 298 TheMcNemartestusingSPSS 301 TheWilcoxonsigned-rankstestforordinaldata 303 TheWilcoxonsigned-rankstestusingSPSS 307 Part3 Measures ofassociation 19 Introductiontomeasuresofassociation 313 Measuresofassociationasdescriptivestatistics 313 Ifanassociationexists,howstrongisit? 315 Thepatternand/ordirectionoftheassociation 316 Measuresofassociationandtestsofsignificance 317 20 Measuresofassociation for nominal data 319 Cramer's V 319 Cramer's VusingSPSS 321 Proportionalreductioninerrormeasuresofassociation 324 Lambda 324 LambdausingSPSS 327 Limitationsontheuseoflambda 329 Appendix:Standardizingcrosstabulations whenlambdaiszero 331 21 Measuresofassociation for ordinaldata 335 Gamma 335 Concordantanddiscordantpairs 336 GammausingSPSS 341 Spearman'srank-ordercorrelationcoefficient 345 Spearman's rhousingSPSS 348 Othermeasuresofassociationforordinaldata 350 Contents ix 22 Regressionand correlationfor interval/ratiodata 356 Scatterplots 356 Linearregression 358 Pearson'scorrelationcoefficient(r) 366 Explaining variance:Thecoefficientofdetermination (,.1) 368 Plots,correlation, andregression usingSPSS 372 Testingforsignificance 378 Theassumptionsbehindregressionanalysis 379 Summary 382 Appendix 386 TableAl Areaunderthestandardnormalcurve 386 TableA2Distributionoft 387 TableA3DistributionofF 388 TableA4Distribution ofchisquare 389 Keyequations 390 Glossary 396 Answers 399 Index 420
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