Primer001Primer002Primer003Primer004Primer005Primer006Primer007Primer008Primer009Primer010Primer011Primer012Primer013Primer9-13.pdfPrimer 9Primer 10Primer 11Primer 12Primer 13APRIMEROFSIGNALDETECTIONTHEORYD.McNicolLecturer in Applied Psychology, University of New South WalesLONDON.GEORGEALLEN&UNWINL.TDSYDNEY.AUSTRALASIANPUBLISHINGCOMPANYFirst published in 1972This book is copyright under the Berne Convention. All rightsare reserved.Apartfrom any fair dealing for the purposes ofprivate study, research, criticism or review, as permittedunder the Copyright Act, 1956, nopartof this publicationmay be reproduced, stored in a retrieval system, ortransmitted, in any form or by any means, electronic,electrical, chemical, mechanical, optical, photocopying,recording or otherwise, without the prior permission of thecopyright owner. Enquiries should be addressed to thepublishers.© George Allen & Unwin Ltd 1972British ISBN 0 04 152006 8 casedo 04 152007 6 paperAustralasian Publishing Company, Sydney SBN 900882 34 4Printed in Great Britainin 10 on 12pt'Monophoto'Times Mathematics Series 569by Page Bros (Norwich) Ltd., NorwichPrefaceThereis hardly a field in psychology in which the effectsofsignaldetection theory havenotbeen felt.Theauthoritativeworkonthesubject,Green's& Swets' Signal Detection Theory and Psycho-physics (NewYork:Wiley)appearedjn1966,andis having aprofoundinfluence onmethodandtheory in psychology. All thismakes things excitingbutratherdifficult forundergraduatestudentsandtheir teachers, because a complete course in psychologynowrequires anunderstandingofthe conceptsofsignal detection theory,andmanyundergraduateshavedoneno mathematics at university 'level.Theirtotalmathematicalskills consistofdim recollectionsofsecondary school algebra coupled with anintroductorycourse instatisticstakenin conjunction with their studies in psychology. Thisbookis intended to present the methods of signal detection theory toa person with such a mathematical background. It assumes a know-ledge onlyofelementary algebraandelementary statistics. Symbolsandterminologyarekept as close as possible to thoseofGreen&Swets (1966) sothatthe eventualandhopedfor transfer to amoreadvanced text will be accomplished as easily as possible.Thebookis best considered as being divided into twomainsections, the first comprisingChapters1 to 5,andthe second,Chapters6 to 8.Thefirst section introduces the basic ideasofdetection theory,andits fundamental measures.Theaim is to enablethereaderto be able tounderstandandcomputethese measures.Thesection ends with a detailed workingthroughofa typicalexperimentanda discussionofsomeofthe problems whichcanarise for the potential userofdetection theory.Thesecond section considers threemoreadvanced topics.Thefirstofthese, which is treated thoroughly elsewhere in the literature,is threshold theory. However, because thiscontenderagainst signaldetection theoryhasbeen soubiquitousin the literatureofexperi-mental psychology,andso powerful in its influencebothin thePREFACEconstructionoftheoriesandthe designofexperiments, it is discussedagain.Thesecondtopicconcerns the extensionofdetection theory,which customarily requires experiments involving recognition tests,to experiments using more open-ended procedures, such as recall;andthethirdtopicis anexaminationofThurstonianscalingprocedures which extend signal detection theory in anumberofuseful ways.Anauthorneeds the assistanceofmanypeople toproducehisbook,andI have been no exception. IamparticularlybeholdentoDavidIngleby, who, when he was working at the Medical ResearchCouncil Applied PsychologyUnit,Cambridge, gave memuchusefuladvice,andwhowas subsequentlymostgenerous in allowing me toreadanumberofhis reports.Thereaderwill notice frequentreference to hisunpublishedPh.D.thesisfromwhich I gainedconsiderable helpwhenwritingChapters7and8ofthisbook.Manyofmy colleagues at Adelaide have helped metoo,andI am gratefultoTedNettelbeck,RonPennyandMaxineShephard,whoreadandcommentedon drafts of the manuscript, to Su WilliamsandBobWillson,whoassistedwithcomputerprogramming,andto myHeadofDepartment,Professor A. T. Welford for his encourage-ment. I am equallyindebtedto those responsible for theproductionofthe finalmanuscriptwhich was organised byMargaretBlaberably assisted by Judy Hallett. Mythanksalso to SueThomwhopreparedthe diagrams,andto my wife Kathie,whodid theproofreading.Theimpetus for thisworkcamefroma project on the applicationsofsignal detectiontheoryto the processingofverbalinformation,supportedbyGrantNoA67/16714fromtheAustralianResearchGrantsCommittee. I am also grateful to StJohn'sCollege,Camb-bridge, formakingitpossible toreturntoEnglandduring1969 toworkonthebook,andto Adelaide University, which allowed me totakeup the StJohn'soffer.A finalwordofthanksis due to some peoplewhoknowmoreaboutthedevelopmentofthisbookthananyoneelse. Thesearethe PsychologyIIIstudentsatAdelaide Universitywhohave servedas atolerantbutcritical provinggroundforthematerial whichfollows.Adelaide University D. MCNICOLSeptember 1970ContentsPrefaceWHATARESTATISTICALDECISIONS?AnexampleSome definitionsDecision rulesandthe criterionSignal detectiontheoryandpsychology2NON-PARAMETRICMEASURESOFSENSITIVITYTheyes-notaskTheratingscaletaskAreaestimationwith only a singlepairofhitandfalsealarmratesTheforced-choicetaskAn overall viewofnon-parametricsensitivity measures3GAUSSIANDISTRIBUTIONSOFSIGNALANDNOISEWITHEQUALVARIANCESTheROC curve for theyes-notaskDouble-probabilityscalesTheformulafor d'ThecriterionForced-choice tasks4GAUSSIANDISTRIBUTIONSOFSIGNALANDNOISEWITHUNEQUALVARIANCESROC curves forunequalvariance casesSensitivity measures in theunequalvariance caseMeasuringthesignaldistributionvarianceThemeasurementofresponse bias5CONDUCTINGARATINGSCALEEXPERIMENTExperimental designpage1136101818253140~45505053575864798086919299100CONTENTSAnalysisofdata105Measuresofsensitivity 113Measuresofbias 1196CHOICETHEORYAPPROXIMATIONSTOSIGNALDETECTIONTHEORY 131Thelogistic distribution 134Determining detection measures from logistic distributions 136Thematrixofrelative response strengths 139Open-ended tasks 141Asummaryofthe procedure for an open-ended task 147Chapter 1WHATARESTATISTICALDECISIONS?ANEXAMPLE7069686566 67x = Height in inches6463Often wemustmakedecisions on the basis of evidence which islessthanperfect. For instance, agroupof peoplehasheights rangingfrom5 ft 3 in. to 5 ft 9 in. These heights are measured with thegroupmembersstandinginbarefeet.Wheneach person wears shoes hisheight is increased by