PSYCHOPHYSICS A PRACTICAL INTRODUCTION SECOND EDITION F A.A. K REDERICK INGDOM McGill University,Montreal,Quebec,Canada N P ICOLAAS RINS UniversityofMississippi, Oxford,MS,USA AMSTERDAM(cid:129)BOSTON(cid:129)HEIDELBERG(cid:129)LONDON NEWYORK(cid:129)OXFORD(cid:129)PARIS(cid:129)SANDIEGO SANFRANCISCO(cid:129)SINGAPORE(cid:129)SYDNEY(cid:129)TOKYO AcademicPressisanimprintofElsevier AcademicPressisanimprintofElsevier 125LondonWall,LondonEC2Y5AS,UK 525BStreet,Suite1800,SanDiego,CA92101-4495,USA 225WymanStreet,Waltham,MA02451,USA TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UK Copyright©2016,2010ElsevierLtd.Allrightsreserved. Coverimage:ThisitemisreproducedbypermissionofTheHuntingtonLibrary,SanMarino,California. Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,electronicormechanical, Includingphotocopying,recording,oranyinformationstorageandretrievalsystem,withoutpermissioninwritingfrom thepublisher.Detailsonhowtoseekpermission,furtherinformationaboutthePublisher’spermissionspoliciesandour arrangementswithorganizationssuchastheCopyrightClearanceCenterandtheCopyrightLicensingAgency,canbe foundatourwebsite:www.elsevier.com/permissions. ThisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightbythePublisher(otherthan asmaybenotedherein). Notices Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchandexperiencebroadenour understanding,changesinresearchmethods,professionalpractices,ormedicaltreatmentmaybecomenecessary. Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgeinevaluatingandusingany information,methods,compounds,orexperimentsdescribedherein.Inusingsuchinformationormethodstheyshould bemindfuloftheirownsafetyandthesafetyofothers,includingpartiesforwhomtheyhaveaprofessional responsibility. Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors,assumeanyliabilityfor anyinjuryand/ordamagetopersonsorpropertyasamatterofproductsliability,negligenceorotherwise,orfromany useoroperationofanymethods,products,instructions,orideascontainedinthematerialherein. ISBN:978-0-12-407156-8 BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress ForinformationonallAcademicPresspublications visitourwebsiteathttp://store.elsevier.com/ Publisher:MicaHaley AcquisitionEditor:MelanieTucker EditorialProjectManager:KristiAnderson ProductionProjectManager:CarolineJohnson Designer:MattLimbert TypesetbyTNQBooksandJournals www.tnq.co.in PrintedandboundintheUnitedStatesofAmerica Dedication FK would like to dedicate this book to his late parents Tony and Joan, and present family Beverley and Leina. NP would like to dedicate this book to his mother Nel and late father Arie. About the Authors Frederick A.A. Kingdom is a Professor at McGill University conducting research into variousaspectsofvisualperception,includingcolorvision,brightnessperception,stereopsis, texture perception, contour-shape coding, the perception of transparency, and visual illu- sions. He also has an interest in models of summation for the detection of multiple stimuli. Nicolaas Prins is an Associate Professor at the University of Mississippi specializing in visualtextureperception,motionperception,contour-shapecoding,andtheuseofstatistical methods in the collection and analysis of psychophysical data. ix Preface to the Second Edition Theimpetusforthisbookwasarecurring comparisons. We have also provided an question: “Is there a book that explains how updated quick reference guide to the terms, todopsychophysics?”Evidently,abookwas concepts, and many of the equations needed that not only explained the theory described in the book. behind psychophysical procedures but also In writing the second edition we have provided the practical tools necessary for endeavored to improve each chapter and their implementation. What seemed to be have extended all the technical chapters to missing was a detailed and accessible expo- include new procedures and analyses. sition of how raw psychophysical responses Chapter 7 is the book’s one new chapter. It areturnedintomeaningfulmeasurementsof deals with an old but vexing question of sensoryfunction;inotherwords,abookthat how multiple stimuli combine to reach dealt with the nuts and bolts of psycho- threshold. The chapter attempts to derive physics data analysis. from first principles and make accessible to The need for a practical book on psycho- the reader the mathematical basis of the physics inevitably led to a second need: a myriads of summation models, scenarios, comprehensive package of software for and metrics that are scattered throughout analyzing psychophysical data. The result the literature. was Palamedes. Initially developed in Writing both editions of this book has conjunctionwiththefirsteditionofthebook, beenaconsiderablechallengeforitsauthors. Palamedes has since taken on a life of its Much effort has been expended in trying to own, and one purpose of the second edition make accessible the theory behind different is to catch up with its latest developments! types of psychophysical data analysis. For Palamedes will of course continue to be those psychophysical terms that to us did developedsoreadersareencouragedtokeep notappeartohaveacleardefinitionwehave an eye on the regular updates. improvised our own (e.g., the definition of The first few chapters of the book are “appearance” given in Chapter 2), and for intendedtointroducethebasicconceptsand othertermswherewefelttherewasalackof terminology of psychophysics as well as clarity we have challenged existing conven- familiarize readers with a range of psycho- tion (e.g., by referring to a class of forced- physicalprocedures.Theremainingchapters choice tasks as 1AFC). Where we have focus on specialist topics: psychometric challenged convention we have explained functions, adaptive procedures, signal our reasoning and hope that even if readers detection theory, summation measures, do not agree with us, they will still find our scaling methods, and statistical model ideas on the matter thought-provoking. xi Acknowledgments We are indebted to the following persons for kindly reviewing and providing insightful commentsonindividualchapters:NeilMacmillanandDouglasCreelmanforhelpingoneof 0 the authors (FK) get to grips with the calculation of d for same-different tasks (Chapter 6); MarkGeorgesonforprovidingthederivationoftheequationforthecriterionmeasurelnbfor a2AFCtask(Chapter6);AlexBaldwinfortheideaofincorporatingastimulusscalingfactor 0 g for converting stimulus intensity to d when modeling psychometric functions within a Signal Detection Theory framework (Chapters 6 and 7); Mark McCourt for providing the figures illustrating grating-induction (Chapter 3); Laurence Maloney for permission to develop and describe the routines for Maximum Likelihood Difference Scaling (Chapter 8); StanleyKleinforencouragingustoincludeasectionontheChi-squaredtest(Chapter9);and Ben Jennings for carefully checking the equations in the summation chapter (Chapter 7). Thanksalsotothemanypersonsdtoomanytomentionindividuallydwhohaveoverthe years expressed their appreciation for the book as well as the Palamedes toolbox and provided useful suggestions for improvements to both. xiii C H A P T E R 1 Introduction and Aims 1 2 Frederick A.A. Kingdom , Nicolaas Prins 1McGill University, Montreal, Quebec, Canada; 2University of Mississippi, Oxford, MS, USA O U T L I N E 1.1 What is Psychophysics? 1 1.4 What’s New in the Second Edition? 5 1.2 Aims of the Book 1 References 9 1.3 Organization of the Book 2 1.1 WHAT IS PSYCHOPHYSICS? According to the online encyclopedia Wikipedia, psychophysics “. quantitatively investi- gates the relationship between physical stimuli and the sensations and perceptions they affect.”ThetermwasfirstcoinedbyGustavTheodorFechner,whoinhisElementsofPsycho- physics (1860/1966) set out the principles of psychophysical measurement, describing the various procedures used by experimentalists to map out the relationship between matter and mind. Although psychophysics refers to a methodology, it is also a research area in its ownright,andmucheffortcontinuestobedevotedtodevelopingnewpsychophysicaltech- niques and new methods for analyzing psychophysical data. Psychophysicscanbeappliedtoanysensorysystem,whethervision,hearing,touch,taste, or smell. This book primarily draws on the visual system to illustrate the principles of psychophysics, but the principles are applicable to all sensory domains. 1.2 AIMS OF THE BOOK Broadlyspeaking, thebookhasthreeaims.Thefirstistoprovidenewcomerstopsycho- physics with an overview of different psychophysical procedures in order to help them Psychophysics http://dx.doi.org/10.1016/B978-0-12-407156-8.00001-3 1 Copyright©2016ElsevierLtd.Allrightsreserved. 2 1. INTRODUCTIONANDAIMS select the appropriate designs and analyses for their experiments. The second aim is to directreaderstothesoftwaretools,intheformofPalamedes,foranalyzingpsychophysical data.Thisisintendedforbothnewcomersandexperiencedresearchersalike.Thethirdaim is to explain the theory behind the analyses. Again both newcomers and experienced re- searchersshouldbenefitfromthedetailedexpositionsofthebulkoftheunderlyingtheory. Tothisendwehavemadeeveryefforttomakeaccessiblethetheorybehindawiderangeof psychophysical procedures, analytical principles, and mathematical computations, such as Bayesiancurvefitting; thecalculationofd-primes(dʹ);summation theory;maximumlikeli- hood difference scaling; goodness-of-fit measurement; bootstrap analysis; and likelihood- ratio testing, to name but a few. In short, the book is intended to be both practical and pedagogical. The inclusion of the description of the Palamedes tools, placed in this edition in separate boxes alongside the main text, will hopefully offer the reader something more than is provided by traditional textbooks, such as the excellent Psychophysics: The Funda- mentals by Gescheider (1997). If there is a downside, however, it is that we do not always delve as deeply into the relationship between psychophysical measurement and sensory function as The Fundamentals does, except when necessary to explain a particular psycho- physical procedure or set of procedures. In this regard A Practical Introduction is not intended as a replacement for other textbooks on psychophysics but as a complement to them, and readers are encouraged to read other relevant texts alongside our own. Two noteworthy recent additions to the literature on psychophysics are Knoblauch and Maloney’s (2012) Modeling Psychophysical Data in R and Lu and Dosher’s (2013) Visual Psychophysics. Our approach of combining the practical and the pedagogical into a single book may not be to everyone’s taste. Doubtless some would prefer to have the description of the software routines put elsewhere. However, we believe that by describing the software alongside the theory, newcomers will be able to get a quick handle on the nuts and bolts of psychophysics methods, the better to then delve into the underlying theory if and when they choose. 1.3 ORGANIZATION OF THE BOOK The book can be roughly divided into two parts. Chapters 2 and 3 provide an overall framework and detailed breakdown of the variety of psychophysical procedures available to the researcher. Chapters 4e9 are the technical chapters. They describe the theory and implementation for six specialist topics: psychometric functions; adaptive methods; signal detection measures; summation measures; scaling methods; and model comparisons (Box 1.1). In Chapter 2 we provide an overview of some of the major varieties of psychophysical procedures and offer a framework for classifying psychophysics experiments. The approach takenhereisanunusualone.Psychophysicalproceduresarediscussedinthecontextofacrit- ical examination of the various dichotomies commonly used to differentiate psychophysics experiments:ClassAversusClassB;Type1versus Type2;performanceversus appearance; forced-choice versus nonforced-choice; criterion-dependent versus criterion-free; objective 3 1.3 ORGANIZATIONOFTHEBOOK BOX 1.1 PALAMEDES AccordingtoWikipedia,theGreekmythologicalfigurePalamedes(“pal-uh-MEE-deez”)is said to have invented “. counting, currency, weights and measures, jokes, dice and a fore- runner of chess called pessoi, as well as military ranks.” The story goes that Palamedes also uncovered a ruse by Odysseus. Odysseus had promised Agamemnon that he would defend themarriageofHelenandMenelausbutpretendedtobeinsanetoavoidhavingtohonorhis commitment. Unfortunately, Palamedes’s unmasking of Odysseus led toa gruesome end; he was stoned to death for being a traitor after Odysseus forged false evidence against him. Palamedes was chosen as the name for the toolbox because of the legendary figure’s (pre- sumed)contributionstotheartofmeasurement,interestinstochasticprocesses(hedidinvent dice!), numerical skills, humor, and wisdom. The Palamedes Swallowtail butterfly (Papilio palamedes) onthefrontcoveralso providesthetoolbox withanattractiveicon. (cid:1) Palamedes is a set of routines and demonstration programs written in MATLAB for analyzing psychophysical data (Prins and Kingdom, 2009). The routines can be downloaded from www.palamedestoolbox.org. We recommend that you check the website periodically, because new and improved versions of the toolbox will be posted there for download. Chapters 4e9 explain how to use the routines and describe the theory behind them. The descriptions of Palamedes do not assume any knowledge of MATLAB, although a basic knowledge will certainly help. Moreover, Palamedes requires only basic MATLAB; the specialisttoolboxessuchastheStatisticstoolboxarenotrequired.Wehavealsotriedtomake the routines compatible with earlier versions of MATLAB, where necessary including alter- native functions that are called when later versions are undetected. Palamedes is also compatible withthefreesoftware packageGNU Octave(http://www.octave.org). It is important to bear in mind what Palamedes is not. It is not a package for generating stimuli or for running experiments. In other words it is not a package for dealing with the “front-end”ofapsychophysicsexperiment.ThetwoexceptionstothisrulearethePalamedes routines for adaptive methods, which are designed to be incorporated into an actual experi- mentalprogram,andtheroutinesforgeneratingstimuluslistsforuseinscalingexperiments. But by and large, Palamedes is a different category of toolbox from the stimulus-generating toolboxes such as VideoToolbox (http://vision.nyu.edu/VideoToolbox/), PsychToolbox (http://psychtoolbox.org),PsychoPy(http://www.psychopy.org;seealsoPeirce,2007,2009), and Psykinematix (http://psykinematix.kybervision.net/) (for a comprehensive list of such toolboxes see http://visionscience.com/documents/strasburger/strasburger.html). Although someofthesetoolboxescontainroutinesthatperformsimilarfunctionstosomeoftheroutines in Palamedes, for example fitting psychometric functions (PFs), they are in general comple- mentary to,ratherthan incompetition with,Palamedes. Afewsoftwarepackagesdealprimarilywiththeanalysisofpsychophysicaldata.Mostof these are aimed at fitting and analyzing psychometric functions. psignifit (http://psignifit. sourceforge.net/; see also Fründ et al., 2011) is perhaps the best known of these. Another optionisquickpsy,writtenforRbyDanielLinaresandJoanLópez-Moliner(http://dlinares. org/quickpsy.html; see also Linares & López-Moliner, in preparation). Each of the packages Continued 4 1. INTRODUCTIONANDAIMS BOX 1.1 (cont'd) willhavetheirownstrengthsandweaknessesandreadersareencouragedtofindthesoftware that best fits their needs. A major advantage of Palamedes is that it can fit PFs to multiple conditions simultaneously, while providing the user considerable flexibility in defining a modeltofit.Justtogiveonesimpleexample,onemightassumethatthelapserateandslopeof thePFareequalbetweenseveralconditionsbutthatthresholdsarenot.Palamedesallowsone tospecifyandimplementsuchassumptionsandfittheconditionsaccordingly.Userscanalso provide their own custom-defined relationships among the parameters from different condi- tions. For example, users can specify a model in which threshold estimates in different conditions adhere to an exponential decay function (or any other user-specified parametric curve). Palamedes can also determine standard errors for the parameters estimated in such multipleconditionfitsand performgoodness-of-fittestsforsuchfits. The flexibility in model specification provided by Palamedes can also be used to perform statistical model comparisons that target very specific research questions that a researcher mighthave.Examplesaretotestwhetherthresholdsdiffersignificantlybetweentwoormore conditions, to test whether it is reasonable to assume that slopes are equal between the con- ditions,totestwhetherthelapseratedifferssignificantlyfromzero(oranyotherspecificvalue), totestwhethertheexponentialdecayfunctiondescribesthepatternofthresholdswell,etc. Palamedes also does much morethan fit PFs;it has routines for calculating signal detection measures and summation measures, implementing adaptive procedures, and analyzing scaling data. versus subjective; detection versus discrimination; and threshold versus suprathreshold. We consider whether any of these dichotomies could usefully form the basis of a fully-fledged classificationschemeforpsychophysicsexperimentsandconcludethatone,theperformance versus appearance distinction, is the best candidate. Chapter 3 takes as its starting point the classification scheme outlined in Chapter 2 and expandsonitbyincorporatingafurtherlevelofcategorizationbasedonthenumberofstim- uli presented per trial. The expanded scheme serves as the framework for detailing a much wider range of psychophysical procedures than described in Chapter 2. Four of the technical chapters, Chapters 4, 6, 8, and 9, are divided into two sections. In these chapters Section A introduces basic concepts and takes the reader through the Pala- medes routines that perform the relevant data analyses. Section B provides more detail as wellasthetheorybehindtheanalyses.TheideabehindtheSectionAversusSectionBdistinc- tion is that readers can learn about the basic concepts and their implementation without necessarily having to grasp the underlying theory, yet have the theory available to delve intoiftheywant.Forexample,SectionAofChapter4describeshowtofitpsychometricfunc- tions and derive estimates of their critical parameters such as threshold and slope, while Section B describes the theory behind the various fitting procedures. Similarly, Section A