ParapsychologyThis page intentionally left blank ParapsychologyRONROBERTSSocial,Geneticand Developmental Psychiatry ResearchCentre,Institute ofPsychiatry,LondonandDAVIDGROOMEDepartmentof Psychology,University of Westminster,LondonA member of the HodderHeadline GroupLONDONDistributed in the United Statesof America byOxfordUniversityPress Inc.,New YorkThe science of unusual experienceFirstpublished in Great Britain in 2001byArnold, a memberof the HodderHeadline Group,338 Euston Road, LondonNW1 3BHhttp://www.arnoldpublishers.comDistributed in the UnitedStatesof AmericabyOxfordUniversity PressInc.,198 Madison Avenue, New York, NY 10016 2001ArnoldAll rights reserved.No part of this publication may be reproducedortransmitted in any formor by any means, electronically or mechanically,including photocopying,recordingor any information storageor retrievalsystem, without either prior permissionin writingfromthe publisher or alicencepermitting restrictedcopying. In the United Kingdom such licencesare issued by the Copyright Licensing Agency: 90 Tottenham Court Road,London WIT 4LP.The advice and information in this book are believed to be true andaccurate at the date of going to press, but neither the author[s] nor the publishercan acceptany legal responsibilityor liability for any errorsor omissions.British LibraryCataloguingin PublicationDataA catalogue record for this book is available from the BritishLibraryLibraryofCongress Cataloging-in-Publication DataA catalog recordfor this bookis available fromthe Libraryof CongressISBN 0340 76169 5 (hb)ISBN 0340 76168 7 (pb)2 3 4 5678 9 1 0Typeset in1 Ipt Timesby Saxon Graphics Ltd, DerbyPrintedand bound in Malta.What do you think about this book?Or any other Arnold title?Pleasesend your commentsto feedback.arnold@hodder.co.ukFor Antjeand Merry(RR)For Glenys, Alexander, Robin and Jenny (DG)Itis not the spoonthatbends,onlyyourself.(quotedfromTheMatrix)ContentsListsoftables, figures andboxesixList ofcontributorsxPrefacexiAcknowledgementsxiiiPreamble1Part1Myth andmethod1Science and experience7Ron Roberts2Probabilityand coincidence19AnthonyE. Esgate and David Groome3The placeboeffect35ChristopherC. FrenchPartIIBeliefs4The psychologyof psychicfraud51Richard Wiseman5Astrology60David GroomeviiiC on t e n t sPart IIIUnusualexperiences6Unconsciousawareness77TonyTowell7Dreams86AntjeMuellerand Ron Roberts8Alien abductions102ChristopherC. French9Meditation117Stephen Benton10Paranormalcognition130CarolineWatt11Near-death experiences141Chris A. Roe12Gateways to the mind: society and the paranormal156Ron RobertsGlossary163References167Index185Tables,figuresandboxesTables5.1The12 sun signs and their associated birth dates625.2Characteristics associatedwith the12 sun signs635.3Sun signs predictedby astrologers as beingappropriatefor10 occupations697.1Stagesin REM dream development947.2Pooledresults fromeight ESP dream studies99Figures1.1Scienceas an iterative cycle121.2Thescience of experience155.1Frequency of sun signs687.1Electrophysiological characteristics of REMsleep87Boxes3.1Should conventional medicine make more use of theplaceboeffect?374.1The Cottingley fairies544.2The psychologyof the seance567.1Belief in paranormal dreams977.2A typical telepathic dream experiment988.1Exercise1028.2Falsememories in other contexts1119.1Correlates of transcendentalmeditation(TM)12710.1The ganzfelddebate13411.1Are peoplewho have NDEs really'dead' ?14311.2Key features of the near-death experience144ContributorsSteve Benton BSc PhD Department of Psychology, University of Westminster,LondonAnthonyEsgateBScMScPhDDepartmentofPsychology,UniversityofWestminster, LondonChrisFrenchBScPhDDepartmentofPsychology,GoldsmithsCollege,Universityof London,LondonDavidGroomeBScPhDDepartmentofPsychology,UniversityofWestminster,LondonAntjeMuellerBScMethodologyInstitute,LondonSchoolofEconomics,LondonRon Roberts BSc MSc PhD Social, Geneticand DevelopmentalPsychiatryResearchCentre,Institute of Psychiatry,LondonChrisRoeBScPhDDepartmentofPsychology,UniversityCollege,NorthamptonTony To well BScPhD Departmentof Psychology, University of Westminster,LondonCarolineWattMAPhDKoestlerParapsychologyUnit,DepartmentofPsychology,Universityof Edinburgh,EdinburghRichardWisemanBScPhDDivisionofPsychology,UniversityofHertfordshire,HatfieldPrefaceOvertheyearsourstudentshaverepeatedlyrequestedmoreinformationabout popular conceptsin psychology about which they have readand heardinthemedia.Currentlytherearefewresourcesavailablewhichpresentarationalapproachto evaluating theseon the basis of researchevidence.Thisbookgrew out of this demand. It is intended to bridge the gap betweentradi-tionalpsychologyanditsso-calledfringeareas,providingaccessibleaccountsof how science workson the border of its last frontier-the humanmind. The emphasis throughout is on evaluating evidence in order todevelopinformedopinions. We have organized the book into threesections. The firstoftheseaddressesaspectsofscientific methodandscientific reasoning.Theopening chapterin thissectiondiscussesthenature of thescientific methodand the particular problems which the study of human experienceposes. Thischaptersets out the'rulesof the game'forinterpretingtheevidencewhichfollowsin therestof the book,anditservesto placesciencewithin asocialcontext.Thiswillfamiliarizereaderswiththeperspectivewhichscientistsbringtothestudyofsuchadifficultsubject.Anthony EsgateandDavidGroomethenconsidersomepitfallsofhumanreasoningwhenfacedwitheventswhoseoccurrenceisexplicableonthebasisofthelawsoflargenumbers(i.e.statistics), butwhichappearsomeaningfulthatadditionalexplanationsare routinely sought. Careful readingof this chapteris particu-larly recommended. Chris Frenchcompletesthis section with a review of thepuzzlingnatureoftheplaceboeffect-whatitisandwhatitisnot.Thisshouldproveilluminating toprofessionalandlayreadersalikeasmanypopular misconceptions are laid to rest. The secondsectionexploresissues ofbeliefand deception in chapters which address belief in the predictivepowerofastrologyandthetechniquesemployedbypsychicfraudsterstofosteraudiencebeliefintheparanormalnatureofdecidedlynon-paranormalphenomena.RichardWiseman,himselfawell-knownmagicianturnedpsychologist, gives the inside story.x iiPre faceThe finalsection-and by far the largest -dealswith an array of unusualand intriguing experiential phenomena. There is something here (we hope) todelight everyone, including up-to-datesummariesof unconsciousawareness,dreams,ESPresearch,reportsofalienabductionsandnear-deathexperi-ences,amongotherthings.Thevariouscontributorstothissectionhaveattemptedto convey not only what is known about these phenomena but alsowhathasyettobeestablished.We believethatraisingquestionsis justasimportantas answeringthem,and we thereforehopethatthesechapters arerevealingintermsofboththesuccessesandthestrugglesofthescientificmethod to come to terms with consciousness in its many forms. We concludethe book with a few thoughts about why the paranormal is so important in oursociety, what lessons can be learned fromstudying it, and how it may (or maynot)helpustoformavisionofhumanitythatiscompatiblewiththeknowledgewhichhasbeenaccruedinthehumansciences.Hereweposequestionsabouttherelationshipsbetweenreligiousandparanormalbeliefwith theintention of fosteringsomeserious debateabout a side of the disci-pline of parapsychology which has too oftenbeenneglected.Asanaddedextra,andinkeepingwithourphilosophythatitistheevidencewhichcounts,wehaveincludedwithin thetextopportunitiesforreaderstoparticipateinongoingresearchprojects. Wesincerelyhopethatyouwillfeelchallengedbythematerialwehavecollectedtogetherinthepageswhich followand that you will be rousedto debateand argument wellinto the wee smallhours of the night. For sceptics and believersalike there ismaterialheretochallengeandunsettleestablishedopinion.Sitbackandenjoythe trip.Ron RobertsDavid GroomeLondon, 2000AcknowledgementsWe would like to thank everyonewho has contributedto the book, as well asanyoneand everyonewhohas contributedideasandsuggestionsonwhat toinclude. Thepreparationof thisbookhas beeninfluenced overtheyears bymanypeople-too numeroustomention,but theirinputtothe finishedproductisgratefullyacknowledged.We wouldalsoliketothankthemanystudents who have appreciatedour endeavoursto teachbothparapsychologyandcriticalthinking inaninformativeandentertainingmanner.Thanksaredue to our editorChristina Wipf Perry,whose light touch and relaxedmannerhas made the processof completingthis project moreenjoyablethan it mightotherwisehave been. Additionalthanksto Antje,Merry, Wandia,Subiraandanyone else who has managedto make us laugh and to support us.This page intentionally left blank PreambleU nusualandp a r a n o r ma le x p e r ie n c e sWe live in an age of science. However, there are many types of human expe-riencewhich continue to defyanyscientificexplanation, at leastin terms ofthescientific knowledge that we have at the presenttime. Insome caseswemay have a partial explanation, but in other cases the underlying mechanismiscompletelyunknown. Thesecaseswhichcompletelydefyanynormalscientific explanation are referred to as'paranormal' phenomena. In practicethere is considerable overlap betweenwhat is regardedas'paranormal' andwhatisconsideredtobemerely'unusual',sothisbookwillreviewbothcategorieswithoutnecessarilymakingadistinctionbetweenthem.Thepurposeofthisbookistoreviewthescientificevidencethatisavailableaboutunusual and paranormalexperiences. The main categories of unusualand paranormal experienceare listed below, and they will all be examined indetail later in the book.Extra-sensory perception(ESP)refers to the perceptionof input throughsomechannelotherthanthefiveknownsenses.Itisalsoreferredtoas'paranormalcognition','telepathy'ortheuseofa'sixthsense'. Allofthese terms basically denote a capacity of the brain to receive informationfromother sources by some unknown mechanism of transmission.Astrology is based on the assumption that the stars have an influence overpeople's lives, characterand destiny. Again the mechanism by which thismight occur is still unknown.Sightingsof aliens and UFOs(unidentifiedflyingobjects)refertoextra-terrestrial visitors and their spacecraft.Some people believe that they havebeen the victims of alien abduction. These experiences(and claimedUFOsightings) are generally classified as paranormal because as yet there is noobjective evidenceof the occurrenceof visits to this planet by aliens.ParapsychologyMany peoplewho are closeto death(or who are resuscitatedafterbeingclinicallydead) describeexperiencesfor which it is difficultto provide astraightforwardscientific explanation. These near-deathexperiencesmayinclude visions of theafterlifeand out-of-body experiences.Meditationinvolvestechniqueswhich apparentlyachieveunusual statesof consciousnesssuch as trances. Hypnotism is generally considered to berelated to these techniques.Dreams are the images that we experience during sleep, and although theyare well establishedas real phenomena, as yet there is no agreement abouttheir underlying mechanism or purpose.Unconsciousawarenessandsubliminalperceptionrefertothebrain'sability to take in information without being conscious of perceiving it.The placeboeffectis the tendency for a therapy to have a beneficialeffectwhich exceedsits known therapeutic mechanisms,sometimesas a resultof mere suggestion and expectationon the part of the patient. Theplaceboeffectisawellestablishedphenomenon, butitsmechanismofactionisnot well understood.Thesearesomeofthemorecommonlyreportedformsofunusualexpe-riencewhichcontinue to puzzlethescientificworld. Theyareall linkedbyone commonfactor,namelythat in each casethe mechanism underlying thephenomenonisstillunknown. However,thesephenomenahaveallbeensubjectedto scientificinvestigation, and thefindingsof this researchwill beconsideredinthis book.Eachofthephenomenalistedabovewillbedealtwithin a separatechapter. Thereisan additionalchapteron probabilityandcoincidence,becausetheseconceptsarefundamentaltoanyevaluationofresearchinto claims of unusual and paranormalexperiences.B e l i e fint hep a r a n o r ma lAlthoughweliveinanageofscience,beliefintheparanormalremainssurprisinglywidespread.Forexample,asurveyof1236adultAmericansconducted by Gallup and Newport (1991)yielded the followingfindings.Threepeopleout of everyfouradmittedto readingtheir horoscopein thenewspaper.One in fourexpresseda firm belief in astrology.One in fourclaimedto have experiencedtelepathy.One in four believedin ghosts.One in six claimed to have seen a UFO.There is evidencethat belief in the paranormal is fairlywidespreadin othercountries,too.Forexample,Blackmore(1997)reportedthat59%ofa UKsampleexpressedsomebeliefinparanormalphenomena,althoughtheseP r e a mbl eindividuals werenot a true cross-sectionof the population,as studysubjectswereobtainedbyanewspaperappeal(intheDailyTelegraph).Withsuchwidespread beliefin the paranormal, it is obviously important for scientists toestablishthe validity of these phenomena.For some people an interest in theparanormalislittlemorethanharmlessfun, butformanyothersitplaysamajorpart in helping them to make decisionsabout important events in theirlives. Some peopledecide to get marriedor change their jobon the advice ofanastrologer.Othersmovehousetogetawayfromaghostorpoltergeist.Some takesignificant actions on the basis of information which theybelievetheyhaveobtainedbytelepathyorfromaclairvoyant. Beliefsaboutpara-normalphenomenamay also create fearsand anxieties.Some people live inconstant fearof alienabduction, or even believethat they have alreadybeenvictims of alien abduction, while others live in fear of ghosts, demons or eventhe devil. There are other moresubtle consequencesof beliefs about the para-normal -for example,when peopleblametheir own failures and misjudge-mentsonparanormalphenomena.Afteranaccidentorcatastrophehasoccurred,itissometimestemptingtoblametheinterventionofsomeunknownforce.Thedisasterwasfated,inthestars,orbroughtaboutbydemonsorthevengefuldead.Thistypeofattributioncanprovideaconvenientexcuseforthosewhoareactuallyresponsible,andinfailingtofaceup to reality they mayalsofailto learnfromtheir mistakes.Manypeoplemaintainbeliefsintheparanormalwhichhaveaveryrealinfluenceon theirlives.If thesebeliefsare basedonvalid phenomena,thentheymightpossiblyaddusefulknowledgeandinsightstothedecision-makingprocess,whichshouldbemadeavailabletoasmanypeopleaspossible.Telepathy,clairvoyanceandastrologymightall havethepotentialtoenrichandimproveourlives,providedthattheyarevalidandgenuine.However,ifitturnsoutthattheseparanormalphenomenaarenotgenuine,thentheyrepresentasourceofconsiderableconfusion,misjudgementandbaddecision-making. A personwho bases theirmajorlifedecisionsonfalsebeliefswillprobablynotbeveryeffectiveindealingwiththedemandsoftheirlifeandtheirrelationships.Thisiswhyitissoimportantthatpara-normal phenomenashould be subjected to scientific investigation, so that wecan judgewhetherornottheyarevalid.Suchinvestigationsareessentiallythe subject matterof the rest of this book.This page intentionally left blank Myth andmethodWhocouldsupposethatangelsmovethe stars,or be sosuperstitiousasto supposethatbecauseone cannotseeone'ssoul attheendofamicroscopeit does notexist?(R.D.Laing)This page intentionally left blank 1Scienceand experienceRonRoberts'Howmany fingersamIholdingup,Winston?'7don'tknow, I don'tknow. You will kill meifyoudothatagain.Four, five,six -in all honesty I don'tknow.''Better,'saidO'Brien.(GeorgeOrwell, NineteenEighty-Four)Howwe proposetounderstandrealityis centraltothepursuit of scientificactivity. Many lay peoplewould be surprised to discover that, as a topic,thequestionof what specific characteristicsdistinguish thetheoryandpracticeofsciencefromotherhumanactivitieshasprovokedfiercedebateamongscientists.Inthischapterweshallconsidersomeofthemainpointstoemergefromthesedebatesandtheirrelevancetoconfronting the unusualandmysterious aspectsof human experiencewhich form thesubject matterof this book.Firstof all, however, let us be clearwith regardto what is fundamental tothenatureofscientificenquiry,aboutwhichfewscientistswouldargue.Simply put, this is that the nature of scientific knowledge does notand oughtnottorelyonauthority.Inthisrespectitisdifferentfromalmostallotherformsofknowledge.AccordingtoKarlMarx,what wethinkofashistorymerely consists of the tales told by the victorious. The alternative renderingswhich the vanquished may have bequeathedare lost. What makes for good artisincreasinglydecidedbythewhimsofartcriticsandcollectorswhoseassessmentsaretaintedbytheinfluence ofthepotentialeconomicvalue ofworks. The postmodernsociety which we all inhabit would proposethat of allthevalues, moralsand judgementswhichmusterexpression,nonemaylayclaimtoanyspecialstatus comparedtoothers.Inthe totalitariannightmarewhichwasOrwell'sNineteenEight-Four,thisprinciplewaselevatedto8 Mythandme t h o dencompass our very definitions of reality. What was real and true consisted ofwhateverwasdecreedinthenameofBigBrothertoberealandtrue.However,theassaultonthenotionofobjectivetruthisfarfromfictitious.Orwell'sown story was rootedin the chilling reality of Stalinist Russia,sincewhich time there have been other appallingvariationson the same theme.Sciencestandsfundamentallyopposedtosuchaphilosophy.Thischal-lenge which science throws down does not claim that scientists have accesstoany absolute knowledge or ultimate truth. Rather, what is assertedis that therelationshipsbetweenevents whichsciencedescribesin some way mirror orapproximateto events that are assumed to occur in a world which is realandexists in someway independently of any human sensory contactwith it. Thisdoctrineisknownasscientificrealism.Forexample,aknowledgeofthemathematicalrelationshipswhich describemotionenablesspacecrafttobeplaced in orbit. These mathematical descriptions are not arbitrary in any post-modernsense -theydo not dependupona socialor publicconsensusthatthey are correct. They must fit with reality in some deepsense -otherwise thespacecraftcould not remain in orbit, and the practicalpossibilitiesof satellitecommunications and human space travel could not be brought into being.S c i e n c e ,be l i e fa n dt r ut h?Science is not without its critics -some fromwithin its own camp. Like Kuhn(1962),Feyerabend(1975)tooktheview thatshiftsinscientificparadigmsowemoretothedominatinginfluenceofpowerfulinterestgroupsandparticularbeliefsystemswithin thescientificcommunity thantoanylogi-callyandempiricallyderivedtruths.Indeed,thephysicistMaxPlanckfamouslyremarked:a new scientific truth does not triumph by convincing its opponents andmaking themsee the light, but rather becauseits opponents eventuallydie,anda new generationgrows upthat is familiarwith it.(cited by Kuhn, 1962:151)Because of this, many worthy and interesting hypotheses simply do not get toseethelightofday,orfindthattheiremergenceintoawiderpublicconsciousnessisseriouslydelayed.Silvers(1997)providesaninterestingcollectionofsuchideasandthefatesthatbefellthem.Whatcanwelearnaboutthenatureofsciencefromthesestories?Certainly theyleadus toaskexactlywhat scienceis or is not. Oneof the recurring themes in the quest topindownitsnature,hasbeenwhethertoconceptualizeitintermsof whatscientistsactually do (which is at times illogical, beset by personaland socialbias,subjecttoculturalandideologicalwhimsandswayedbypowerpolitics), or instead to describeit in the ideal abstract terms of what scientistsought to do. In a nutshell, the questionis whetherto depictit in a descriptiveor a prescriptivelanguage.Those who leantowardsthelatterpositionmaycitetheviewsofKarlPopper(Popper,1972),whoarguedthatscienceS c i e n c ea n de x p e r i e n c eprogressesthrough cyclesof hypothesis generationand refutation. However,he was acutely awarethat the firsthalfof this cycle -the business of gener-atinghypotheses-couldnot becapturedby any formalsystemof (hypo-thetico-deductive) rules. It is in essence a creative act.He was alsocognizantthattheorieshavefrequentlystoodtheirgroundandprevaileddespiteapparent falsificationsand their inability to account for well-known observedphenomena.Forexample,during hisown lifetime Newton'slaws of motionwereknown to be incapable of explaining the observedmotion of the planetMercurythrough the heavens.Suchdifficulties,amongothers,ledFeyerabendtocontendthatnocoherentaccount ofa universal unchanging scientificmethodwouldsuffice(in short, that there is not nor could not be such a thing as scientific method).Furthermore,it is true that science also embodies an article of faith -a funda-mental principle, if you like, that the'laws of nature' are in principlecompre-hensibleandconsistentthroughouttheuniverse.Withoutsucha guidingbeliefitisdifficultifnotimpossibletocontemplatehowsciencecouldbe'done'atall.Beyondthatonearticleoffaith,however,noideasaretobeconsideredsacrosanct.Yetifscienceissodifficulttopindown,howisitpossible thatideas come to fruitionwhichin their structureandfunctioningseemtocorrespondsocloselytothatwhichisobservableintheworld?Considerourexampleof thelaws of motionasset forthinitially by NewtonandlaterbyEinstein. We doneedtounderstand this ifwearemaintain thatthescientificpathoffersthebestprospectofcomingtotermswith humanbehaviour and the wealth of reportedhuman experiencewhich is onoffer.Althoughworkableandtestablehypothesescannotbeproducedbyfollowingarecipe,therearecertainaspectsofscientificactivitywhich,ifviewedfromabroadenoughperspective,dopermitittobedistinguishedfromotheractivities which might alsolay claim to truth. At the beginning ofthischapterwementionedwhatisperhapsthemostimportantofthese,namelythedisjunction betweentruthandauthority. TheproclamationsofNobel-prizewinningscientists andothereminentauthoritiesarenottrue byvirtueofwhotheyareorthepositionwhichtheyholdinthescientificcommunity.Certainlyovershort periodsoftimethis factcansometimesbeobscuredandtheartofpoliticalpersuasionmaytriumphoverreality.Forexample,Boyle(1990)providesaconvincing casefortheabandonmentofschizophrenia as a scientific concept because,afteralmost100 years, there isno empiricalevidencetosupportits validity. Perhapsweshould bethankfulthat thework of Machiavelli doesnot form part of thescientific curriculum!However,becausescienceisfundamentally pursuedinordertosolveintel-lectualandpracticalproblems,theflawsinanyproposedsolutionswhichrely more on power and persuasion than on reason tend more oftenthan not tobe rootedout eventually. It is less than certainbut morethan a hopethat thiswill happen.Theself-correctingtendencywhichscience(inanyfieldworthyofthename)tendsto exhibitover timeis thereforeanotherhallmarkwhich distin-guishessciencefromothersubjects.Andwhatisbeingcorrectedisthe10 Mythandme t hodmismatch(or potential mismatch) between what is predictedfromtheory andwhatmaybesuggestedbyobservation.Forexample,thereareelementsinthe presentationof astrologyor psychoanalysis which superficiallyresemblethosefoundinscientificwork,suchasdatacollection,itsrepresentationingraphicalform,andagrandtheoryto'explain'whatis'inthedata'.However,theories in truly scientificdomainsdo not simply consist of ad-hocideas(however interesting they may be)and nicepictures. To qualifyforthestatusofatheory,anideamustorganizealreadyexistingdatawithinacoherentexplanatoryframework, that allows new propositionsto bederivedlogically -propositions which necessitate making new observationswhich inprinciplecaneithersupportthetheoryorfailtodoso.Ifmoreandmoreobservationsare built up which challenge a particular theoretical stance, thenpressureisgeneratedtorejectthatstanceandcomeupwithanalternative.The alternative should be equally adept at explaining the old observations,beable to accommodatethe new ones,and also permitfurtherempiricaltestingofitself.Assuch,inconsistencyorapparentinconsistencyasexpressedthrough people's ideasandtheoriesis thefertilegroundonwhich scientifictheoriesareconstructed.Neitherastrologynorpsychoanalysishasanenviabletrackrecordfordealingwithpredictivefailures.Thesamecouldalso be said for religionand politics.This reiterative cycle of generatingideas and testing them has beenlikenedtoaformofartificialselectionwhereby'unfit'frameworks,theoriesandconjecturesare progressively weeded out, leaving in the long term only thosewhich tend to fit thefactswell and therebyaccordwith reality. Viewedfromthis perspective science is a form of cultural evolution.Its environmentis theworldof competingtheoriesand explanations. Thisallows usto understandthoseinstanceswheretheoriespersisteventhoughtheyfailcertaintests.Whatiscrucialis thecontextwithin which theyoperate.Failuretoaccountforknown factsmaynotbefatalif thecompetitionis no bettereither,and ifin additionit faresworse in otherrespects.A flawed state of orderisdeemedto be preferable to unbridled intellectualchaos.As c i e n c eo fe x p e r i e n c e : q ue s t io n so fme t h o dAllpsychologicalsciencebeginswithreal-worldexperience-fromintro-spectionofourown mentalprocessesto ourexperienceof ourowninterac-tionswithothers.Inthisrespectinvestigatorsinpursuitofascienceofpersonsfunctionasinstrumentsofbothdatacollectionanddatainterpre-tation. In recent years a vehementargumenthas been unfoldingaboutwhatmethodsare most appropriatefor studying human beings. In close proximitytothisdebatehasbeenanother,namelywhethertheconceptoftruthin(psychological)sciencecanbeprotected.Someadvocatesofqualitativeresearchmethodshavequestionedtheverynotionofobjectivity.Theycontendthatinpsychologicalresearchitisinextricablyboundupwiththenormative beliefsofgroups(chieflywestern,economicallypowerful,whiteS c i e n c eande x p e r i e n c e11males)whohaveforsolongoccupiedpivotalrolesat theheartof political,economic,culturalandsociallife.Thesenotionschieflypertaintomain-tainingemotionalandphysicaldistancebetweentheinvestigatorandtheinvestigated,andtheperpetuationofthisasastandardthroughtherepro-ductionofexistingpowerstructuresineachnewgeneration.Undersuchconditions,ourideasoftruth(which,forexample,stressuniversality,emotionalneutralityandfreedomfrommoralvalues)mirrorthemeansbywhichthoseinpowerhaveconductedthemselvesinthepursuitofbothpersonaland public profit.Because of this, it is argued that the use ofimper-sonalmethods-mostnotablythosewhich describeaspectsof humanrela-tionships in a quantitative fashion -contributesfurtherto our alienation andcan tell usnothingusefulaboutwhat it meansto behuman. Thereforetheyshould be rejected outright. The dismissal of quantitative methods of workinghasalsofrequentlybeenaccompaniedbycallstorejectrepeatabilityasanecessarycriterionforscientifictruth. Itisheldthathumanmeaningsandactions conjoin at unique moments and may never berepeated.Thereisundoubtedforce(bothpolemicalandlogical)behindthisargument.Paradoxically,however,therejectionofideasoftruth andobjec-tivitywouldmeanthattheverycategoriescriticshaveusedtolocatetheoriginsofthemanufacture anddistortionof'objectivity'and'truth'(e.g.social class and gender) cannot be regardedas belonging within the realm ofthereal,fortheveryideaoftherealhasbeendiscarded.Theyareinsteadmerely socially constructed entities, discredited because of theirclass/genderorigins. Assuchit isproblematictoconsiderfromsucha perspectivewhattheaimsofknowledgeareorcouldbe.Iftheyaremerelylinkedtosomecompeting ideological project, then the more extreme dangers of the politicalmanufacture of scientific truth loom on the horizon -and what would it meanto make assertionsif the evidential basisfor them was not replicable?Shornof realism and replicability, what goals can inform research? History alreadybearswitnesstothecostsofthisapproach.TherejectionofMendeliangeneticsin the Soviet Union during theStalinist eraled to massfamine, andthe promotion of racial sciencein the Nazi era led to genocide and world war.Whenconceptsoftrutharerejectedthroughoutasociety,thentyrannyappearsa willing beneficiary. Whatstartsas intellectual tyranny is usually asign of physical tyranny to come.A more consideredcriticism ofscientific practicein boththe quantitativeandqualitative realmsacceptsthepresenceof biasemanatingfromcertaininterestgroups,andindeedregardsthestudy of this as important in its ownright. Furthermore,theaddition of qualitative researchto extendthe role ofhumanmeaninginscientificdiscourseiswelcome.Proponentsof'criticalrealism'asithascometobecalledacceptthebasictenetsofscientificrealism(i.e.thatthe worldexists independentlyof our attempts to describeit,andthatsuccessfulscientifictheoriesdescriberelationshipsbetweentheoreticalconstructs which approximateto thosewhich existbetweenrealentities or processesin the world). Against this backdropthey seeksimulta-neouslytorevealthedistortinginfluencesofspecificsocialandhistorical12Mythand methodprocesses as they bear upon the institutional organization of scienceand theactual reasoningof practisingscientists.Because historicalanalysesrevealthatnumerouschangesinthefundamentaltenetsofscientificreasoninghaveoccurred(seeChalmers,1999),auniversalconceptionofscientificmethodthatistrueforalltimeis rejected.However,atanyonetimetheprocess of askingquestionsand interpreting evidenceis broadlysimilarinall scientific disciplines,although each favours the use of methods and tech-niques that are particularly well suited to handling the problems which arisein that domain. The more common elements that comprise scientific methodinthemodernagedonotcomprisetheuseofmathematicalorstatisticalcomputations per se. As we have said, what is crucial is the gatheringof dataforthepurposeofgeneratingandtestingideasaboutwhatisorcanbeobserved. The reiterative use of this process, informing and in turn influencedby the cultural milieu,is what leads over time to a more accurateandusefulaccount of things (see Figure1.1).Figure 1.1 Science as an iterative cycleExperience and science: the morallandscapeWe havearguedthus farthatsciencedoesnotfollowperfectlyprescribedrules,and that although subjectto a number of differentsourcesof bias, itsorganizationandpracticetendovertimetofavourthesurvivalofwell-orderedtheoreticalschemesthatareablecoherentlytoaccountforlargeS c i e n c eande x p e r i e n c e13bodiesofdata,whilstatthesametimepossessingsufficientflexibilitytomakenoveltestablepredictions.Inordertoaddresstheissueofwhetherscienceisasuitablevehicleforundertakingthestudyofexperience,weneedfirstto lookat thewider question of its moralfitnessto do this. One ofthefiercestobjectionstoascientificstudyofexperiencecontendsthatscienceobjectifieshumanbeings,ignoresourfundamentalstatusassentient, reasoning, feeling, self-consciouscreatures,and thus threatensourdignity.Itmustbeadmittedthat,inthenameofscience,manyactshavebeen carried out which provideammunition for this argument. The twentiethcenturywitnessedtheforgingofevercloserlinksbetweentheglobalmilitaryindustrialcomplexandthescientificcommunity.Themeanstowagemasscampaignsoftechnologicalandpsychologicalwaragainstcivilianpopulations(Glover,1999)hasonlybeenmadeavailablebecausescienceincreasinglyservestheinterestsof big business -and the manu-factureofthemeanstokillandterrorizepeoplewithevergreater'effi-ciency'is bigbusiness. To manythis isasource ofdismayandagrotesqueparodyofthebeautyandelegancewhicharemorefittingtestamentstoscientificenterprise.Oneoftheproblemsisthatsciencewasoriginally invented, constructedandelaboratedforthestudyofnatural objects.However,unlike inanimateobjects,thebehaviourofpeopleinobjectivethree-dimensionalspaceisafunctionoftheirexperienceofthemselves,theirexperienceofothersandtheir experience of the worldaroundthem,as wellas the behaviourof otherpeopleandmaterialobjects.Thisposesuniquechallengesforthestudy ofexperience. The task of constructing an appropriatescienceof people has forsomebeentheholygrailofpsychology.Asanexplicitgoalithasbeenaddressedbyengineer-turned-psychologistGeorgeKelly(Kelly,1955)andpsychiatrist R.D. Laing (Laing and Cooper,1964; Laing,1967). Through histheoryof personalconstructs, Kelly sought to develop an idea of the'personasscientist'activelyconstructing andreconstructing thebuilding blocksoftheirmentallifeas they negotiatedtheirway through thesuccessiveexperi-ments which constituted their unfoldinglife. Highly influentialas this notionhasbeenattimes,itsradicalpremiseofreconstructingpsychologyasanentire discipline has floundered. Meanwhile, the emerging metadisciplines ofneuroscience, cognitive science, health science and social sciencethreaten topickoffthevarious constituents ofwhatappearsincreasinglytobeafrag-mented discipline. Laing's effortsembodieda synthesis of Marxism, psycho-analysisand existentialismin which normalitywas depicted as an estrangedand appalling state of alienation, andset outa radical agenda for a science ofpeopletosupportanddiscoverpathwaysbacktoreality.Aspsychiatrybecameentrenched in biological reductionism and the optimism of the1960sfaded,Laing'scritiquewasleftonthesidelines.Thecurrentdominance ofglobal free-market capitalism and its invasion of the private domain (through,forexample, the twin channels of pornographyand the'talk show', wherebypeoplebare their bodiesand their souls for mass-market entertainment) onlymakestheneedforustoreassessourpositionallthemoreurgent.The14Myth andmethodproblemthus remains.How can westudy experience in a way that does notdo psychologicalviolence to us?E x p e r i e n c ea n dme t h o dAconsistentdifficultyforpractitionersofthescientificmethodhasbeenwhat status to accordthe self-reported experiences of humans. Dreams,near-deathexperiences,apparentinstancesof telepathyandalienabductionsarejustsomeof thereportedexperiencesthatscientistsmust contendwith,yettheprivateunobservablenatureofhumanexperienceseemstorenderitunsuitableforscientificscrutiny.Cansystematicmethodsofenquirybeapplied bothto the empiricaldataof self-reports and within the experientialrealm? If so, how are these to beapproached?Anchored in the philosophy of realism, one strategy is to seekcorrelationsbetweensuchreportsandothermoreeasilyobservablephenomena,andtoattempt to establish the conditions(e.g. biological,social or cognitive)underwhich such reports are made. This might tell us something about the nature ofthereports,butbyitselfitisinsufficienttoestablishtheveracityoftheputativeexperiences towhichthe reportsallude.For example,evidencefortheexistenceof bothsleepanddreaming(seeChapter7) reliesontheself-reports of human subjects (Malcolm,1959). In the case of sleep, these reportsarevalidatedbytheappearanceof particularbehaviouralandphysiologicalindicatorslinkedtolevelsofarousalwhichoccurimmediatelypriortoareport.Wheredreamsareconcerned,itismorethecognitivecorrelatesofreporting,incombinationwiththetemporalcorrelateofreportingthemimmediatelysubsequent to waking, that points to the existenceof adifferentmentalstate -which is unobservableto others -occurringunder the condi-tionsofsleep.Thisinferenceisfurtheraidedbythefactthatanover-whelmingmajorityofpeoplereporttheseexperiences.Iwouldstressthatwhat is beingvalidatedhere is the notionthat dreamingas a differentmentalstateoccurs -not the contents of any one particular dream.Despiteearliermisapprehensions,dreamsarereportedfromallstagesofsleep,notsimplyduringthestagewhererapideyemovementsoccur(REMsleep)(Foulkes,1960).Ifappliedtoexperientialreports,systematicinvestigationsoftheirproperties,correlatesandimplicationsarelikelytoyieldvaluableinsightsintowhatthesemean,notjustinframingcausalexplanationsforthesereports(i.e. what the reportscan tellusabout theinternaland externalreal-ities in which people live),but in what theyalso tell us abouthuman life andthe struggles which being human entail.Similarrationaleshavebeenemployedinthestudyofmeditation.However,it is importantto note that oncescientific practitionersaresatisfiedthat a particular phenomenon is real, if they wish to explore furtherthe natureofa particular typeof consciousexperience,then they must orientatethem-selves with respectto the actual contents of the experienceand systematicallyexplore ways in which the experiencescan be modified or transformed. SuchScienceand experience15means may be externally induced (e.g. through drugs or sensory deprivation),but may also be induced through intended acts of will or cognition, which arethemselvesrepeatableandwhichothersmaylearnthroughinstruction.Accordingly,it canbeargued that a certaintypeofsystematicquestioningandevaluationofthenature ofsomekindsofexperienceanditsattendantpossibilitiesisonly possiblethrough having the experience.Laterchapterswill consider the merits and potential of applying such an approach to statesof consciousness induced by meditationand lucid dreaming.It is importantto note here that this is only made possible through the replicablenature ofthephenomenon. However, theinitialstages ofscientific exploration mustbegin with establishing the veracity of experience -determining its boundaryconditions,if you like -moving through exploringits contentand structureand proceeding to ascertain the means to mould and transform theexperience(see Figure1.2 for a summary of this process). Although experiencessuch asdreaming, remembering and consciously experiencingthe world are private,weassume their veracity in others, partly through our mutual identificationwith them as beings like us who have the same kind of conscious experiencesthat we do. When it comes to claims of more esotericexperiences(e.g.alienabductions), this type of common ground simply does not exist.Figure 1.2 The science of experienceInadditiontoexploringtheveracity,content,formandmalleabilityofexperience,allpsychologiesofexperiencealsoinvariablyaddresssomeaspectofhowexperientialknowledgecontributes toandtransformsone'sactions in the world. Such study can involve taking an anthropologicalstance16Mythandmethodtowardstheculturewherecertainexperiencesarecultivatedorareheldtooccur.Thismayinvolve asking howbeliefinparticular experiencesshapesthe actions of those who adhere to it.Inthetermswehave justdescribed,then,scienceisnotopposedinanyfundamentalwayto thestudyof experience. Wheresciencediffersis intheinterpretative stance towards reported experience.'Seeing is believing', so thesayinggoes.Andalthough Aristotleconsideredrelianceon thesensestobecritical for establishing scientific truth, this criterion has long since been aban-doned (Chalmers, 1999). By itself experiencecannot be and is not regarded assufficientevidencefortheindependentrealityofwhat peopleobserve.Thedifficultiesof interpreting reports of certain experiences,particularly the kindaddressed by the contributorsto this book,are compoundedby virtue of theirfrequentlybeingpresentedin termsof an interpretation-an explanation oftheirorigins-ratherthanan accountofonlythe contents(thephenome-nology) of the experience. For example, reports of alien abductions, out of thebody experiences(OBEs) or apparent telepathy are usually describedin termswhichalreadypresupposethecauses behind them(i.e.peoplereportexperi-ences of being abducted by aliens because they have been so abducted, OBEsare caused by the mind leaving the body, and peopleshare common thoughts,feelingsor impressions becausetelepathy,or thought transmission, occurredbetweentwo or more people). Whenfacedwith this, it is importanttodisen-tangletheprocessbywhich peoplearriveataninterpretationoftheirexpe-riencefromwhatitwasthattheyoriginallyexperienced.Forexample,indiscussionswithpeoplewhoclaimtohavesensedthepresenceofdepartedspiritsinhaunted houses, closerquestioning frequentlyrevealsa distinctionbetween perceived physical sensations (e.g. coldness) or psychological sensa-tions (e.g. anxiety, fear)experiencedat the location, and thesubsequent attri-butionthatthesearecausallylinkedtosomeonehavingdiedthere.Thisattribution may be made immediately after the experienceif information aboutadeathwasalreadyknown, oritmayoccursometimelaterasinformationcomesintosomeone'spossession.Thepsychologyofhowandwhypeoplemake attributions about the world in which they live has much to offerhere. Itcan help us to shed light not just on the wild and wonderfulexperienceswhichpeoplereportthat theyhave, butalsoontheirbeliefsabout theveryway inwhich the world is structured.One of the critical features whichdistinguishesscientificfromlay accounts of events concerns not just the methods adopted toarrive at an answer, but also what is being accounted for. Fletcher (1987:136)expressed this succinctly: 'an important part of our understanding of the worldlies in knowing what not to explain'. Thus science begins with the report as theprimedata,nottheassumedrealityofwhatisreportedasexperienced.Similarly, it may be more instructive to investigate people'sunderstanding ofcoincidence ratherthanto beginbyassumingthatsomeacausalconnectingprinciple(e.g.synchronicity, telepathy,etc.)underlies thetemporal juxtapo-sition of two events which to one personare highlymeaningful.Werepeatthatthisdoesnotmeanthatscienceisantagonistictoexpe-rience, butmerely that something moreis required before one moves fromaS c i e n c eande x p e r i e n c e17person'sexpressedbeliefinaphenomenontobelievingwholeheartedlyintherealityofthephenomenonasdescribed.Thecorrectattitudeofthescientist faced with reportsof unusual experiencesis to seek furtherevidencefororagainsttheexistenceofsuch experiences.Itdoesnotmeanthatsuchaccounts must necessarily be dismissed. Absence of evidence is not of coursethesameasevidenceofabsence.However,whenverylargenumbersofpeople make persistent extraordinary claims (e.g. the presence of alien beingson Earth)in theabsenceof anysupporting evidence (which onewould logi-callyexpecttoexistwere theclaimsactually to betrue), andwheread-hocuntestable explanations are continually proposedto account for the failure toproduceevidence,oneisentitledtoremainscepticaluntilsuchevidenceemerges (Sagan,1997).Weneedtoexerciseconsiderablecautionwherebeliefsareconcerned,particularlythosewhich arefirmlyhelddespitecontradictoryevidence,andwhichappeartobeunfalsiflablebyanycriterion.Onestancethat investi-gatorsintounusual (orindeedcontroversial)beliefscantakeistocontem-plate the kind of contradictoryevidence which might lead a rational person togivethemup.Ofcourse,tovarying degreeswehaveall beenguilty atonetimeoranotherofholdingontobeliefswhichhavepassedtheir'sell-bydate', and methods suited to investigating unusual beliefs and experiences,iftheybelongtothegeneralcorpusofscientificknowledge,willalsoveryprobably be fruitfulin the study of more familiar aspects of humanbehaviour.However, it must be rememberedthat beliefs cannot be validated in thesameway that the existence of differentstates of consciousness can. No amount ofneurophysiological reductionism will ever be able to point to the neurophys-iologicallocationofoureverydaybeliefs(Dennett,1995a).Beliefsareunavoidablygroundedinoursharedsocialrealities.Onthebasisoftheirbeliefspeoplemaybedeemedcriminal,eccentric,worthyofpsychiatrictreatmentor may even be murdered. But is there a paradox here?On the onehandwearesayingthatscienceisconcernedwith discoveringwhatisrealand true, and on the other we are faced with a social reality which is groundedon consensus -a consensus whichnumerousstudies of human historyhaveshowntobemalleable.Undersuchconditionswearebroughtbacktothequestion of how sciencecan lay claim to any kind of objective truth about theworld.Wehaveseenthatsuchclaimscanonlybemadeprovidedthatthesocial consensus which exists is not one brought about by coercion,and is notacollectionofsimplepersonalopinions(sharedcommonsense),but ratherwhichdependsonadherencetobroadlyagreedconventionsforcollectingand reportingdata, formulating conjectures or hypotheses to explain the data,andprovidinglogicalandempiricalargumenttosupportthem.Thenatureandlimitations ofscienceneed to bewell understood. At theendof thedayno theories can lay claim to a final or ultimate truth. Scientifictruths,unlikedogmaticassertion,must of necessitybe temporalin their nature and open torevision.Theyarefallible,butthereinliesoneoftheirmajorstrengths.Scienceis of coursenot the only way to understand human experiencebut ifwe are to use our experiencesas a basis for understanding the world in which18 Mythandme t hodwe live -and not merelya source of recreation or wonder -then an alliancewithasystematic criticaloutlookshould yield usefulrewards. Someoftheclaims made by peoplewith regard to their experiences presentfundamentalchallengestoviewsoftheworldwhicharedominantinthescientificcommunity.Theymustnotberejectedsimplyonthebasisofthisdiscor-dance. However, inafairandcriticalhearing mattersof evidenceandlogicmust be paramount.S ug g e s t e df ur t h e rr e a d i n gChalmers,A.F.(1999)Whatisthisthingcalledscience?,3rdedn.Buckingham:Open University Press.Popper, K. (1972) Conjectures andrefutations.London: Routledge and Kegan Paul.Sagan, C. (1997) The demon-haunted world. London:HeadlineBooks.2ProbabilityandcoincidenceAnthonyE .E sgate and David GroomeGoddoesnot playdice.C h a n c ea n dc o i n c i d e n c e(Albert Einstein)Unexpectedeventsandcoincidenceshappenfromtimetotime,andwhentheydo,itisamatterofpersonaljudgementwhetherweattributethemtochanceortosomeotherfactorsuchas paranormal influences. Considerthefollowing three examples, and try to decide whether they offersupport for theoccurrenceofparanormalphenomena,orwhethertheycanbedismissedasmerely chanceevents.1.Inanexperimentonextra-sensoryperception(ESP),theexperimenterturnsoverplayingcardsoneatatimeandtriestoconveytoapartnerwhethershe is looking at a red cardor a blackone. Although thepartnercannotseethecards,hebeginstheexperimentbyguessingthecorrectcolour three times in a row. Is this just luck or was it due to ESP?2.A student looking through a list of his classmates discovers that one of theotherstudents has thesame birthday as him. There are only 23 people inthe class,so would you regardthis as a fairlyamazingcoincidence?3.A man dreams about a plane crash, and then wakes the next day to read inthenewspaperthatthereactuallyhasbeenarealplanecrash.Wasthedream a premonitionor just acoincidence?In all of these examples we are faced with the same basic dilemma. Can theeventsbedismissedasmerechance,orweretheyjusttooimprobablefor20 Mythandme t h o dsuchamundaneexplanation?Thisquestionreallyisquitefundamentaltoevery claim of a'psychic' or'paranormal' experience,and in order to answeritwe needto beableto judgehowprobableitwasthatsuch aneventcouldhave occurredby chancealone.P r o ba bi l i t yAlloftheseexamplesrequirea judgementofhowprobableitwasthattheeventwouldoccurby chance.Insomecasesthislevelof probabilitycanbepreciselymeasured,andisusuallyexpressedaseitherapercentageorafraction.Forexample,theprobability(P)ofacoinfallingdown'heads'isone chance in two, which can be expressedeither as a percentage(50%) or asafraction(P= 0.5).Wecannowreturntothethreeexamplesgivenabove,this time makingan estimateof probability.1.In the ESPexperiment(example1), the probability of guessing thecolour(redorblack)ofeachcardcorrectlyis0.5(50%),sothechancesofguessinga wholeseriesof cardscorrectlywill behalvedwitheachcardselected.Thismeans that thereis a 50% chanceof guessingthe firstcardcorrectly,a25%chanceofguessingtwoinsuccessioncorrectly,anda12.5% chanceof guessing three cards in a row correctly. From this we canconcludethatthereisactuallyafairlyhighprobabilityofmakingthreecorrectguesses in a row by sheer chance(P = 0.125 or12.5%), so thereisno reasonto lookfor any otherexplanation.2.Withtheclassmates'birthdays(example2)wecancalculatetheproba-bilityoftwopeoplesharingthesamebirthdayfromagroupofagivensize,although it is a little complicatedbecausewe need to considereverypossiblecomparisonbetweeneachmemberof the group and every one ofthe other23 members.Thisproducesa surprisingly largenumberof paircomparisons,andconsequentlytheprobabilityofasharedbirthdayishigherthanmostpeoplethink.Infact,thechanceoffindingasharedbirthday in a group of 23 people is 50%(P = 0.5),so such a coincidenceisfarfromremarkableandcanbeexpectedtooccurasoftenasnot.Thisratherhighprobabilityillustrates howpeopletendtounderestimatethechances of an event happening when there are a large number of possibil-itiesorcombinationstotakeintoaccount.(Notethatafulleraccount ofthe methodof calculating this probability is given later in thischapter).3.With the plane crash premonition(example3) we are dealingwith eventswhichcannotbereadilyquantifiedormeasured.Howlikelyarewetodreamofaplanecrash? Andwhatarethechancesofa realplanecrashoccurringon the same day? A precise probabilitycannot be calculated, soweneedtoacceptafairlyroughestimate.WhatwedoknowisthataircrashesarereportedontheTVnewsfairlyregularly,anddreamsofdisastersandaccidentsarealsofairlycommon.Giventhatbotheventshave a high probability of occurring, the likelihoodof their coinciding byP r o ba bi l i t ya n dc o i n c i d e n c e21sheerchancewillalsobereasonablyhigh. Onemust thereforeconcludethatthedream/aircrashcoincidencecanbeadequatelyexplainedbychance,withoutanyneedtoassumeanypsychicorparanormalexpla-nationsuch as a premonition.Theseexampleshighlight thebasicquestionwemustaskwheninvesti-gatingclaimsof'paranormal'experiences.We needtoestimatetheproba-bilityoftheparticulareventoccurringbychancealone.Iftheeventwasreasonablylikely,thenweneedlooknofurtherthanchancetoprovideanexplanation. We should only considerthe possibility of a non-chanceexpla-nation(e.g.theinterventionofpsychicforces)whentheprobabilityofachanceoccurrenceisextremelylow.Eventhen,ofcourse,weshouldnotautomaticallyacceptaparanormalexplanation,astheremaybeotherpossible causes which need to be ruled out. For example, in the ESPexampleabove there could be subliminal cues passing between the two partners in theexperiment,oroneofthemcouldhavebeencheating.So-called'para-normal'experiencesoftenturnouttohaveanormalandstraightforwardexplanation, so it is necessaryto lookcarefully forthesebeforeweconsiderparanormal explanations.Insciencessuchaspsychology,experimenterstesttheirfindingsagainstprobabilities, in this case the probability of their finding being just a 'chance'event. By convention, if the probability of obtaining a result by chance is lessthan1 in 20(also expressedas P = 5%or P = 0.05), then it is deemedto bea'significant'finding-one whichisunlikely tohaveoccurredbychance.Alternatively,a probability of lessthan1 in100 (P = \%or P= 0.01)repre-sents a higher level of significance,where we can have far greaterconfidencethat our findings would not have occurredby chance.P r o ba bi l i t yj u d g e m e n t sa n dbe l i e fin t h ep a r a n o r m a lThere is some evidence that people who believe in the paranormal may be lessaccuratein making judgements of probability than non-believers(Blackmoreand Troscianko,1985). Specifically, the believersare morelikely to underes-timate the probability of a chance event. This might explain why they are morelikelyto accepta paranormal explanation of their experiences,sincethey aremorelikely to consider an unusual event to be so improbable as to be beyondcoincidence.Thosewithamoreaccurategraspofprobability, ontheotherhand,wouldjudgethesameeventtofallwithintheboundsofchance.Believersmay thus tend to misperceive chance events as being beyond coinci-dence. A number of experiments have provided support for the hypothesis thatbelieversintheparanormalhaveatendencytounderestimateprobabilities.These studieshave useda variety of tasks, including estimatesof probabilityincomputer-controlledcoin-tossing(BlackmoreandTroscianko,1985),random number generation (Brugger et al., 1990) and estimationsof the prob-abilityofsharedbirthdays(MatthewsandBlackmore,1995).However,22Mythandme t hodalthoughtheseexperimentsprovidedsomesupportforthe'probabilitymisjudgement'theoryofparanormalbelief,notallstudieshavefoundthis(Blackmore,1997),soitappearsthatbelieversintheparanormalmaybeprone to probabilitymisjudgements in some situations but not in others.P r o ba bil it yj u d g e m e n t sine ve r y d a yl ifeThe notion of probability is fundamental to many forms of human endeavour,andactuallyunderpinsmostformsofhumanreasoning.AmongthemoreobviousexamplesaregamblingandgamesofchancesuchastheUKNational Lottery. However, most other types of judgement involve estimationofaprobability,eventhoughitmaynotbeobvious.Inacourtoflaw,adefendantisusuallyfoundguiltyorinnocentonthebasisofabalanceofprobability.Thejurymustdecidewhetherthedefendantislikelytobeinnocentorguilty. Absolutecertaintyisrarelypossible,soinsteadthe juryonlyhastodecidethedefendant'sguiltorinnocence'beyondreasonabledoubt'. That is, they must decide in which direction the balance of probabilitylies.Similarly,inscientificwork justabouteverythingweknowabouttheworld is basedon observationof patterns and regularities. We then takethosepatterns to imply certain things about the probability of such events occurringagaininthefuture.Forexample,thesun hasrisenoneverymorning oftheauthors'life,so it willprobablydoso tomorrow.However,wecannever beabsolutelycertainthatthiswillbethecase,sinceonsomemorninginthedistant futurewhen thesun has burnt itself out there will beno sunrise. Thistype of inference, in which we base futurepredictions upon regularitiesin thepast, is referred to as inductive reasoning and is characteristic of much scien-tificthought. On a moremundane level probability pervadesour daily activ-ities,sincewheneverwemakeadecisionweimplicitlymakesomeassessmentsofprobability.Forexample,indecidingtodoa universitydegree,allkindsofassumptionsaremadeconcerningtheprobabilitiesofvariouscostsandbenefits,butmoststudentsarebettingontheprobabilitythattherigoursanddeprivations of university studywillpayoffinthelongrun(e.g. in termsof increasedsalary).D e f i n i t i o n sa n dme a s ur e so fp r o ba bi l i t yForaconceptthatissopervasive,probabilityisremarkablypoorlyunder-stood.Muchoftheblameforthismaylieinthewaythatmathematicsistaught(since a proper treatment of probability requiressomemathematics),butatleastsomeblamemaybeattachedtothefactthathuman intuitionseems to be ill equipped to handle probability. Probability may be defined ina number of ways. Manktelow(1999) suggeststhree ways of defining it. Thefirstof theseis in termsof observedfrequencies. For example, ifI stand at astreetcornerandcount boththenumberof passingcarsandthenumber ofP r o ba bil it ya n dc o i n c i d e n c e23passing carsthat happento be red, then it may be possiblefor me to arrive atan estimate of the probabilityof the next car being red. Defined in this way, interms of observedfrequencies, the probabilityof an event A, written P(A), isthefrequencyofevent Adividedbythefrequency ofalltypesofeventsinwhich A couldhave occurred. That is:_ ,,,numberof redcarscountedP(nextcarred) =totalnumberof carscounted.Ofcourseitisnotalways possibletocarryoutafrequencycountofthekinddescribedabove.Undersuchcircumstanceswemayinsteadusetheseconddefinition,whichisbasedonthetotalnumberofpossibilitiesavailable. The probability of an event A is now thetotal number of ways thatA can occur divided by the total number of possible outcomes.We can applythis definitionreadily to the probabilityof winning the UK NationalLottery.Itwould take many human lifetimestoassessthe probabilityof a particularcombinationofnumberscomingupifwedidthisbyfrequency counting.However,if we work out the probability of a particularsequence by enumer-atingpossibilities,it isquitesimple toassesstheprobability. Thereisonlyoneway in which a particular sequence can comeup, and that is by all of thesix numbers beingchosen(providedthat we ignorethe actual orderin whichthey occur). Again ignoring the order in which individual numbers are called,the total number of sequencesthat can possibly comeup is approximately14million (14,000,000).Hence:/^winning lottery) =14,000,000 (approximately).This ratio illustrates one of the problems that people have in handling proba-bilities,namely the difficultyin comprehendingvery large numbers. What doesa probabilityof1 in14 million actually mean? In factit means that in ordertohave a reasonableexpectation of winning thelottery once,you would needtocompeteeveryweekfor250,000years,duringwhichtimeyouwouldhavespent 14 million and lived for twice as long as modern humans are thought tohave beenin existence. In other words, your chances are so low as to be almostnegligible. Whatis the relationship betweenfrequency-based and possibility-baseddefinitionsof probability? Fortunately, thelaw of largenumbers canbeinvoked(ofwhichmorelater)toshowthatbothdefinitionsareequivalent.Givenalargeenoughnumberofobservationsfromwhichtoestimatefrequency,the probabilityvalue that is obtained comes closer and closer to the'true'value basedonpossibility.However, justasitis notalways feasibletoconduct a long enough study of frequencies (as with the lottery), so it maynotbe possible actually to enumerateall of the possibilities available.Consider theprobabilityofbeingknockeddownintheLondontraffic.Itissimplynotpossibletoenumerateallofthecombinationsofeventsthatmaybringthisabout.Ourestimatesinthelattercasewouldthereforehavetobebasedonobserved frequencies (e.g. the frequencyof accidentsper pedestrianmile).24MythandmethodThethirdandfinalwayofestimatingprobabilityisbyusingsubjectiveestimates,where we essentiallymakean informedguess. Thisis what book-makersdo when theyofferoddsona horsewinning a race(although in thiscasemattersarecomplicatedbythefactthattheoddsofferedactuallyrepresentsomethingmoreliketheamount that the bookiecanaffordto payyouiftheirprobabilityestimateiswrong,whilststillmakingaprofit!).Subjectiveestimatesofthistypeunderliemuchintuitive decision-making.Althoughsubjective probabilityestimation may be the greyest area of proba-bility,theredoexistwaysofmakingtheestimatesmorereliablebymodi-fyingthemin the lightof the available data. Thestatistician Bayes called thesubjectiveestimatethe'prior' odds,andshowed how this could be modifiedtogivethe'posterior'oddsbyreferencetoobservedfrequencies.Unfortunately,researchindicatesthat humans are fairlypoorBayesianesti-mators,(i.e.theyarenotskilledinmakingthesetypesofmodificationstosubjective probabilities)(Kahnemann et al., 1982).Whicheverdefinition of probability we apply, one thing is clear -the eventswe are interestedin can never be morefrequentthan the possible events, sincetheywillonlyoccuronsomeoccasionsandnotonothers.Thusthelowestvalue that a probability can be is zero. This value indicates that the event has notoccurred(frequencycount) or cannot occur (possibility). Again, if the event ofinterest happensall of the time, then the ratio of thenumber of times that thishappenstothenumberoftotaleventsis1,sincethosenumbersareequal.Therefore probability, when expressedmathematically, is a simple matterof anumber between 0 and1. A probabilityof 0 means that one can be certain thataneventwill nothappen. Avalue of1 indicatesthatit certainlywill happen.Moreoftenwehaveanumberbetween0and1,indicatingthattheeventhappens some of the time. The nearer this number is to1, the more often we canexpectthe event to occur. We can alsoexpress probabilitiesas percentagesbymultiplyingthemby100.Thusaprobabilityof0.41isequivalent toa41%chance of a particular outcome happening.I n d e p e n d e n te ve n t sa n d t h eg a m b l e r ' sf a l l a c yAnimportantaspectofprobabilityisthenotionofindependentevents.Theseare eventsthathave no bearinguponeachother.For example,whentossinga coinseveraltimes, eachspinofthecoinisan independentevent,and its outcomeis unaffected byany previousoutcomes.Each timewe spinthe coin, it is equally likely to comedown'heads' (H) or 'tails' (T), so thereisa probabilityof0.5ineithercase. Theconceptofindependenteventsisnotalwayswellunderstood.Rouletteplayerssometimesmaketheassumptionthatif'red'hascomeupseveraltimesina row,thenthe nextspin of the wheel is more likely to come up'black'. This is an example of the'gambler's fallacy'.In reality, theoutcome of the next spinis unaffected bytheoutcomeoftheprecedingones,andtheprobabilityof'red'or'black'remains50:50(assuming, ofcourse,thatthewheelhasnotbeentamperedP r o ba bi l i t ya n dc o i n c i d e n c e2 5with).Thegambler'sfallacyistypicalofthetypeoferrorsthatpeoplecommonlymakewhen estimating probabilities. The reasonswhy peopleareprone to such flawed thinking are probablyquite complex.It seemsthat theyeitherfailtounderstandthenatureofindependentevents,orelsetheyactuallyprefertobelievethatoneeventcansomehowaffectanother.Perhapssomepeoplelike to believethat events are in somewaycontrolled,eitherbythemselves(e.g.byblowing onthediceor'willing'redtocomeup)or bysomeinfluence which theybelievetheycanpredict.Suchbeliefsmayallowthegamblertoattributetheirsuccesstotheirowneffortsratherthantopureluck,whichmayincreasetheirself-esteem.Thissituationiscompoundedbypeople'spronenessto'confirmationbias',whichisthetendencyto focuson events which confirm their beliefsand to ignoreeventswhich contradictthem(Wason,1968).For example, a roulette wheelwhichhas come up red twice in successionis still only 50% likely to come up blackon the next spin, but this means that it will do so about half the time,and thegambler'stendencytooverestimatethisfrequencymayleadtoafalseconfirmationoftheirbelief.Thegambler'sfallacyisonlyoneexampleofthesystematicflawsin thinking towhich peopleare pronewhenestimatingprobability.Thereareothersimilarfallacies,includingthoserelatingtoconjunctionsofevents.C o n j un c t i o n sIfwespintwocoinsintheair,whatarethechancesofbothcomingdown'heads'?Thisisanexampleofa'conjunction'oftwoevents,andweshallnowconsiderthe possibilities.If wespina coinonce,thereare twopossibleoutcomes,heads(H)ortails(T),eachofwhichhasthesameprobability of0.5.However,ifwespinacointwice,therearefourpossibleoutcomes,namelyHH,TT, HTorTH.Eachofthefouroutcomesisequallylikely,soeachhas a probability of 0.25. This illustrates the basic rule for combining theprobabilitiesofindependentevents,whichis thattheprobabilitiesmultiply.For example, the probability of obtaining the outcome HH is 0.25(0.5x0.5).Thisisknownastheprobabilityofaconjunction ofthetwoevents(inthiscaseHH).TheprobabilityofaconjunctionoftwoeventsAandBcanbeexpressedas follows:P(AandB)= P(A)x />(B).Thisbasicformuladescribestheconjunctionofanytwoindependentchanceevents.Forexample,the probabilityofdreamingofanaircrashonthesamedayasanactualaircrashwouldbe calculatedbymultiplying thetwoprobabilitiesinthisway.However,firstwewouldneedtohaveanestimateofthoseprobabilities,forwhichpurposewewouldneedtoknowthe frequency of air-crashreportsin the newspaperand the frequencyof air-crashdreamsforthatparticularindividual.Oneconsequenceof thewayinwhichprobabilities of independentevents combine is thatthe probability of26Mythand methodaconjunctioncanneverbegreaterthantheprobabilityoftheeventscomprisingit.Thisisbecausebothofthelatterprobabilitiesarenumberslessthan1,andwhentheyare multipliedtogethertheanswermust belessthan each(for example - x ^ = -).People oftenfallvictim to a type of conjunctionfallacy that was illustratedby Tverskyand Kahneman (1983). They used the following example.Pr obl e m 2.1ImaginesomeonecalledLindawhois'31 years old,single,outspokenand v erybright. Asas t u de n t ,shewasdeepl yi n v ol v e dwi thi ssu esof di s c r i mi n at i o nands o c i alj u s t i c e ,andalsoparticipatedinant i - nu c l earde mon s t r at i on s ' .Whatdoy outhinkishermostl i k el ycu rrentsituation.Isshe:( a) abank c l e r k( b) a f e mi n i s t( c) abankc l e r k whoisaf e mi n i s t ?Whenaskedto rank theoptions(a), (b) or (c) inorderof likelihood,89% ofsubjectsthought(c)wasmorelikelythan(a).However,since(c)isaconjunction,we know thatthis has to be the least likelyalternative.It seemsthatsubjectsusesomeother(andlessaccurate)basisfor judgementthanprobability,andKahnemanand Tversky(1983)arguethatsubjectsactuallymake use of certain heuristics or rules of thumb in probability estimation, andthattheseinturngive risetobiases.Onesignificance ofsuchbiasesis thatthey may underlie many examplesof social judgement. Thesewould includeprejudiced judgements in which, for example, membersof one group wouldbeseenasmorelikelythanmembersofanothergrouptohavecommittedcertaincrimes.U n r e ma r k a bl ec o i n c i d e n c e sWhatare the chances of two or morepeoplein a group having thesamestarsign? When it happens to you it may seem an unlikely coincidence,but in factthe number of peoplerequiredforsuch coincidencesto occuris quite low. Ifinsteadoflookingforabsolutecertaintythatsuchacoincidencewilloccur(whichwillrequireagroupof13 people),onecaninsteadcontentoneselfwithit having a likelihoodof50%(i.e.aslikelytohappenasnot), thenthenumbersrequiredare quite easy to calculate. The probabilityof someone nothavingthesamestarsignassomeoneelseis11/12.Ifthegrouphasa thirdmember,then the probability of him or her not sharing a star sign with eitheroftheothertwois10/12. Theprobabilityof a fourthmembernotsharing astar sign with the otherthreeis 9/12.Sincetheseare independentevents, theprobabilityofnoneofthemhavingacommonstarsignistheproductofmultiplyingallofthoseprobabilitiestogether.Thisvalueis0.573,whichmeansthatthereisaprobabilityof0.427thattwoofthefourpeoplewillProbabil it yandc o in c ide n c e27share a starsign,sinceconjunctiveprobabilitiesadd (and1 -0.573 = 0.427).Thus it isalmost as likelyas notthat ina group offourpeople,twoofthemwill share a star sign.Ifweconsiderbirthdays,weobtainanevenmoresurprisingresult.Weneedonly 23 peoplein a group in orderfor there to be a 50% likelihoodthattwo of those peoplewill share a birthday. The reason for this low figure is that23peoplecanactuallybepairedoffforcomparisoninnolessthan253differentways. With 30 people,as may befoundon the averagerugby pitch,thelikelihoodisinfact70%thattwopeoplewillshareabirthday.Note,however, that this doesnotspecifywhich peopleorwhich day, but just thatsucha pairing is likely. AsDawkins (1998) points out, someonecouldmakeagoodlivinggoingaroundrugbypitchesonSundaymorningsofferingtotake bets on exactly this outcome.Mostpeople will underestimate the proba-bilityofsuchacoincidenceoccurring,andthebookmakercouldexpectstatisticallytowinon7outof10 occasions.Exactlythesamebasiscanbefoundfor many othergamesof chance,which all give thebookmakermuchgreaterchancesof winning than they give the punters.Quacksoftenpeddlefraudulentmedicaltreatmentswithremarkablesuccess,atleastasmeasuredbythewillingnessofpeopletopayfortheirservices.Paulos(1988) describes whysomanypeople maybe easilytakenin. The knowingly fraudulent operatortakes advantage of the natural ups anddowns of the disease cycle, preferably becoming involved while the patient isgettingworse.Thereare onlythreepossibleoutcomes-thepatientgetsbetter, stays the same or gets worse. In two of those casesthe quack may takecredit for a desirableoutcome -either he stabilized the patient's condition orhe caused them to improve. Thus there is a 2/3 probability that the quack willappearto be successful. Moreover,these two out of every threecaseswill bethe onesrememberedas 'miracles'. In line with confirmationbias, theotherswill be discounted as'he did his best, but it was too late'. Thus simply takingadvantageofthelawsofchanceandanabilitytoenumerateoutcomesenables a fraudster to make a goodliving.R an domn e ssandchan ceManyexamplesof erroneoususeof probabilityinformation derivefromthedifficultiesthathumans haveindealingwithconceptsofrandomnessandchance.Randomnessisanarticleoffaithinstatisticalscience,andit formsthe basis of many of our most importantscientific theories. For example,bothmodernphysicsandevolutionary theoryexplicitly acknowledgetheroleofrandomorchancefactors.However,itisnotmerelylaypeoplewhohavedifficultyin dealingwith these ideas. Albert Einstein,one of the founders ofmodern physics, famously remarked that he could not believethat 'God playsdicewith the universe'.Givena set of events that are equallylikely,such as a coinfalling'heads'or'tails',thenwhat happensis a matterofchance.Ina lumpofradioactive28 Myth andmethoduranium the atom which emits its radioactive particle at a particular momentis decidedentirelyby chance. All of the atoms are equally likely to decay, anditistherefore impossibleinprincipletodeterminewhich willdosoatanygiventime-it justhappensbychance.Itisdifficulteventoprogramacomputertosimulatetherandomselectionprocessesatworkhere.Anycomputeralgorithmthat is used to generaterandom numbers must operateinamechanicalanddeterministicway,sincethecomputerisamachineinwhich any event must be causedby a predictableprocess.Any number that isgenerated must therefore be determined by the previous state of the machine(thelastnumberproduced).However,sincethenumberisdetermined,bydefinitionit cannot be random. For this reason, computer-generated randomnumbersareoftenreferredtoas'pseudo-random'numbers.Trulyrandomnumberscanonlybeobtainedbysomeanalogueprocesssuchas pickingnumberedballsfroma bag.Althoughthereisgoodevidenceforrandomprocesses,humans haveapoorappreciationofrandomnessandhavedifficultyinsimulatingit.Strategies that people employ when fillingin lottery sheets are informative inthisregard.Thusif askedtogeneraterandomlynumbersbetween1 and 49,most naive lottery players chooseone number between1 and 9, one between10and19,andsoon,somehowbelievingthistobealikelysequence.However,as players becomemoresophisticated andexperiencedat playingthe lotterytheynotethatnumbersoftencomeup in clusters-forexample,threenumbersbetween1and9andnoneinsomeoftheotherintervals.Playersmaythenstarttotrytosimulatethebehaviouroftherandomselectiondevicethatchoosesthewinningnumbersbysimilarly clusteringnumbers.Ofcourse,theactualnumberschosenareoflittleconsequence,since all combinations are equally likely to come up,with a probability of 1in14,000,000.Themotivebehindnumberselectionforthetrulysophisti-catedplayerthenbecomesoneofestimatingaconditionalprobability(ofwhich more later). Basicallythey are saying to themselves'If I win I want toshare my winnings with as few people as possible, so I need to choosea veryunusualsequenceofnumbers'.Inordertodothismanypeoplestartedtochoosesequencessuchas1, 2,3, 4,5, 6. Theauthors are reliably informedthatsome10,000 peoplecompetingin the UK NationalLotteryeachweekactuallychoosethatverysequence,therebycompletelydefeating theirobjectiveofnothavingtosharetheirwinningswithanyoneintheunlikelyevent of a win!Condit ionalpr obabil it ie sConditionalprobabilitymaybeexpressedastheprobabilitythatsomethingwilloccurgiventhatsomething elsehasoccurred.Bydefinition,such eventsare not independent.Considerthe case of someonebeing able to speakEnglish.If they live in England this probability is high, say 0.95. If, on theother hand,they are merelylivingsomewhereon the planet,then the probabilitythat theyP r o ba bi l i t ya n dc o i n c i d e n c e29canspeakEnglishismuchlower,say0.4.Inthesecaseswecanexpresstheconditional probabilitiesas:1.theprobabilitythatthepersonspeaksEnglish,giventhattheyliveinEngland; and2.the probability that theyspeakEnglish, given that they are human.Conditional probabilities are written as /3(AIB), which is read'theprobabilityof A given B'. Thus:P(XspeaksEnglishlX is English) =0.95.B a s e r a t e sWhen considering conditional probabilitiesit is important to take baseratesinto account. Thebaserateis essentially the backgroundfrequency ofsomeoccurrencein the generalpopulation. Considerthe following illustration.For most peoplehaving pains in the chest is a worrying experience.This isbecausetheyknowthatmostpeoplewhohaveheartdiseasesufferpains inthechest,so they worry that they, too,may have a seriousheartcondition oranimpending heartattack.However, what they maynotrealizeis thatchestpainsareextremelycommoninpeoplewhodoNOThaveheartdisease(usuallybeingcausedbysomethinginnocuoussuchasindigestion),andthereare farmorepeopleinthis group. Thismeansthat thevast majorityofchest pains actually occur in peoplewho have no heart problems, or any otherserious health problemsfor that matter. However, in orderto understand this,youneedtoknowthefrequencyofchestpainsamongthegeneralpublic,which is the base rate in this particular example.The following is another example fromTversky andKahneman (1983):Pr obl e m2.2Ataxiisi n v ol v e dinanac c i de n t atni g ht.I ntheci tyt h e r e aretwot ax i - c abf i r m s .O ne hasg r e e nt ax i sandtheot he rhasbl u e t ax i s.I nt ot al ,8 5 % of thet a x i si nthecityar eg r e e n . Awi t n e s si dent i f i es thetaxii n v ol v e d as bl u e.I n t e s t si n v ol v i n gthewi t nessi ni denti f y i ngcabcol ou r satnight,she cor r ectl yidentified thecolou rofthecab 8 0% ofthetime.Shouldwebe l i e v ehe rt e s t i mo n y ?Thisquestion actually concernsconditional probability. In orderto believethewitness weneedtoestimatetheprobabilitythatthecabwasblue, giventhat the witness says that it was blue. There is a way of working out this prob-ability mathematically using Bayes' rule, but it is somewhat complex. Instead,a simpler version is presentedhere which involves enumerating possibilities.Imaginethatthereare100cabsinthecity.Weshallconsiderwhathappens when thewitnessseeseachone of these. We know that 85 cabsaregreenand15 cabsareblue.Thewitnesssaysthatthetaxiwasblue, butis30 Mythandmethodonlyright80%of thetime.Enumerating allofthepossibilities,ifsheseeseachof the15 blue cabsthenshewillbecorrectinidentifyingtheir colouron12 occasions(80% of15). On the other hand, if she sees all 85 green cabs,thenshewillmisjudgetheircolourandidentifythemasblueon17occa-sions(20%of85).Thus there are 29 (12+17) ways in which she can identifya cab as blue. Ofthese, only12 are correct (i.e.those which actuallyare blue). Theconditionalprobabilitythat the cab is blue when she says that it is blue is therefore:P(cab is bluelwitnesssaysit is blue)=number of timesshesays'blue' correctlynumberof timesshe says'blue'= I*=0.41.29Thusthewitnesswasprobablywrong,sincetheprobabilitythatthecabwasbluegiventhatshesaysitwasblueislessthan0.5.Intheirstudies,Kahneman and Tverskypresentedproblemssuch as the aboveto subjects. Arobustfindingwas thatsubjects ignored the baserate.In theaboveexamplethebaseratereflectstheoverwhelmingprobabilityofacabbeinggreen,given that 85%of the cabs in the cityare that colour. Neglectof base rates isalsoevident in the lottery playerwho tries to evaluate the conditional proba-bilityof having to share hiswinnings with others when choosingasequenceof numbers, but who completely ignores the absolutelydismal probability ofever actually winning!B aser a t e s ,p r e j u d i c ea n dme d i c a ld i a g n o s i sOneofthemoredisturbingimplicationsofKahnemanandTversky'sresearchisthattheprocessesunderlyingneglectofbaseratesmayresemblethoseinvolvedinprejudice.Inaningeniousexperiment,Hewstone et al. (1988) presentedan exactanalogue of the cabsproblemtosubjects,thistimephrasedintermsofcrimeandthecolourofresidents.Theymadethealarming discoverythat whitesubjectsweremore inclinedtotakeaccountof baseratedataif thewitnessreportedthattheassailantwaswhite,therebyproducingalowerprobabilityestimateofthatsuspect'sguilt.Thusbaseratedatamaybeusedselectivelytoj ustifyjudgementsbasedonexistingprejudices.Medicaldiagnosisprovidesanotherexamplewhere baseratesare frequentlyignored.Mostdiagnostictestsproducebothmisses(i.e.do notdetectpeoplewhoareill)andfalsealarms(i.e.produceapositivetestresultforpeoplewhoarewell).Inaddition,theactualbaserateofdiseaseprevalenceisoftenverylow.KahnemanandTverskypresentedproblemssimilartothefollowingexampleto theirsubjects.Probabilityand coincidence31P r o bl e m2.3F r edhasat e stf orprostatec anc er .T hetestisposi t i v ein9 0% of peoplewhohavethedi se ase .I talsop r o du c e sf a l s e - p o s i t i v e sin2 0% of we l lp e op l e .P eopl e of F r ed's ag e wi t hs y mp t o msl i k ehishave thedi sease1% of theti me.H is testc o me sbackposi t i v e.S hou l dhebe w o r r i e d ?PerhapsthemajorityofreaderswouldbeveryworriediftheywereinFred'sshoes.However,applyingreasoninganalogoustothatappliedto thetaxis problemabove yields a conditional probability that Fredhas thedisease-given that he has a positive testresult -of only 0.043. This is becausein apopulationof, say,10,000 the test correctlyidentifiesthe disease in 90 peoplebut incorrectlyidentifies it in1980 healthy people.Thus:P(personhasdiseaseltest identifies disease)=numberof timestestidentifies diseasecorrectlynumberof times it identifiesdisease90= 0.043.2070Thatis, Fred almostcertainlydoes not have the disease. This is a statisticalconsequenceof theprevalencerateof thediseaseandthefalse-positiverateofthetest.Unfortunately,doctorstendtobeextremelypooratcommuni-catingthiskindofinformationtopatients,whoconsequentlyexperiencemuch avoidable anxiety.Thelawofl argenumbersandthelawof smallnumbe rsMostpsychologystudents are aware of the law of large numbers. Theyuse itintuitivelyeverytimetheywriteat theendof oneof their laboratoryreports'moresubjects areneeded'.Bythistheymeanthattheeffectunderinvesti-gationis ratherweakand requiresa largersamplein order for it to bedemon-strated. More generally, the law of large numbers states that a samplewill onlyberepresentativeofapopulationiftheformerissufficientlylarge.Asmallsample may well have similar characteristics(mean and standard deviation) tothe whole population, but in most casesit will not. Fortunately,smallsamplesare not a complete deadloss, as the centrallimit theoremof statistics tells ussomething about the distribution of means of samples and this forms the basisof much ofstatisticaltesting.Kahnemanet al. (1982) identifieda number ofheuristics or rules of thumb that peopleapply when handling probabilitiesthatserve to introduce errorsand biasesinto their thinking. One of theseisrepre-sentativeness. This is a 'law of smallnumbers'that leads people to believe thataverylimitedfindinghassomeabilitytorepresentawiderpopulation.In3 2Mythandmethodmany casesthe item that is chosen to be representative just happens to be onethat the individual has to hand. This is the so-called'availability heuristic'. Ineffectthis works on the basis of'If I know about it then it must be important'.Thussomeonemayinallseriousnessclaimthatcigarettesmokingisnotharmfulbecause their Uncle Sid smoked 500 cigarettesa dayand lived to be93. Unusual, yes -but it tells us absolutely nothing about smoking and health,asUncleSidisunlikely toberepresentativeofmuch. Perhapshe justhadgeneticresiliencetolung cancer(lucky him!). Thetruepicturecanonly beobtained by examining a large sample that is representative of the populationasawhole.The'Linda'example(the caseofouranti-nucleardemonstratorabove)mayalsobeanapplicationofrepresentativeness.Herdescriptioncausessubjectstothinkintermsofaverysmallgroupofwomenwithparticular likely characteristics, and judgements are then made by reference tothis stereotype, rather than by referenceto considerationsof probability.R iskp e r c e p t i o nWhat is the most risky activity in which you can legally engage in most coun-tries? Having unprotectedcasualsex? Eating British beef? Flying in a plane?Rock-climbing?Bungee-jumping? Goingtouniversity? Nodoubtthereasonablysophisticatedreaderknowstheanswertothis.Byfarthemostrisky activity you can legally engage in is cigarette-smoking. This is followed(someconsiderablewaybehind,astherisksofsmokingaresohigh)byinvolvementwith motortransport. Ofcourseitdependsonthetypeofriskoutcome we are talking about. Risk theoristssuch as Adams (1998) provide ameasure of risk that combines the probability of an outcome with the impor-tanceofthatoutcome.ThusagameliketheUKNationalLotterywhichcarries an almost100% chance of losing 1 would not be seen as very riskybecause1 is not a serious loss. Even though the probabilityof winning is solow,losinga pound is nota great concernto most people,especially if theyenjoythegame.Thegreatestriskiswhentheoddsareagainstyouandthepotential lossis high. This is why smoking is such a poor risk. The outcomesthatthesmokerrisksareextremelyunattractive.Theyincludedeathanddisablingillnesses,many ofwhich eventuallyresult ina longand lingeringdeath.Theseillnessesincludeheartdisease,bronchitis,emphysemaandarangeof cancers (lung, bronchus, throat, mouth, etc.). Moreover,the proba-bility of these outcomesis extremelyhigh. The following are truestatements:1.Mostsmokers(i.e.morethan50%)dieasaresultofsmoking-relateddiseases.2.Smokingkillsmorepeoplethanallotherdrugs,legalandillegal,including alcohol, put together.Individualsemployarangeofpsychologicalrusestodefendthemselvesagainst thesefacts.Some usean availability heuristic. Others areignorant ofthe diseases and therefore do not worry about them. Yet more are fatalistic andP r o ba bil it ya n dc o i n c i d e n c e3 3think that something else will get them first, since the time-course of smoking-relatedeffectsis so long (perhaps they think that they will give up smoking intime).Someemployotherheuristics,suchasthebetter-than-averageeffect(Klarand Giladi,1997),which leadsthem to believethat their chancesof notacquiring diseases are somehow better than those of most otherpeople.Therecanbefew betterillustrations of the irrationalnature of anxiety andobsessive-compulsivedisordersthaninthedifference inattitudesto varioustypesofrisk.Theauthorshaveneverencounteredacigarettephobic,eventhoughthiswouldseemtobeanentirelyrationalfeartohold.Incontrast,many peopleexperienceterribleanxiety aboutair travel,a modeoftransportthat is extremely safe. The chances of dying as a result of air travel are approx-imatelythesameasthoseofwinning theUKNationalLottery.Ithasbeencalculated that someonecould fly everyday for more than 8000 yearsbeforeexpectingtobeinvolved ina planecrash.Perhapsthefearofflyingderivesfromitsunnaturalness and,formostpeople,itsrarity, aswellasthelackofcontrol experiencedby the passenger, who hands over all responsibility for hisorhersafetytothecrew.However,manyoftheseconsiderations(withtheexceptionof rarity) alsoapply to travel in motorcars.Car phobiais rare,butcarcrashesaremuchmorecommonthanair crashes,andtheconsequencescan be little better.Bizarrely, many drivers, despitethosestatistics, think thatcar-drivingisasuitablearenaforrisk-takingbehaviour.Mediaexposureisprobablyamajorfactorhere,sinceaircrashes,despitetheirrelativerarity,tend to be sensationalized by televisionand the newspapers,whereas car acci-dents occur every day on a huge scale but go largelyunrecorded.Whilstmanyindividuals experienceirrationalphobias,manyothersmaketheir lives a misery with obsessive-compulsive attention to dietary andexerciseregimes that at best have only a marginal effecton health. One of the authors hashad personal experienceof being provided with unsolicited dietary and exerciseadvice bysomeonewho was bothsmokinga cigaretteand driving a car at thetime. The following example, from Paulos (1988), illustrates just how poor indi-viduals' risk assessmentscan be. Thisexampleconcernsunprotectedsex withan AIDSvictim. Althoughnooneintheir right mindwould advocateunnec-essary risk-taking, the example illustrates the extent to which risks may be over-estimated. This exampleconcerns the risk of acquiring AIDS heterosexually. Itshould be noted that the exampleis simplified,since a single figureis given forinfectability(the probability of becoming infected froma sexual encounter), butthisis actually thought tobedifferentinmalesandfemales.Itshould alsobenoted that the figure applies only to heterosexualsex and are basedon UK data.Inother partsof theworlda variety offactors mayincreasetheriskof trans-mission of the HIV virus and the subsequent progressionto AIDS.P r o bl e m2 .4I thasbeeni n d e p e n d e n t l yesti matedthatthep r obabi l i t yof g ettingi n f e c t e dbyas i n g l eu n p r ot e c t e dhe t e r ose x u ale p i s o d ewi t hani n f e c t e dpar tneri sabou t1i n5 00. T hu sthepr obabi l i t yof notg et t i ngi n f e c t e di s49 9 /5 00.I f t he s eri sk sarei ndependent,t he n ,s i n c e3 4Mythand me t h o d499/500multipliedbyitself 346timesisapproximately0.5,thereisanevenchanceofac q u i r i n gH I V i n f e c t i o nbyhavingu n p r o t e c t e dh e t e r o s e x u a li n t e r c o u r s ee v e r ydayf ornearlya y earwi t hs ome on ewhohas thedi sease.H owev er,wi t hac o n d o mthec han c eofbei ngi nf ect edf al l sto1i n5 000pere p i s o de .O ne c o u l dthenhavesaf esexe v e r y day wi thaninf ectedpartnerf or10y e a r s( assu mi ngtheirsu r v i v al ) bef or eone'schancesof beingi nf ect edr e ac he d5 0% .If thepartner'sdi se asestatu sisnotk nownbutheorsheisnotame mbe rof an at- riskg r ou p ,thec han c epere p i s o deof bei ngi nf ect edisesti matedtobe 1in 5 ,000,000if u n p r o t e c t e dand1 in 5 0,000,000wi t h a c on dom.O ne ismu chmo r el i k el ytodieinacarcr ashonthewayhomef r o ms u c hane n c ou n t e r .S imilarc o n s i de r at i o n smaywe l lapplytoother' r i s k y 'acti v i ti es,su chas t ak i n gr ec r eat i onaldru g s.T heseacti v i ti escaninf ac tbesu bstantiallylessr i sk ythanother,soci allyc o n do n e driskss u c hassmok i ngordrivingin a car.SummaryAnumberofsourcesoferrorthatarisewhenassessingprobabilitieshavebeenoutlined. A failure to understand independent events or the probabilityofconjunctionsmakespeoplepreytoanumberofsystematicerrorsinhandlingprobabilitiesintuitively. Individuals typically have greatdifficultyin appreciatingrandomness, even when trying to generate random sequencesof numbers when competingin a lottery. Conditionalprobabilitiesare partic-ularlydifficulttohandleasaresultofthetendencytodisregardbase-rateinformation. This can leadto prejudiced judgements and to a chronic overes-timationof the likelihood of certain desired events,such as winning lotteriesandothercompetitions.Inaddition,peoplehaveatendencytobasetheirjudgements on a small sample of information and to be unduly impressedbytheoccurrenceofunremarkablecoincidences.Finally,individualshaveavery distorted notion of risk, oftenbeing terribly worried about safe activitiesbutunconcernedaboutveryunsafeones,suchassmoking. Forallofthesereasonstheaveragepersontendstomakehighlyinaccurate estimations ofprobability,and in most cases this takes the formof a considerableunderesti-mationoftheprobabilityofaneventoccurringbychance.Thissystematicerrormayinsomecasesleadpeopletoattributechanceeventstootherfactors,which may sometimes include paranormalphenomena.S ug g e s t e df ur t h e r r e a d i n gHewstone, M., Benn, W. and Wilson, A. (1988) Bias in the base rates: racial prejudiceindecision-making. Cognition18, 161-76.Kahneman, D., Slovic, P. and Tversky, A. (eds) (1982) Judgement under uncertainty:heuristics and biases. Cambridge: Cambridge University Press.3 The placeboe ffe ctChristopherC. FrenchUsenewdrugsquickly,whiletheystillwork.(Nineteenth-century medical dictum,sometimesattributed to Trousseau)Ifyoucanbelieve ferventlyin your treatment,even though controlledstudiesshowthatit is quiteuseless,then your results are muchbetter,your patientsare muchbetter,and your incomeis muchbetter,too.(Richard Asher,1972, quoted in Skrabanek and McCormick,1989: 7)I n t r o d uc t i o nEvelynWhitewasapatientwithadvancedrecurrentbreastcancer.Thetumour had recurred in theleftarmpit and above theleftclavicle,andhadblockedthelymphaticchannelsofherarmsothatithadbecomeswollen.Therehadbeenatemporaryresponsetothefirstchemotherapywehadtried,butafewmonthslaterthediseasebecameprogressiveagain,andwesuggestedasecondtypeofchemotherapy.MrsWhitewasunenthusiasticaboutthesecond-linechemotherapyandwantedtotryacomplementarymedicationcalledCancell.IagreedtolethertryitandaskedhertokeepseeingmeregularlysothatIcouldassessherprogressandperhapsoffersymptomatictherapyifrequired.Shevisitedeverytwoweeks.Overaperiodoftwomonthsorso,shetoldmethatherleftarmwasdefinitelylessswollenandfeltmorecomfortableandlesstight.AteachvisitI36Mythandmethodmeasuredthegirthofthearm(atexactlythesameplace,toavoiderrors)andfoundthatitwasactuallybecomingmoreswollen.Sheaskedme not to tellher what the measurementswere,and I honouredher request. She graduallybecame iller as the disease progressed, butevenattheendofherlifeshewasconvincedthattheCancellhaddonesomethingforher.Noneofusarguedwithher-simplythesubjectivefeelingthatherarmwasimprovinghadgivenherapsychologicalboostwhichitwouldhavebeenheartless(andpointless)todestroy.(Buckmanand Sabbagh,1993:172-3)Untilfairlyrecently,it was commonto assertthat a placebowasany formof medicineor treatmentwhich was given to patientsmoreto pleasethan tocurethem.Theword'placebo'is infactLatinfor'Iwill please'.However,manyaspectsoftheconceptofplacebosarecontroversial.Indeed,ShapiroandShapiro(1997a)devoteanentirechaptertothedifferentdefinitions ofplaceboandplaceboeffectwhichhave beenemployedinthemedicalliter-ature. Theseauthors define a placebo as 'any therapy prescribed.. .for its ther-apeuticeffectonasymptomordisease,butwhichisactuallyineffectiveornotspecificallyeffectiveforthesymptomordisorderbeingtreated'.Theydefine the placeboeffectas 'the nonspecific, psychologicalor psychophysio-logic therapeuticeffectproducedbya placebo,ortheeffectofspontaneousimprovementattributedto the placebo' (Shapiroand Shapiro,1997b:12).Beforediscussingthe nature of placeboeffectsin more detail, the reader'sattentionshouldbe drawn to the existenceof the placebo'swickedalterego,theso-callednocebo(whichtranslatesas'Iwillharm'). Whereasplacebosleadtopositiveeffects,nocebosleadtonegativeeffects.Thusifsugarpillsare administeredto a group of peopleand they are told that, say, headachesordrowsinessmayresult,asizeableproportionofthegroupmaywellreportsuch effects.Evenlessresearchhas beendirectedtowards understanding thenocebo effectthan towards the placeboeffect,but it seems likelythatsimilarexplanationsmay applyto bothphenomena(Benson,1997; Hahn,1997a, b;Spiegel,1997; Wynder,1997). It is claimed that, as with placebos,effectscanvary fromslight to extremely strong. Indeed, in the most extreme case, claimsthat voodoocurses can actually leadto death have beenexplained in terms ofextremenoceboreactions!Th en a t ur eo fp l a c e b oe f f e c t sFromthevantagepointofmodernWesternmedicalknowledge,fromantiquityuntilthelastfewdecadesvirtually alltreatmentsweretherapeuti-callyworthlessoverandabovetheirvalueasplacebos.Thisviewisrein-forcedbytheextensivelistsofdrugtreatmentsinpharmacopoeiasfrompreviouscenturies,whichincludedsuchus