PUBLISHED VERSION Anastasia Ejova, Daniel J. Navarro, Paul H. Delfabbro Success-slope ...

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PUBLISHED VERSION

Anastasia Ejova, Daniel J. Navarro, Paul H. Delfabbro
Success-slope effects on the illusion of control and on remembered success-
frequency
Judgment and Decision Making, 2013; 8(4):498-511

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http://hdl.handle.net/2440/81271
JudgmentandDecisionMaking,Vol.8,No.4,July2013,pp.498–511
Success-slope effects on the illusion of control and on remembered
success-frequency
AnastasiaEjova(cid:3) DanielJ.Navarroy PaulH.Delfabbroy
Abstract
Theillusionofcontrolreferstotheinferenceofaction-outcomecontingencyinsituationswhereoutcomesareinfact
random. Thestrengthofthisillusionhasbeenfoundtobeaffectedbywhetherthefrequencyofsuccessesincreasesor
decreasesoverrepeatedtrials,inwhatcanbetermeda“success-slope”effect. Previousstudieshavegeneratedincon-
sistentfindingsregardingthenatureofthiseffect. Inthispaperwepresentanexperiment(N=334)thatovercomes
several methodological limitations within this literature, employing a wider range of dependent measures (measures
of two different types of illusory control, primary (by self) and secondary (by luck), as well as measures of remem-
beredsuccess-frequency). Resultsindicatethatdifferentdependentmeasuresleadtodifferenteffects. Onmeasuresof
(primary, butnotsecondary)controloverthetask, scoreswerehighestwhentherateofsuccessincreasedovertime.
Meanwhile,estimatesofsuccess-frequencyinthetaskdidnotvaryacrossconditionsandshowedtrendsconsistentwith
thebroaderliteratureonhumanmemory.
Keywords:illusionofcontrol,sequenceofoutcomes,successslope,primaryandsecondarycontrol.
1 Introduction
Inlightofthemanypotentialreal-worldconsequences
of illusory control inferences, a large number of labora-
Participantsaskedtodeterminethedegreeofcontingency torystudieshaveaddressedtheirsituationaldeterminants
betweentheirpressofabuttonandtheonsetofalightin- (for a review, see Thompson, Armstrong & Thomas,
creasetheirratingswithlightonsetfrequencyevenwhen 1998). The studies typically involve a laboratory task
the light is objectively uncontrollable (Alloy & Abram- with objectively random outcomes, and the task tends
son,1979; Jenkins&Ward,1965). Peopleplacegreater to be either familiar (e.g, roulette) or novel (e.g., a
valueonlotteryticketstheyhavepersonallychosenthan button-and-light device). A single situational determi-
onticketsthathavebeenhandedout(Langer,1975;Wohl nant is manipulated and post-session estimates of con-
& Enzle, 2002). Slot-machine players choose machines trolorsuccess-frequencyserveasthedependentmeasure.
thathavenotpaidoutinsometimeandmakeuseofritu- Themostfrequentlyinvestigatedsituationaldeterminants
alsandluckycharms(Henslin,1967;Livingstone,Woo- have been success-frequency (e.g., Alloy & Abramson,
ley & Borrell, 2006; Wood & Clapham, 2005). All of 1979;Thompsonetal.,2007)andopportunityforchoice
these phenomena are considered instances of the “illu- andphysicalinvolvement(e.g.,Ayeroff&Abelson,1976;
sion of control”, the overestimation of contingency be- Ladouceur&Sevigny,2005;Langer,1975). Otheriden-
tweenpersonalactions(strategies)andtaskoutcomesin tified determinants include need for the outcome (e.g.,
games of chance. The illusion is thought to be caused Biner, Huffman, Curran & Long, 1998; Gino, Sharek &
bysituationalfactors(e.g.,theavailabilityofachoicebe- Moore, 2011)andtheopportunityforpractice(e.g., Be-
tweenactionalternatives)ininteractionwithheldbeliefs nassi,Sweeney&Drevno,1979).
about these factors. In this sense, the illusion is an in- Thispaperaimstoresolveconflictingfindingsregard-
ferencebasedonsituationalinformationandpriorbeliefs ing another identified situational influence, namely the
(Crocker, 1981; Harris & Osman, 2012). The illusion “success-slope” (also known as “the sequence of out-
expressesitselfinrepeatedbehaviours(e.g.,strategicer- comes”; Langer & Roth, 1975). This term refers to
rors, rituals) as well as explicit ratings of control over howsuccessesandfailuresarepositionedrelativetoeach
real-worldandlaboratorygamblingtasks. otherinarandomly-generatedoutcomesequence. Ase-
quence with a descending success-slope begins with a
string of successes and concludes with a string of fail-
Copyright:©2013.Theauthorslicensethisarticleundertheterms ures. In contrast, a sequence with an ascending slope is
oftheCreativeCommonsAttribution3.0License.
characterisedbyapreponderanceofsuccessesattheend.
(cid:3)SchoolofPsychology,UniversityofAdelaide,NorthTce.,South
Itisnotdifficulttoproposetheoreticalreasonsforwhy
Australia,5005.Email:[email protected]
ySchoolofPsychology,UniversityofAdelaide thesethreeconditionsmightleadtodifferentjudgments.
498
JudgmentandDecisionMaking,Vol.8,No.4,July2013 Illusionofcontrol 499
For instance, it has been argued that in a “descending” mary” and “secondary”. Primary control refers to the
condition, people are motivated to see themselves as ef- belief that outcomes can be influenced through personal
fective agents in the task, and so focus heavily on early skill. In contrast, secondary control refers to the belief
successes(Langer&Roth,1975;Thompson,Armstrong thatexternalforces(e.g.,luck,God)controltheoutcome,
& Thomas, 1998). On the other hand, it has been sug- but one can be aligned with these forces. A statement
gestedthatarunoflatesuccessesinthe“ascending”con- like “I knew how to make my luck work for me” is a
dition acts to strengthen control inferences by creating goodexampleofabeliefinsecondarycontrol,insofaras
theimpressionoflearning(Matute,1995). Thedifficulty, it implies that luck controls the outcome but is favour-
however,liesinthefactthattheempiricalfindingsonthis ing the speaker. In the broader cognitive science litera-
effectaremixed. ture,asimilardistinctionhasbeendrawnbetweenbeliefs
To date, five experiments have examined ratings of aboutphysicalentitiesandsuperstitious(orreligious)be-
control and success-frequency following the experience liefs about supernatural entities (e.g., Atran & Norenza-
of 30 or so outcomes conforming to the “descending”, yan,2004;Wellman&Gelman,1992). Theillusionthat
“ascending”, or “flat” structures. Their findings regard- physical (i.e., skilled) actions are effective in a game of
ing the direction of the effect were not consistent. Four chancewouldcorrespondtotheillusionofprimarycon-
studies concluded that inferred control is greatest in the trol,whileabeliefintheeffectivenessofsuperstitiousor
“descending”condition(Burger,1986;Coventry&Nor- religiousritualswouldcorrespondtotheillusionofsec-
man, 1998; Ladouceur & Mayrand, 1984; Langer & ondarycontrol.
Roth,1975),butonestudyfoundthatinferredcontrolwas In view of the evidence that primary and secondary
largerinthe“ascending”condition(Matute,1995). control are distinct constructs, it seems sensible to mea-
Whenonelooksattheliteraturealittlemoreclosely,a sure inferred primary and secondary control separately.
numberofdifficultiespresentthemselves. Thefirstissue To that end, we will follow a previous study (Ejova,
is the potential conflation of the illusion of control with Delfabbro&Navarro,2010)inadoptingafactor-analytic
memoryeffects;thatis,theconflationofwhatisinferred
approach. That is, we will treat primary and secondary
with what is remembered. This issue arises when par-
controlaslatentvariables,estimatedbyanalysingaques-
ticipantsareaskedtojudgethenumberofsuccessesthat
tionnaire that asks people to rate their agreement with a
theyhavehad,andthesejudgmentsareusedasameasure
number of statements, such as “I got better with prac-
of inferred control. To illustrate the problem, we note
tice”, “My skill in playing the game [helped me win]”,
thattheconclusionsofLangerandRoth(1975)arebased
“I’vealwaysbeenaluckykindofperson”,and“Acertain
onobservingthatparticipantsinthe“descending”condi-
luckywayofplayingjustseemedtoworkforme”. Fac-
tionprovidedsignificantlyhigherestimatesinresponseto
toranalysisoftheresponsesisexpectedtorevealclusters
thefollowingthreequestions:“Howmanycorrectpredic-
of “primary” and “secondary” statements (Ejova et al.,
tionsdidyouhaveonthe30trials?”,“Howmanycorrect
2010). Thefactorscoresrecoveredforindividualpartici-
predictionsdoyouthinkyouwouldhavehadonthenext
100trials?” and“Howgooddoyouthinkyouareatpre- pantscanthenbeusedasthemeasuresofinferredcontrol.
dicting outcomes like these?”. None of these questions Athirdissuethatweconsideristhechoiceofcontrol
directly ask about the degree of control people perceive conditions. As noted earlier, thesuccess-slope literature
themselves to have. Responses to these questions could uses the “flat” condition as a control for the two condi-
be influenced by factors other than one’s beliefs about tions that have success-slopes, namely the “descending”
abilitytocontroltheoutcome. conditionandthe“ascending”condition. Notallstudies
A second problem pertains to the issue of what it ac- have used all three conditions. In our study, we include
tually means to measure “inferred control”. Even when allthree,andincludeanadditional“U-shaped”condition,
inferred control is measured separately from estimated
inwhichthereareclustersofwinsatthebeginningandat
success-frequency,theliteratureonthesuccess-slopeef-
theend. Ifearlywinsandlatewinshavedistincteffects
fect tends to treat inferred control as a unitary construct
onperceivedcontrol,thisconditionmightbeexpectedto
thatcanbemeasuredusingasinglequestion. Asanex-
lead to the highest levels of perceived control. Even so,
ample, Burger (1986) relied on a single question asking
the inclusion of this new condition is more exploratory
peopletoratethe“extenttowhichyoubelievethatyour
thanhypothesisdriven.
correctanswersweretheresultofyouabilitytocorrectly
anticipate events”. There is some evidence to suggest In sum, our study aims to test the direction of the
that the illusion of control is a more complicated phe- success-slopeeffectinawaythataddressesanddemon-
nomenon. In a review of the illusion-of-control litera- stratestwomethodologicalissues:thedifferencebetween
ture, Rothbaum, Weisz and Snyder (1982) distinguished inferredcontrolandrememberedwinfrequency,andthe
between two different kinds of perceived control, “pri- two-facetednatureoftheillusionofcontrol.
JudgmentandDecisionMaking,Vol.8,No.4,July2013 Illusionofcontrol 500
3 Materials, measures and proce-
Figure1: Experimentaltaskinterface
dure
Theexperimentwasaself-contained30-minutecomput-
erisedexercisedividedintofourstages. Thesewere: (1)
apre-experimentalquestionnaire, (2)48trialsoftheex-
perimentaltask,a“soccer-themedgamblingtask”,(3)the
post-experimental questionnaire, and then (4) additional
trials of the experimental task, if the participant so de-
sired1. The four different success-slope conditions (the
independentvariable)correspondedtodifferencesinthe
sequenceofoutcomesexperiencedduringtheexperimen-
taltask(stage2), butinallotherrespectstheconditions
were the same. The dependent measures and covariates
all derive from the two questionnaires. The description
belowgivesabroadoverviewofthestudy:additionalde-
tailscanbefoundintheAppendices(AandB).
3.1 Thepre-experimentalquestionnaire
To maximise ecological validity, our experimental task
resembledareal-worldgamblingtask. Toaccommodate
this, a pre-experimental questionnaire was used to mea-
sure participants’ beliefs about gambling. The obtained
scores were, in turn, used as covariates in analyses of
therelationshipbetweensuccess-slopeandinferredcon-
trolandbetweensuccess-slopeandrememberedsuccess-
frequency.Similarly,becausethesurfaceformofthetask
wasbasedonsoccer, thepre-experimentalquestionnaire
also measured interest in soccer, which then served as a
covariateinthemajoranalyses.
Themeasuresusedwereasfollows. Forbeliefsabout
gambling, we used the Drake Beliefs About Chance In-
ventory(DBC;Wood&Clapham2005),a22-itemques-
tionnaire that is organised into two scales, one relating
tosuperstitiousbeliefs(DBC-Secondary)andtheotherto
2 Participants moreconventionalerroneousbeliefsaboutchanceevents
(DBC-Primary; seeAppendixA.1). Tomeasureinterest
insoccer,weaskedpeopletoratetheirinterestonafive-
pointLikertscale(seeAppendixA.1).
Therewere334participants(171males), ranginginage
from 18 to 80 (M = 25.0, SD = 11.0) and incorporat- 3.2 Theexperimentalmanipulation
ingmembersofthegeneralcommunityalongsideunder-
graduate psychology students at the University of Ade- The independent variable, success-slope, was manipu-
laide. Recruitment was conducted through a newspa- latedacrossfourbetween-subjectsconditions.Inthe“de-
peradvertisement,advertisementsplacedaroundcampus, scending”condition (N = 85), early wins were followed
and through a research participation website accessible byastringoflosses. Forthe“ascending”condition(N =
to undergraduate psychology students. As is standard 79),theoppositewasthecase,andinthe“flat”condition
in studies of gambling, participation was conditional on (N = 84), wins were approximately evenly distributed
being over the age of 18, having gambled at a licensed acrosstheplayingsession. The“U-shaped”condition(N
venueatleastoncepreviously, andnotbeinginthepro- = 86) featured a concentration of wins at the beginning
cess of receiving treatment for gambling-related prob-
1Thetotalnumberofroundsplayedwasrecordedaspartofabroader
lems. Psychologystudentsreceivedcoursecreditforpar-
investigationintobehaviouralandquestionnaire-basedmeasuresofthe
ticipating. illusionofcontrol.
JudgmentandDecisionMaking,Vol.8,No.4,July2013 Illusionofcontrol 501
andattheend. Inallconditions,participantsexperienced
Table1:Themainmeasureofinferredcontrolinthepost-
awinon8ofthe48trials.
experimentalquestionnaire(Ejova,Delfabbro&Navarro,
2010).
3.3 Thesoccer-themedgamblingtask
Whenthinkingaboutyourwins/goals,towhatextent
Theexperimentaltaskwasasoccer-themedcomputerised wouldyouuseeachofthefollowingstatementsto
task modelled after a slot machine in several respects: describehowtheycameabout? Rateeachofthe
the option to bet on the results of multiple trials corre- statementsusinganumberfrom0to10. Asaguide,
spondedtotheoptiontovarythenumberoflinesplayed givearatingof0ifyouthinkthatthephenomenon
onaslotmachine; thereweremorenearmissesthanfar describedbythestatementwasnotoneofthereasons,
misses;soundeffectscorrespondedtothoseheardonslot aratingof5ifyouthinkthephenomenonwasa
machines;andbetandwin-amountsforeachbettingop- moderatelyimportantreason,andaratingof10ifyou
tionwerecalibratedtoresultinalong-termlossof10% thinkthatthephenomenonwasoneofthemost
of used money, the return rate on South Australian slot importantreasons.
machines. 1. Igotbetterwithpractice.
Thetaskinstructions,issuedverballyandinwritingat
2. Ilearnedhowtopredictthemovementsofthe
thestartofthesession,emphasisedthatthetaskoperated
goalkeeper.
onthesameprinciplesasrealslotmachines,andthatany
3. Myskillinplayingthegame
creditswonduringthegamewouldbeexchangedforcash
4. Experienceatplayingcomputergames
attheend.Participantsplayedthegameforacompulsory
48trials,withanyadditionalroundsbeingvoluntary.Par- 5. ThekickdirectionsIchose(cid:11)
ticipants began the task with 5000 credits, which, they 6. Myknowledgeofsoccer
wereinformed,wasequivalentto$AUD5.
7. Idevelopedalogicalstrategyforplayingthe
AnoverviewoftheexperimentaltaskisshowninFig-
game.
ure1.Eachtrialofthetaskdisplayedanon-screensoccer
8. Theplayer(s)Ichose
playertakingafreekick, and participantswererequired
9. ThebetoptionsIchose(cid:11)
tobetontheplayerscoringagoal.Severalbettingoptions
wereavailable,includingsomeoptionsthatinvolvedbet- 10. Ideservedtowin.
tingontheresultsofmultipletrials(e.g., thattheplayer 11. I’vealwaysbeenaluckykindofperson.
wouldscorethreetimesinarow;Screen2inthefigure).
12. Acertainluckywayofplayingjustseemedto
Otherchoiceswerealsorequired. First,atthestartofthe
workforme.
game, participants were required to choose from among
13. Itookadvantageofmomentswhenmyluckwas
four different real-world players, each of whom had an
good.
entertainingbiographyprovided(Screen1). Achangeof
14. Iknewhowtomakeluckgomyway.
player profile could be made after any round. Also, on
each trial, participants chose which of the four corners 15. Itwasallchance.
ofthegoaltheplayerkickedtowards,a“random”option
Statementorderwasrandomisedforeachparticipant.
alsobeingavailable(Screen3).Noneofthesechoicesin-
(cid:11)StatementsaddedtothesetusedbyEjova,Navarro
fluenced the outcome sequence, which was fixed for the
andDelfabbro(2010).
first48trialsinallfourexperimentalconditions.
The outcome itself was displayed as an animation
showing a goal being scored or a miss (Screen 4). The
option.
ballwasshowntomoveinthedirectionthatthepartici-
pantselected,witharandomnumbergeneratordetermin-
ing, onatrial-by-trialbasis, whetherornottheoutcome 3.4 Thepost-experimentalquestionnaire
was shown to be “close”. For example, for misses, the
randomly-generatednumberdeterminedwhethertheshot After participants completed the experimental task, we
wasshowntobeanear-misscaughtbythegoalkeeper,or administeredaquestionnairedesignedtoelicittheircon-
afarmisswellclearofthegoalposts. clusionsaboutthetask. Itisfromthisquestionnairethat
The animation was followed by confirmation of the ourdependentmeasureswereconstructed.
outcome, sounds of applause in the event of a goal, and To measure perceived control, we presented partici-
adjustment of the credit count (Screen 5). Credits were pantswiththe15itemsoutlinedinTable1,andusedfac-
subtracted in each round, and added whenever a goal or toranalysistoreducethese15manifestvariablestotwo
multiplegoalswerescoredinlinewiththechosenbetting latentvariables,which(asoutlinedintheResults)loosely
JudgmentandDecisionMaking,Vol.8,No.4,July2013 Illusionofcontrol 502
correspond to illusory primary and secondary control. Finally, debriefingfocusedonexplainingthatnoneof
Thesetwovariablesformedourdependentmeasuresfor thetask’schoicefeatures(playerprofiles,kickdirections,
thetwokindsofillusorycontrol. bettingtiming)influencedoutcomes.Wealsotookcareto
The other dependent measures related to success- checkwhetherourparticipantswereatriskofexperienc-
frequency. The retrospective success-frequency item inggamblingproblems.Tothatend,thepre-experimental
askedpeopletostatethepercentageofshotsthatresulted questionnairealsoincludedtheProblemGamblingSever-
ingoals,whereastheprospectivesuccess-frequencyitem ity Index (Ferris & Wynne, 2001). If a participant’s re-
framed the question in terms of the percentage of suc- sponses indicated that a risk of problem gambling ex-
cessestheparticipantwouldexpecttoseeifthetaskwere isted,thiswassurreptitiouslycommunicatedtotheexper-
continued(seeAppendixA.3).Fortheretrospectiveitem, imenterviathecolouroftheon-screenmessagedisplay-
thequestionwasframedintermsof numberofwins for ingthecash-outamounttobepaidtotheparticipant. De-
halftheparticipants,andintermsofthenumberoflosses briefing for these participants additionally involved pro-
fortheotherhalf(fordataanalysis, weconvertedallre- vidingthemwithaninformationsheetwithhelp-service
sponsestothe“wins”formatbysubtractingresponsesin contactnumbers.
thelossframefrom100).
The final component of the post-experimental ques-
tionnaire was a manipulation check item, intended sim- 4 Results
ply to verify that participants noticed the success-slope
towhichtheywereexposed. Responsestothisquestion
4.1 Estimatinginferredcontrol
confirmed that the manipulation was successful, espe-
cially in the “descending” condition, where 78% of par-
Asnotedintheprevioussection,weuseda15-itemques-
ticipantsindicatedthat“noticeablymorewinsoccurredat
tion (Table 1) to assess participants’ inferences about
thebeginning”(seeAppendixA.4formoredetails).
control, and used factor analysis to reduce responses to
two theoretically interpretable latent variables. Ejova,
3.5 Additionalmethodologicaldetails NavarroandDelfabbro’s(2010)procedurefordoingthis
wasfollowed,withtheitemsfirstbeingscreenedforsuffi-
Three additional methodological details are worth not- cientvariabilityandintercorrelation.Giventhatthisanal-
ing. Firstly, wewished tocheckthat participantsunder- ysiswascomplexandisnotthecentraltopicofinvestiga-
stood the instruction that the task was a gambling game tion,detailsarerelegatedtoAppendixD,andonlyabrief
ratherthanasolvablevideogame. Tothisend,thepost- overview is provided here. Two items (9 and 15) were
experimental questionnaire contained a yes/no question removedfromtheanalysisbecausetheircorrelationsdid
aboutwhetherastrategywasused. Thoseansweringaf- not appear robust. The remaining 13 items loaded natu-
firmatively were asked to describe the strategy. Partici- rally onto two factors. The first factor consists of items
pants, on the whole, could be concluded to have under- 1-8,andcanbeinterpretedasprimarycontrol,insofaras
stood the instruction if some of the described strategies itconsistsofstatementsthatrefertostrategiesandgame
reflectedreasoningtypicallyobservedinthefaceofran- features. Items 10–14 form a factor that resembles sec-
dom outcomes—gambler’s-fallacy-type reasoning (e.g., ondary control, inasmuch as it is defined by statements
increasingbetamountsafteranumberoflossesinexpec- referringtoluckanditssensitivitytodeservingness. The
tationofanimminentwin;Tversky&Kahneman,1974). factorswerehighlycorrelated2.
AsalistingofthestrategiesinAppendixCshows,asub- In addition to estimating the factor loadings of each
stantialnumberofdescribedstrategiesappearedtobein- item on the two latent variables, we calculated the fac-
formedbythegambler’sfallacy. tor scores for each participant. These scores correspond
Secondly, to conceal the purpose of the experiment tothescorethateachparticipantisestimatedtohaveon
from participants, the pre- and post-experimental ques- the latent variables. Specifically, because our two latent
tionnaires contained distractor items in addition to the variableswerecorrelated,wecomputedregressionfactor
theoreticallyinterestingonesmentionedearlier. Amood scores,anaggregatescoresuitablefordescribinganindi-
questionnaire (Lorr & Wunderlich, 1988) was included vidual’spositiononcorrelatedfactors(DiStefano,Zhu&
in both the pre- and post-experimental questionnaires, Mîndrila˘,2009).
and the post-experimental questionnaire required Likert
or10-point-scale-basedratingsofenjoymentofthegame, 2Thisistobeexpected, giventhatnumerousresearchershavere-
strengthofexperiencedemotionalresponses,andtheex- markedthat,ingamblingcontexts,beliefsinpersonalskillatpredicting
tenttowhichtheplayerprofilefeatureandsoundeffects chanceoutcomesandsomebeliefsaboutluck(namely,thecommonbe-
liefthatgoodluckcomesin“cycles”)mighthavethegambler’sfallacy
added to or reduced enjoyment. For the sake of brevity,
asacommonsource(Keren&Wagenaar,1985;Livingstone,Wooley&
wedonotdescribeoranalysetheseitems. Borrell,2006).
JudgmentandDecisionMaking,Vol.8,No.4,July2013 Illusionofcontrol 503
beliefs (DBC-Primary) was controlled for (F(1,328) =
Figure2:Estimatedmeans(and95%CIs)ofinferredpri-
120.21, p < .001, (cid:17)2 = .27)4. Figure 2 shows the es-
mary control across success-slope conditions when co- p
timated means for primary control when DBC-Primary
variateswereevaluatedattheirmeanvalues.
wassettoaconstant(mean)value5.Asthedistributionof
6
0. means suggests, and as was confirmed by post-hoc tests
d) withBonferroniadjustmentofthefamilywise(cid:11)-levelto
e 4
at 0. .05,theestimatedprimarycontrolmeanwasgreaterinthe
m
sti 2 “ascending”conditionrelativetothe“descending”condi-
ol (e 0. tion(p=.04).
ntr 0 Perceived secondary control was not affected by
co 0. success-slope,butwaspredictedbyslot-machinebeliefs
ary 2 (F(1,328)=114.63, p<.001, p(cid:17)2 =.26). Thus, thecru-
prim −0. cial result pertained to perceived primary control, with
n 4 the“ascending”conditionproducingstrongerinferences
Mea −0. thanthe“descending”condition.
6 To formally test the widespread methodological as-
0.
− sumption that estimated success-frequency is a suitable
Descending U−shaped Ascending Flat
proxy for control, success-frequency estimates (retro-
Success−slope condition spectiveandprospective)wereexaminedfortheirpattern
acrosssuccess-slopeconditions. Thispatterncouldthen
be compared to that observed for inferred primary con-
Forthepurposesofsubsequentanalyses,notethatthe
trol.
regressionfactorscoresstandardisedtoameanofzero,so
Since success-frequency estimates on both measures
negativefactorscoresindicatedlowerratingsonthestate-
were not normally distributed (as is typical with count
ments associated with the factor, while positive scores
data), the analysis of responses to each measure across
indicated greater endorsement (greater inferred control).
success-slope conditions involved fitting a generalised
The distributions of both primary and secondary control
linear model with an assumed negative binomial distri-
factorscores were highly positivelyskewed (skew = .73
bution and log link function. Gambling-related beliefs
and.67,respectively),andhadstandarddeviationsof.96
(DBC-Total) and soccer interest served as covariates in
and .92, respectively. It is these factor score variables
bothanalyses,andtheanalysisofretrospectivefrequency
thatweuseasourmeasuresofperceivedcontrolinsub-
estimateshadquestionframing(frequencyof“goals”vs
sequentanalyses.
frequency of “misses”) as an additional predictor. The
analyseswereconductedusingIBMSPSSStatistics19.
4.2 Inferredcontrolacrosssuccess-slopes
Estimates of retrospective success-frequency were
foundtobeinfluencedbyquestionframing(Wald(cid:31)2(1)=
Totestthedirectionofthesuccess-slopeeffect,scoreson
21.32,p<.001)butnotsuccess-slope(Wald(cid:31)2(3)=5.23,
thetwoperceivedcontrolmeasuresproducedbythefac-
p=.16)ortheinteractionbetweenframingandsuccess-
tor analysis were examined across success-slope condi-
slope (Wald (cid:31)2(3) = 6.82, p = .08). Table 2 shows the
tions. Thisinvolvedanalysesofcovariance(ANCOVAs)
estimates across success-slope conditions, broken down
withsuccess-slopeconditionasthepredictorandtwoco-
according to question frame. It can be seen that, across
variates: soccerinterestandslot-machinebeliefsasmea-
all conditions, estimates were higher when the question
suredbytheDBC.The“Primary”scaleoftheDBC,re-
referredto“misses”. Asfarastheeffectofsuccess-slope
lating to non-superstitious beliefs about chance, was the
itselfisconcerned,thetableshowsthattherewasatrend
covariate in the analysis of the perceived primary con-
towards higher estimates in the “descending” condition
trol measure. Correspondingly, the DBC’s “Secondary”
relative to the “ascending” condition. This trend is in
scale, concerned with superstitious and supernatural be-
liefs, was the covariate in the analysis of perceived sec- 4Since the distribution of perceived primary control scores was
ondarycontrol3. highlyskewed,ageneralisedlinearmodelsuitableforordinaldatawas
Thedegreeofperceivedprimarycontrolwasfoundto alsofitted. Theindependentvariableandcovariateswerethesameas
forthe ANCOVA,butthe model assumeda multinomial distribution
varyasafunctionofsuccess-slope(F(3,328)=1.95,p=
andusedacumulativelogitlinkfunction. Theeffectofsuccess-slope
.03p(cid:17)2 =.03)oncethesubstantialeffectofslot-machine wasfoundtobemarginallysignificant(Wald(cid:31)2(3)=7.35,p=.06).
5Themarginalmeansforperceivedprimarycontrolacrossexper-
3All three covariates were checked for homogeneity of variance imental conditions were as follows. Descending: M = -.2, SD = .8;
acrossexperimentalconditionsusingunivariateanalysisofvariance(all U-shaped:M=.04,SD=1.0;Ascending:M=.2,SD=1.1;Flat:M=
F(3,330)<1). DBC-Total,usedasacovariateinsomelateranalyses, .02,SD=1.0.
wasalsohomogenousacrossconditions(F(3,330)<1).
JudgmentandDecisionMaking,Vol.8,No.4,July2013 Illusionofcontrol 504
Table2: Meanrememberedsuccess-frequencyestimatesacrosssuccess-slopeconditions.
Descending U-shaped Ascending Flat
M CI95 M CI95 M CI95 M CI95
Estimatetype: (SD) (SD) (SD) (SD)
Retrospective: 22.2 17.7–26.8(cid:3) 14.6 11.7–17.4 17.8 13.6–22.0 15.6 11.6–19.7
goals (14.7) (8.8) (12.7) (12.8)
Retrospective: 30.9 23.7–38.0(cid:3) 33.2 26.0–40.5(cid:3) 19.6 15.4–23.8 33.4 24.9–41.8(cid:3)
misses (22.9) (24.7) (13.3) (28.7)
Prospective 22.9 19.5–26.2(cid:3) 20.0 14.9–24.5 19.4 16.2–22.6 21.4 18.4–24.4(cid:3)
(15.7) (14.0) (14.3) (13.7)
(cid:3)CIcontainsonlyvaluesabovetheobjectivebaselinesuccess-frequency(16.7%),suggestinggeneral
overestimation.
the “miss” framing were largely overestimations of the
Figure 3: Estimated means (and 95% CIs) of retrospec-
objectivesuccess-frequency(1/6=16.7%).Afurtherreg-
tive success-frequency estimates across success-slope
ularitywasageneraltendencytowardsoverestimationin
conditionswhencovariateswereevaluatedattheirmean
the“descending”and“flat”conditions.
values.
d)
ate 35 5 Discussion
m
sti
e
q. ( 30 5.1 Thesuccess-slopeeffect
e
s fr The main goal of this study was to determine which
s 5
ce 2 success-slopesproducestrongerpost-experimentalinfer-
c
su encesofillusorycontrol. Theresultssuggestedthatper-
e 0
v 2 ceivedprimarycontrolislargestinthe“ascending”con-
cti
e ditionandlowestinthe“descending”condition,withthe
p
etros 15 “flTath”eanfadc“tUth-asthathpeed“”asccoenndditiinogn”sclyoinndgitiinonthpermodiudcdeled.the
n r
Mea 10 sMtraotnugtee’sst(i1n9fe9r5e)npcreospoofscaolnthtraotleixspberroieandcliyncgoannsiisntcernetawsiinthg
Descending U−shaped Ascending Flat
rateofsuccessescancreatethefalseimpressionoflearn-
Success−slope condition
ing the correct strategy. The findings can alternatively
be interpreted as evidence that experiencing a decreas-
ing win rate in the “descending” condition leads to an
the opposite direction to that observed for inferred con-
accurateperceptionthatnolearningisoccurring. Specif-
trolratings. Tohighlightthiscontrast, Figure3comple-
ically,the“descending”conditionmightprovidepartici-
ments Figure 2 in showing mean retrospective success-
pantswithastrongsignalthatwhateverstrategytheyare
frequency estimates across conditions, adjusted for co-
attemptingtoemploydoesnotwork.Afterall,thepartici-
variates.
pantispresumablytryingtoproducethesuccesses,butin
Estimates of prospective success-frequency also did
the“descending”conditiontherateofsuchsuccessesde-
not differ significantly across experimental conditions
clinesovertime,makingitveryclearthattheseattempts
(Wald(cid:31)2(3)=1.31,p=.72),butshowedthesamegeneral
havebeenunsuccessful.
trend of higher estimates in the “descending” condition.
Themeansoftheprospectiveestimatesacrossconditions
5.2 Primaryandsecondarycontrol
areshowninTable2.
Success-frequency estimates showed additional no- A second goal of the study was to employ more refined
tableregularitiesacrossconditions,ascanbeseeninTa- measures of the extent to which people perceived them-
ble 2. Namely, answers to the retrospective question in selvestobeincontroloftheoutcome. Inthisrespect,the
JudgmentandDecisionMaking,Vol.8,No.4,July2013 Illusionofcontrol 505
outcomes are a little more mixed. On the positive side, in the “descending” and “flat” conditions, and in accu-
thefactoranalysisdidsuggestthattherearetwodistinct racy rather than underestimation in the other two condi-
(but correlated) kinds of beliefs about control involved, tions. The effect refers to the tendency to overestimate
consistent with Rothbaum et al. (1982) and Ejova et al. loweventfrequenciesandunderestimatehighones(e.g.,
(2010). Moreover, it is reassuring to see that our mea- Begg, 1974; Erlick, 1964; Fiedler & Armbruster, 1994;
sure of primary control within a complicated and realis- Lichtenstein et al., 1978). Background beliefs about the
tic task produced a success-slope effect consistent with task determine what constitutes “low” and “high” fre-
theresultsofapreviousstudythatusedasimplerdesign quencies (Lichtenstein et al., 1978), so, given partici-
(Matute, 1995). These results suggest that the success- pants’ beliefs about gambling and soccer, it is possible
slopeeffectisnotanartefactofaparticularwayinwhich thatthesuccess-frequencyof1/6waslowinthecontext
questions about perceived control are worded, nor is it of the soccer task. The resultant upwards-adjustment of
restrictedtosimplisticexperimentaldesigns. estimates in all conditions could have produced the ob-
On the negative side, part of our motivation for using served pattern in the following ways. In the “flat” con-
richer measures of perceived control in the context of a dition,the“spacingeffect”couldhaveproducedaccurate
rich and complicated task was to see if we could detect estimates, which were adjusted upwards to result in the
anyinterestingeffectsforsecondarycontrol. Asnotedin observedoverestimation. Inthe“descending”condition,
theIntroduction, inrealworldgamblingsituations, peo- thewell-known“primacyeffect”, involvingbettermem-
pledomakeclaimsaboutsecondarycontrol.Peopleoften ory for items and events at the beginning of a sequence
refer to “luck” as an entity that can be on the gambler’s (e.g., Murdock, 1962), could have resulted in accurate
side,forinstance(e.g.,Keren&Wagenaar1985). Thisis estimates,whichwerethenadjustedupwardstoproduce
partlyreflectedinourresults,totheextentthatthedegree the observed overestimation. In the “U-shaped” condi-
ofsecondarycontrolthatparticipantsreportedinourtask tion, the “primacy effect” would have been weaker be-
didcorrelatewiththeirscoreontherelevantscaleofthe causetherewerefewertargetitems(successes)toremem-
DrakeBeliefsaboutChancequestionnaire. However,we ber at the beginning of the sequence. Likewise, in the
did not uncover any evidence for a success-slope effect “ascending” condition, there were no target items at the
withrespecttosecondarycontrol. beginning of the sequence, so a “primacy effect” could
not occur. Thus, in these conditions, memory for suc-
cesses might have been poorer but estimates might have
5.3 Memoryversusinferredcontrol
beenadjustedupwardsaspartofthe“over-undereffect”,
resultingintheobservedaccuracy.
One of our major concerns outlined in the Introduction
A “recency effect”, involving better memory for the
wasthepossibilitythataskingpeoplewhattheyremem-
last items in a sequence, has also been widely docu-
beraboutoutcomefrequencyisnotagoodsubstitutefor
mented and might have been expected to manifest it-
asking them about the amount of control they perceived
self in higher estimates in the “U-shaped” and “ascend-
over that outcome. This concern was borne out, in that,
ing” conditions. However, the “recency effect” is easily
unlike ratings of inferred control, estimates of remem-
disrupted by interference tasks (e.g., Glanzer & Cunitz,
bered success-frequency were found not to be affected
1966), which, in this experiment, occurred between the
by success-slope. Moreover, the success-frequency es-
end of the experimental session and the time when the
timates displayed trends consistent with those observed
success-frequencyquestionwasanswered.
in the memory literature. For instance, studies of mem-
orypointtoa“spacingeffect”—consistentlybettermem- Of course, these memory-based explanations for the
ory for stimuli more distributed across time (e.g., Glen- success-frequency findings are only speculative and re-
berg, Bradley, Kraus&Renzaglia, 1983; Varey, Mellers quireformaltesting.However,theextenttowhichourre-
& Birnbaum, 1990). The fact that we observed higher sultsappeartoagreewiththememoryliteraturedoessug-
estimatesinresponsetothe“miss”framingoftheretro- gest that success-frequency estimates in illusion of con-
spective success-frequency question (“What percentage trolstudieshave,todate,reflectedmemoryofthenumber
of the shots you kicked over the course of the game re- of obtained wins rather than inferences about how wins
sultedinmisses?”) isconsistentwiththiseffect. Specif- canbeobtained.
ically,missesmighthavebeenrememberedmorepoorly
than goals because they were less widely spaced, with
5.4 Directionsforfutureresearch
reverse-scoring of responses, therefore, producing over-
estimations. One direction for future research could involve testing
Similarly, what has been termed an “over-under ef- competing explanations for our main result—the find-
fect” might have been operating in all conditions, mani- ingthatthe“ascending”conditionhadhigherassociated
festingitselfinoverestimationratherthanaccuraterecall inferred control levels than the “descending” condition.
JudgmentandDecisionMaking,Vol.8,No.4,July2013 Illusionofcontrol 506
Matute(1995)obtainedasimilarfindingandinterpreted “ascending” condition due to the time that elapsed be-
it to mean that participants in the “ascending” condition tweentheendofthetaskandthepresentationofsuccess-
believedthattheyhadlearnedthe“correct”response. An frequencyquestions. Thishypothesiscanbetestedbyin-
alternativeinterpretationisthatexperiencingadeclining vestigating whether the “ascending” condition produces
successrateinthe“descending”conditioncausedpartic- higher success-frequency estimates when questioning is
ipantstoaccuratelyperceivethatnolearningwasoccur- immediateratherthandelayed.
ring.TestingMatute’sexplanationwouldinvolveobserv-
ingbehaviouralpatternsovertime,asMatutedidinfind-
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