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Paranormal Belief and Susceptibility

to the Conjunction Fallacy

PAUL ROGERS*, TIFFANY DAVIS and JOHN FISK

School of Psychology, University of Central Lancashire, UK

SUMMARY

Numerous studies have shown paranormal believers misperceive randomness and are poor at judgingprobability. Despite the obvious relevance to many types of alleged paranormal phenomena, no onehas examined whether believers are more susceptible to the conjunction fallacy; that is tomisperceiving co-occurring (conjunct) events as being more likely than singular (constituent) eventsalone. The present study examines believer vs. non-believer differences in conjunction errors for bothparanormal and non-paranormal events presented as either a probability or a frequency estimationtask. As expected, believers made more conjunction errors than non-believers. This was true for bothevent types, with both groups making fewer errors for paranormal than for non-paranormal events.Surprisingly, the response format (probability vs. frequency) had little impact. Results are discussedin relation to paranormal believers susceptibility to the conjunction fallacy and more generally, totheir propensity for probabilistic reasoning biases. Copyright # 2008 John Wiley & Sons, Ltd.

Despite limited scientific evidence for the validity of paranormal claims (Alcock, 1981,

2003; Hines, 2003; Irwin & Watt, 2007), belief in the existence of paranormal phenomena

remains prevalent the world over (e.g. Haraldsson, 1985; Rhine-Feather & Schmicker,

2005). Psychologists have become increasingly interested in understanding why such

beliefs are maintained with various ideas, including the notion that paranormal believers

have certain cognitive deficits, being proposed (for reviews see French, 1992; French &

Wilson, 2007; Irwin, 1993, 2008; Irwin & Watt, 2007; Wiseman & Watt, 2006). Becausemany seemingly extraordinary coincidences are actually quite common (Gilovich, 1991;

Martin, 1998; Watt, 1990/1991), one suggestion is that paranormal believers are especially

prone to misunderstanding probability and thus that a misunderstanding of probability

(chance) underlies the formation and maintenance of belief in the paranormal.

Paranormal belief and probabilistic reasoning biases

It is widely recognised that most people are poor at judging probability and that under

conditions of uncertainty, will rely on heuristics cognitive rules of thumb to simplify

the reasoning process so as to make quick, easy and proximate, but ultimately flawed,judgments (e.g. Gilovich, Griffin, & Kahneman, 2002; Kahneman, Slovic, & Tversky,

1982; Shaifi, 2004; Sutherland, 1992). Further research suggests a persons pre-existing or

APPLIED COGNITIVE PSYCHOLOGYAppl. Cognit. Psychol. 23: 524542 (2009)Published online 8 June 2008 in Wiley InterScience(www.interscience.wiley.com) DOI: 10.1002/acp.1472

*Correspondence to: Dr Paul Rogers, School of Psychology, University of Central Lancashire, Preston,Lancashire PR1 2HE, UK. E-mail: [email protected]

Copyright # 2008 John Wiley & Sons, Ltd.


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a priori beliefs can have a significant influence on these heuristical judgements (e.g. Watt,

1990/1991).

Blackmore and Troscianko (1985) were first to test whether paranormal believers were

especially prone to probabilistic reasoning biases. They had paranormal believers and

non-believers answer questions relating to the generation of random strings (i.e. list

20 numbers as if drawn from a hat), randomness judging (i.e. indicate whether various boy/

girl mixes were biased or unbiased), coin tossing outcomes (i.e. indicate whether the

number of heads scored from 20 throws was biased or unbiased) and sampling decisions

(e.g. indicate which is more likely to be drawn from a given number of red and blue

sweets). Whilst no group differences were found for the random string generation or

randomness judging tasks, Blackmore and Troscianko found that those who believed in the

possibility of extrasensory perception1 made more coin tossing and sampling errors than

non-believers. These data suggest paranormal believers underestimate the likelihood of a

chance outcome and look beyond coincidence in search of causal usually super-natural explanations. According to Blackmore and Troscianko (1985), this under-

estimating of chance expectationstermed the chance baseline shiftmay strengthen

ones belief in psi even when there is no evidence that psi actually exists.

Subsequent work examining believers tendency to misunderstand chance offers mixed

results. Henry (1993) found most people believe intuition (71%) and psi (64%) are the best

explanations for everyday coincidence experiences (see also Henry, 2005) whilst Bressan

(2002; Study 1) found paranormal believers reported having more frequent meaningful

coincidences than non-believers. Likewise, Tobacyk and Wilkinson (1991) found those

with a more pronounced belief in the paranormal (specifically, in superstition, psi and

precognition) had a higher preference for games of chance and were more prone todeveloping illusory correlations between statistically unrelated events (see also Vyse,

1997). Marks (2002) goes further by suggesting believers misperceive chance events as

somehow being related because their a priori beliefs in the paranormal demand such a

relationship and thus, that they are especially prone to making subjective validations.

But other findings fail to support the chance baseline shift hypothesis (cf. Blackmore &

Troscianko, 1985). Blackmore (1997) found paranormal believers and sceptics were

equally likely to underestimate the odds that statements such as I have a scar on my left

knee and I once broke my arm would apply to most people. Similarly, Roberts and

Seager (1999) found belief in the paranormal correlated with conditional but not

probabilistic reasoning ability. More recently, Bressan (2002) gave believers andnon-believers the same four probability tasks first used by Blackmore and Troscianko

(1985), plus Kahneman and Tverskys (1972) classic maternity ward problem (i.e. indicate

whether a larger or smaller hospital is more likely to have a higher proportion of male births

over the next year; Study 1) and a modified version of Bar-Hillels (1982) pollster problem

(i.e. indicate whether you have more confidence in a larger or smaller sample of voters;

Study 2). Overall, Bressan found believers and sceptics were equally prone to errors on the

sampling, maternity ward and pollster problems, implying that the two groups were equally

insensitive to sample size differentials. Interestingly, Musch and Ehrenberg (2002) found

that believers initial biases in probabilistic reasoning disappeared once general cognitive

1Extrasensory perception (ESP) is defined as the alleged ability to obtain information via non-sensory means andcomprises three sub-components, namely the non-sensory awareness of distant individuals (telepathy), of distantobjects or events (clairvoyance) and of future events (precognition). Due to a philosophical overlap between thesethree concepts, the term psi is often used to denote the unknown paranormal element underlying all ostensiblypsychic experiences (Beloff & Henry, 2005; Irwin & Watt, 2007).

Copyright# 2008 John Wiley & Sons, Ltd. Appl. Cognit. Psychol. 23: 524542 (2009)

DOI: 10.1002/acp

Paranormal belief and the conjunction fallacy 525


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ability (measured by final exam grades) was controlled for. Finally Blagrove, French, and

Jones (2006) asked participants to solve sampling problems relating to dice throwing (i.e.

indicate the best way to throw 10 sixes) and lottery play (i.e. indicate how someone else

picking your lottery ticket would influence your chances of winning). Blagrove and

colleagues found that those with a more pronounced belief in paranormal phenomena

(specifically precognition) made more probabilistic reasoning errors for the lottery task

although not the dice throwing taskthan did those with a lower level of belief. Additional

evidence that both types of error correlated positively with the reported number of

(allegedly) precognitive dreams suggests these results are more indicative of believers

greater susceptibility to probabilistic reasoning biases than to a stronger illusion of control

(c.f. Langer, 1975).

Evidence that paranormal believers are especially prone to misperceiving randomness is

also mixed. Contrary to earlier claims (Blackmore & Troscianko, 1985), Brugger, Landis,

and Regard (1990) found paranormal believers were less normative and predicted fewernumber repetitions from a sequence of dice throws than paranormal sceptics. Brugger,

Regard, Landis, Krebs and Niederberger (1991; Study 1) later found that within in

customised die throwing task, believers predicted fewer repetitions for both conceptually

identical outcomes (e.g. carrot-carrot) and conceptually related outcomes (e.g. carrot-

rabbit) than would be expected by chance. The same authors also found that belief in ESP

was positively associated with misperceiving semantic relatedness in both pairs of

drawings (Study 2) and in random dot patterns (Study 3). Bressan (2002) reports similar

trends regardless of whether previously generated strings were visible or hidden from

participants. According to Bressan, paranormal believers are not especially prone to

underestimating the likelihood of chance events per se but instead, are more susceptible tomisperceiving patterns in randomness (i.e. the absence of meaning). This suggests

believers and non-believers have different internal representations of what constitutes

randomness, with believers requiring less subjective evidence of relatedness before they

misattribute a cause-and-effect relationship to objectively (i.e., statistically) unrelated

events. This lowered threshold of subjective chance may explain why believers often see

coincidences as more meaningful (Brugger & Taylor, 2003). Finally, Dagnall, Parker, and

Munley (2007) found that only perceptions of randomness predicted scores on a global

paranormal measure which, according to the authors, implies believers general weakness

in probabilistic reasoning stems from a specific deficit relating to the misrepresentation of

randomness (chance).

Paranormal belief, representativeness and the conjunction fallacy

According to Bressan (2002) paranormal believers generally require less objective

evidence of causal relatedness before they perceive a cause-and-effect relationship

between events. That is, they are more prone to misperceiving meaning (relatedness) in

random noise (see also Marks, 2002). The implication here is that believers employ a

more relaxed internal representation of what constitutes a random event and that their

perceptions of chance are unduly influenced by factors such as the salience or

observability of possible causes (Bressan, 2002). This, in turn, suggests paranormal

believers base their probability judgements on the representativeness heuristic.

The representativeness heuristic is a cognitive rule of thumb in which the subjective

probability of an event is judged by the extent to which that event resembles is


DOI: 10.1002/acp

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representative ofeither the salient features of its parent population or alternatively, the

process by which that particular event is generated (Kahneman & Tversky, 1972; Tversky

& Kahneman, 1982). In the first instance, representativeness implies people believe a given

category exemplar ought to resemble the category prototype. In the second, it implies

people (mis)perceive a given outcome as being associated with, or caused by, a particular

process.

Representativeness biases are robust and can be applied to people, objects, situations and

even abstract concepts such as chance and randomness (Tversky & Kahneman, 1982,

1983). In lottery play for example, random looking number combinations (e.g. 08, 15, 21,

30, 39, 46) are deemed more likely to win than numbers which appear sequentially related

(e.g. 16, 17, 18, 19, 20, 21), with regular lottery players more prone to these misperceptions

than non-players (Rogers, 1999; Rogers & Webley, 2001). Gilovich & Savitsky (1996)

describe how similar biases underlie pseudoscientific beliefs in astrology, graphology

and dream interpretation. For instance, the personality characteristics associated witheach astrological sun sign appear to be anthropomorphised representations of the sign

itself. Thus, people born under the sign of Libra (the scales) are often stereotypically

described as being well-balanced and fair-minded (see also Eysenck & Nias, 1982;

Groome, 2001). Ironically, Irwin (2008) criticises Blackmore and Trosciankos (1985)

studyand by implication many subsequent studiesfor not being representative of

real-life situations.

Representativeness biases are prevalent when people are asked to judge co-occurring or

conjunct events. Tversky and Kahneman (1982) famously gave participants a fictitious

personality sketch in which the central character (Linda) is described as 31 years old,

single, outspoken and very bright who majored in philosophy and who, as a student, hadbeen deeply concerned with issues of discrimination and social justice and who had

participated in antinuclear demonstrations (p. 92). Thus, Lindas character was

constructed so as to be representative (typical) of an active feminist and unrepresentative

(atypical) of a bank teller. Participants had to rank order eight possible conclusions

including a representative outcome (Linda is an active feminist), an unrepresentative

outcome (Linda is a bank teller) and a conjunction of the two (Linda is a bank teller and

an active feminist).2 Tversky and Kahneman found that regardless of their level of

statistical sophistication, between 85 and 90% of participants ranked the co-occurring

(conjunctive) outcome as being more likely than the singular (constituent), representative

outcome of Linda being a bank teller. According to the laws of normative probability this isnot possible. Since being a feminist bank teller was more representative of Lindas

description than simply being a bank teller, it seems the vast majority of participants

ignored normative statistics and erroneously judged the former possibility (feminist bank

teller) more likely than the latter (bank teller) thereby succumbing to the conjunction

fallacy (Tversky & Kahneman, 1982).

Fisk (2004) argues that representativeness accounts of the conjunction fallacy are

invalid. Following his review of several alternative models Fisk (2004) concludes that

despite some limitations, the best explanation of the conjunction fallacy is one that

highlights the potential surprise value of constituent events. According to surprise theory

(cf. Shackle, 1969) potential surprise determines subjective likelihood estimations with

2Italic were not in the original text but are added here to emphasis the conjunction. For the record, the remainingfive outcomes in Tversky and Kahnemans (1982) original study were that Linda was an elementary schoolteacher, a bookstoreworker who took yoga classes, a psychiatric social worker, a member of the League of Womenvoters or an insurance salesperson (Tversky & Kahneman, 1982; within subjects version).


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more surprising events seen as less probable and less surprising events deemed more

probable (Fisk, 2004). In terms of conjunctive events it is the surprise value of the more

surprising and less likely constituent which alone is key in determining the probability

assigned to the conjunction (Fisk, 2004; Fisk & Pidgeon, 1996).

Conjunction biases have been demonstrated in a wide variety of hypothetical contexts

where, in most cases, the proportion of individuals violating the conjunction rule ranges

from between 50 and 90% (Fisk, 2004; Tversky & Kahneman, 1983). Given previous

claims that paranormal believers susceptibly to reasoning biases may be context or domain

specific (e.g. Gray & Mills, 1990; Merla-Ramos, 2000; Wierzbicki, 1985; although see

Lawrence & Peters, 2004; Roe, 1999), it seems reasonable to expect believers will be more

prone to the conjunction fallacy, particularly when conjunctive events appear to reflect

paranormal phenomena. Take the common example of when one is thinking about an old

friend just at the moment he/she unexpectedly calls (e.g. Rhine-Feather & Schmicker,

2005). Here, the two constituent events namely (a) thinking about the friend and (b) thatfriend unexpectedly calling may not be unusual in their own right. One may have thought

about the same friend many times before or alternatively, many other friends may have

unexpectedly called in the past; neither would be particularly surprising (cf. Fisk, 2004). It

is only when these two constituent events co-occur in close temporal proximity that this

conjunction is deemed too unlikely to be a simple coincidence. In such cases, many

experients will dismiss chance and look for a causal, often paranormal, explanation (cf.

Blackmore & Troscianko, 1985; Bressan, 2002; Marks, 2002). Similar logic can be applied

to other aspects of the paranormal including the apparent accuracy of psychic predictions

where the co-occurrence of two constituent eventsnamely (a) the prediction and (b) the

predicted outcomeseems too unlikely to be just a coincidence.Given previous claims that paranormal believers often misunderstand chance and

randomness (e.g. Bressan, 2002), it seems reasonable to suggest believers may be

especially prone to the conjunction fallacy. Evidence that believers tend to adopt an

intuitive (heuristical) as opposed to an analytic thinking style (Aarnio & Lindeman, 2005;

Irwin & Young, 2002; Lester, Thinschimdt, & Trautman, 1987), which in turn is associated

with more conjunction errors (Fisk, 2004; Toyosawa & Karasawa, 2004), adds further

support to this assertion. Moreover, given that personal experience of alleged paranormal

phenomena is the single biggest predictor of paranormal belief (Blackmore, 1984),

a tendency to misjudge conjunctive events as having some underlying causal rela-

tionship may help explain the maintenance, and perhaps even the development, ofsuch beliefs.

To date, the only study to examine the relationship between paranormal belief and

susceptibility to the conjunction fallacy is that by Dagnall et al. (2007). They had university

students complete a series of probabilistic reasoning tasks including one asking whether in

a local football match it was more likely for (a) Team A to score first, (b) Team A to score

first and win, (c) Team A to score first and lose or (d) Team A to score first and the game is

drawn. Contrary to expectations, Dagnell and colleagues found susceptibility to the

conjunction fallacy was unrelated to paranormal belief ratings and that believers and

non-believers performed equally well in solving the conjunction task. One problem with

this study, as the authors note, is that the sample comprised psychology students who

presumably had some basic understanding of probability theory. In addition, the study

employed a global measure of paranormal beliefTobacyks (1988) Revised Paranormal

Belief Scale (RPBS) which has been criticised on both content and psychometric

grounds (see Holden & French, 2000; Irwin, 2008). Finally, Dagnall et al. presented just


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one conjunction problem relating to a football match and it may be that non-significant

results were an artefact of this particular event type. As such, the present study controls for

previous training in maths, statistics and psychology, employs a narrower and arguably

more appropriate measure of paranormal belief, and presents a series of 16 conjunctive

events incorporating both paranormal and non-paranormal contexts. In addition, the

current study also investigates whether believers are unduly influenced by the formatting of

conjunction problems.

Fisk (2004) argues that the formatting of questions is an important factor underlying

conjunction biases. Whereas the original Linda Problem (Tversky & Kahneman, 1982)

asked participants to rank order the likelihood of each outcome, some researchers (e.g. Fisk

& Pidgeon, 1996) have asked participants to estimate the probability (i.e. chances between

0 and 100) of each constituent and conjunct outcome occurring. Others (e.g. Fielder, 1988)

have presented conjunction problems as absolute frequency estimates (i.e. if 100 people fit

Lindas description, how many would be feminists, how many would be bank tellers andhow many would be both?). According to Fisk (2004), more people succumb to the

conjunction fallacy when asked either to rank order the statements or to produce

probability estimates for them. In contrast, few people commit the fallacy when asked

to produce frequency estimates. With this formatting bias in mind, one might also expect

paranormal believers to make more conjunction errors for probabilistic over frequency

estimations (cf. Blackmore & Troscianko, 1985). The present study explores this

possibility.

Study overview and hypotheses

The present study is the first to explore paranormal believers susceptibility to the

conjunction fallacy for both paranormal and non-paranormal events. Using 16 newly

created vignettes, participants were asked to rank order the likelihood of two constituent

and one conjunct event occurring.3 Of these, eight vignettes described an ostensibly

paranormal event such as dreaming of a future house fire which later happened, whilst eight

described an everyday, non-paranormal event such as having a mild case of food poisoning.

In line with Fisk (2004), half of these were formatted as a probability, and half as a

frequency, estimation task. Finally, the present study also controls for participants level of

qualification in mathematics, statistics and/or psychology.Several hypotheses are proposed. First, given their potential proneness to representa-

tiveness biases, paranormal believers should make more conjunction errors than

non-believers. Second, if such biases are domain-specific, believers should make more

conjunction errors for paranormal than for non-paranormal events. Third, both groups

should make more conjunction errors when problems require probabilityrather than

frequencyestimates. Further, this formatting bias should be more pronounced amongst

believers and/or for paranormal events. Finally, individuals who report having a greater

number of paranormal experiences should make more conjunction errors than those who

report having fewer paranormal experiences.

3The number of response outcomes was limited to three (i.e. two constituent events plus one conjunctive event)due to space and participants time considerations. A full copy of the Scenario judgements questionnaire (SJQ) isavailable from the first author (PR).


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METHOD

Participants

An opportunity sample of 200 participants (82 males, 118 females) was recruited from themain campus of a large university in the North West of England. Participant age ranged

from 18 to 56 years (mean 22.2 years; SD 5.3 years) with the majority of either

Caucasian (67.5%) or Asian (24.0%) ethnicity. Most respondents were either full or

part-time university students (90.0%) and educated to at least A Level or equivalent

(85.0%). A sizeable proportion (19.5%) had obtained at least A Level qualifications or

equivalent in maths, statistics and/or psychology.

Design

A 2 paranormal belief group (believer vs. non-believer) 2 event type (paranormal vs.

non-paranormal) 2 conjunction response format (probability vs. frequency) mixed

factorial design was employed.

Materials

Paranormal belief

Paranormal belief was assessed via the Australian SheepGoat Scale (ASGS: Thalbourne

& Delin, 1993), a psychometrically sound measure of paranormal belief comprising

18 statements assessing peoples acceptance of extrasensory perception, psychokinesis andlife after death as genuine phenomena. The ASGS has a narrower focus and was deemed

more suitable for assessing probabilistic reasoning biases than other, broader measures of

paranormal belief (e.g. see Irwin, 2008; Tobacyk, 1988). Traditionally, the ASGS utilises

either a visual analogue or a trichotomous (true/do not know/false) scale (Holden &

French, 2000). But following methodological debate over the former (Roe, 1998, 2002;

Thalbourne, 1998, 2003), and in order to obtain a broader range of paranormal belief scores

afforded by the latter, all ASGS items in the present study were rated on a 7-point Likert

scale from 1 strongly disagree to 7 strongly agree.

Paranormal experiences questionnaire (PEQ)The PEQ comprised six items assessing participants personal experiences of events which

couldbe termed paranormal. Specifically, items asked if they had ever dreamt of something

they later witnessed (precognitive dream), had an intuitive feeling about something which

was later confirmed as accurate (precognitive intuition), had a fortune teller either

accurately predict their future (fortune teller prediction) or accurately describe their

personality (fortune teller profile), inexplicably imagined an event just before it happens

(waking precognition) or finally, if they had ever experienced an effective spiritual healing

(healing). All six PEQ items were rated along a 7-point Likert scale from 1 strongly

disagree to 7 strongly agree.

Scenario judgements questionnaire (SJQ)

The SJQ comprised 16 conjunction vignettes of approximately 40 words in length

(mean 43.8; SD 9.3) which describes either an ostensibly paranormal or a

non-paranormal event (eight of each). The former included descriptions of an apparent


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spiritual healing, various forms of alleged precognition, an apparitional experience, a

seemingly accurate horoscope prediction and a near-death experience (cf. Irwin & Watt,

2007). In each case, only one of the two constituent events referred to these paranormal

concepts. By comparison non-paranormal scenarios incorporated more mundane events

such as getting food poisoning, queuing for airport coffee and a womens rights protest. In

line with previous work (De Neys, 2006; Fisk, 2004; see footnote 3) participants were

asked to indicate which of three different response optionsthe conjunction or either of

the two constituent eventsthey felt was most likely for each of the 16 scenarios. For

example one paranormal SJQ item states:

Billy has a long lost friend who he has not seen in years. They were good friends in

school but drifted apart when they went away to different colleges. Billy comes home

from work one evening and sits down to eat his dinner.

Here, participants were asked to indicate the likelihood of the following three

statements: (a) Billy thinks about his long lost friend, (b) Billys long lost friend

unexpectedly phones him or (c) Billy thinks about his long lost friend and suddenly his long

lost friend unexpectedly phones him. Following Fisk (2004), participants gave their

responses in one of two formats; either as a probability (i.e. chances in 100) or as a

frequency estimate (i.e. the number out of 100 occurrences). In each case, a conjunction

error was made whenever the third (conjunct) option was rated more likely than one or both

of the singular (constituent) options. To counterbalance potential order effects a second

version of the SJQ with item order reversed was also created. Finally, a practice scenario

was included at the start of the SJQ to ensure participants understood task instructions.

Demographics

Participants were also asked to indicate their gender, age, ethnicity, highest qualification

generally and highest qualification in mathematics, statistics and/or psychology to date.

Ethnicity was coded as one of 16 standard response options covering Caucasian, Asian,

Afro-Caribbean, Chinese and mixed race backgrounds. Both general qualifications and

qualifications in maths, statistics and/or psychology were rated on a 6-point ordinal scale

from 1 no qualifications through to 5 professional/postgraduate degree, plus 6 other

level of qualification.4

Procedure

Volunteer participants were recruited via the main campus library at the University of

Central Lancashire; a large university in the North West of England. Those who agreed to

take part in this study of beliefs and judgements were given a questionnaire pack

containing a brief sheet, the ASGS, the SJQ and the demographics questionnaires. To

control for potential order effects still further, the order of the ASGS and SJQ

questionnaires was reversed in half of the packs before these were randomly distributed to

volunteers. Participants were instructed to complete all questionnaires as quickly as

possible without conferring. No time limit was given. Completed questionnaires werereturned to the second author (TD) in person who then handed each participant a full

debrief sheet. No form of payment was made to any participant.

4No respondents reported having other qualifications either generally or specifically in maths, statistics and/orpsychology. As such, this sixth response level was dropped from both qualification items.


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RESULTS

Belief in the paranormal

ASGS ratings were (re)coded such that high scores reflected a greater paranormal belief(potential range 17; actual range 1.006.61; median 3.58). No outliers were

revealed. Median split analysis5 reclassified participants as either paranormal believers

(mean 4.50; SD 0.68; n 98) or sceptics (mean 2.48; SD 0.69; n 102). Whilst

no group differences were found in participant age, gender, ethnicity or general educational

attainment, believers were less well qualified in maths, statistics and/or psychology

compared to non-believers (U 4374.5; z2.04; p .041). Future analyses will control

for this difference.

Conjunction fallacies

As noted above, a conjunction error was made whenever participants rated the conjunctive

event to be more likely that either of the two constituent events. Inspection of individual

SJQ items confirmed that some proportion of the sample made conjunction errors for each

of the 16 scenarios (range 11.562.5%). Thus, all SJQ items were deemed suitable for

inclusion. The total number of conjunction errors made by each participant was then

computed separately for paranormal vs. non-paranormal event types (range 08). Over half

(53.5%) the sample made at least one conjunction error for paranormal events

(range 17; median 1) with a much larger proportion (91.5%) making at least one

conjunction error for non-paranormal events (range 18; median 4).A 2 paranormal belief group (believer vs. sceptic) 2 event type (paranormal vs.

non-paranormal) 2 conjunction response format (probability vs. frequency) mixed

Analysis of Covariance (ANCOVA)controlling for participants level of qualification in

maths, statistics and/or psychologywas performed on the number of conjunction errors

made. Mean and standard deviation scores (adjusted following ANCOVA) are given in

Table 1.

ANCOVA revealed qualifications in maths, statistics and/or psychology to be a

significant covariate (F1,195 27.02; p< .001; h2 .12) with more qualified participants

making fewer conjunction errors. This trend was reinforced by a significant

qualification event type interaction (F1,195 14.69; p< .001; h2

.07) such that thosewith higher qualifications made fewer conjunction errors for paranormal events than they

did for non-paranormal events (r0.18 and r0.40, respectively; z 2.19; p .014;

n 200).

Having controlled for these qualification levels, ANCOVA also revealed highly

significant main effects for both paranormal belief group (F1,195 53.89; p< .001;

h2 .22) with believers making more conjunction errors than non-believers and event

type (F1,195 55.44; p< .001; h2 .22), with participants generally making fewer

conjunction errors for paranormal events than they did for non-paranormal events. In

5

Median split analysis of paranormal belief measures is a valid way of differentiating between believers vs.sceptics (e.g. Dagnall et al., 2007; Wiseman & Morris, 1995). Whilst technically, it would have been moreappropriate to refer to low vs. moderate paranormal believers here, the original terms believers andnon-believers/sceptics are retained for the sake of convenience. For further discussion of methodologicalissues surrounding the measurement of paranormal belief, see Irwin (2008). Interestingly, many parapsychologistsargue that there is sufficient empirical evidence to suggest certain phenomena such as ESP and PK do exist and assuch, challenge the entire notion of a belief (aka. faith) in the paranormal (Delanoy, Personal Communication).


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contrast, format type had no impact on the number of conjunction errors made

(F1,195 .22; p .643; ns; h2 .00).

ANCOVA also revealed three significant or near-significant interaction effects. First, a

significant paranormal belief group event type interaction (F1,195 4.76; p .030;

h2

.02) was found. Subsequent inspection of CI graphs suggested the need for fourpost-hoc comparisons. Simple effects analyses via mixed ANCOVA controlling for

maths, statistics and/or psychology qualification and with a adjusted to .0125confirmed

that believers made more conjunction errors than non-believers for both paranormal

(F1,197 71.28; p< .001; h2 .27) and non-paranormal events (F1,197 16.01; p< .001;

h2 .08). In addition, believers made fewer errors for paranormal than for non-paranormal

events (F1,100 22.19; p< .001; h2 .18). Similar trends were also found for

non-believers who made relatively few conjunction errors for paranormal compared to

non-paranormal events (F1,96 32.73; p< .001; h2 .25). In sum, most conjunction errors

were made by paranormal believers for non-paranormal events, with fewest made by

non-believers for paranormal events. These data are illustrated in Figure 1.Second, analyses also revealed a significant event type format type interaction

(F1,195 9.43; p .002; h2 .05). Inspection of CI graphs again suggested the need for

four post-hoc comparisons. Simple effectsalso controlling for maths, statistics and/or

psychology qualification and with a adjusted to .0125confirmed that participants made

fewer conjunction errors when paranormal events were formatted as a probability

(F1,98 18.03; p< .001; h2 .16) or a frequency (F1,98 34.24; p< .001; h

2 .26)

estimation task than they did for corresponding non-paranormal events. No other

differences were found.

Finally, the hypothesised paranormal belief group format type interaction was just

short of significance (F1,195 3.57; p .060; h2 .02). Since the effect approached

significance, it was deemed worthwhile to perform post-hoc simple effects comparisons to

explore the basis of the interaction. Analysis revealed that paranormal believers made more

conjunction errors than non-believers for both the probability (F1,97 43.77; p< .001;

h2 .31) and frequency (F1,97 16.10; p< .001; h

2 .14) formatted questions. In

Table 1. Mean no. of conjunction errors across paranormal belief group, event type & conjunctionformat (controlling for participants maths/statistics/psychology qualifications)

Event type Format type

Believers

Non-

believers All

Sig. effectsM (SD) M (SD) M (SD)

Paranormal Probability 2.69 (1.92) 0.61 (1.13) 1.67 (1.89) B

Frequency 1.94 (1.85) 0.29 (0.68) 1.13 (1.62) E

All 2.31 (1.91) 0.45 (0.94) 1.40 (1.78) BE

BFa

Non-paranormal Probability 4.43 (2.17) 2.73 (2.24) 3.60 (2.36) EF

Frequency 4.51 (1.99) 3.51 (2.24) 4.02 (2.16)All 4.47 (2.08) 3.12 (2.26) 3.81 (2.27)

All

y

Probability 7.12 (3.44) 3.35 (2.74) 5.27 (3.63)Frequency 6.45 (3.24) 3.80 (2.49) 5.15 (3.18)All 6.78 (3.34) 3.57 (2.61) 3.57 (2.61)

Note: Range 08 errors exceptyrange 016 errors: Adjusted means following ANCOVA. Significant paranormal

belief group (B), event type (E), conjunction format (F) and subsequent interaction effects found at the: p< .05,

p< .01 and

p< .001 levels; a, approaches sig. (two-tailed).


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contrast, neither believers nor non-believers differed in the number of errors they made

across the two format types. These data are summarised in Figure 2. No other significant

differences were found.

Personal experiences of ostensibly paranormal events

Table 2 presents the mean number of reported paranormal experiences. Overall,

participants claimed to have experienced a moderate number of accurate dream, intuitive

and waking precognitions but fewer accurate fortune teller predictions, fortune teller

profile or spiritual healing successes. Correlations (rho) between the six personal

experiences items and the number of conjunction fallacies made are also given in Table 2.

In general, participants who reported having more ostensibly paranormal experiences also

0

1

2

3

4

5

6

7

8

BelieversNon-believers

Errors Probability

Frequency

Figure 2. Number of conjunction errors across paranormal belief group format type (with5% confidence intervals)

0

1

2

3

4

5

6

7

8

BelieversNon-believers

Errors

Paranormal

Non-Paranormal

Figure 1. Number of conjunction errors across paranormal belief group event type (with5% confidence intervals)


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made more conjunction errors. This was true of all experience types except spiritualhealing successes.

DISCUSSION

Contrary to previous claims that the conjunction fallacy is largely unaffected by peoples

level of statistical awareness (Tversky & Kahneman, 1983), current findings suggest

participants who were less qualified in maths, statistics and/or psychology made more

conjunction errors than those who were more qualified in these subjects. With these

qualifications controlled for, participants still made a sizeable number of conjunction errors(mean 3.57), further highlighting the general the robustness of the conjunction fallacy

(Fisk, 2004; Kahneman & Tversky, 1972, Tversky & Kahneman, 1983). All subsequent

discussion relates to data in which levels of maths, statistics and/or psychology

qualification have already been controlled for.

The aim of the present study was to test the notion that paranormal believers are more

susceptible to the conjunction fallacy, in particular, for paranormal events and/or those

requiring probability estimates. Partial support for these hypotheses was found.

First, as predicted, believers made more conjunction errors than non-believers. This

suggests believers are more susceptible to the conjunction fallacy and thus, that they are

especially prone to erroneously judging the conjunctive event to be more likely than one orboth of the constituents events alone (cf. Kahneman & Tversky, 1972; Tversky &

Kahneman, 1982, 1983). Thus, current findings contradict those of Dagnall et al. (2007).

As noted earlier, this misperception contravenes the laws of normative probability

(Tversky & Kahneman, 1982). One possibility is that paranormal believers base these

judgements on what they see as being representative of a typical coincidence (i.e. on their

own internal representation of chance and/or randomness) which differs from that of

paranormal sceptics (Blackmore & Troscianko, 1985; Bressan, 2002; Gilovich & Savitsky,

1996; Marks, 2002; Tversky & Kahneman, 1982). Another is that believers are somehow

more sensitive to the potential surprise value of the less surprising constituent event (cf.

Fisk, 2004). Either way, believers greater susceptibility to the conjunction fallacy is

consistent with previous claims that they are especially prone to misperceiving randomness

(Bressan, 2002; Brugger et al., 1990; Brugger & Taylor, 2003; Regard et al., 1990), to poor

probabilistic reasoning (cf. Blackmore & Troscianko, 1985; Blagrove et al., 2006; Dagnall

et al., 2007; Marks, 2002; Tobacyk & Wilkinson, 1991) and ultimately, to deficits in

Table 2. Frequency of reported paranormal experiences and correlations (rho) with number ofconjunction errors

Reported paranormal experience

Frequency

Correlation (rho) with no.of conjunction errorsM (SD)

Accurate dream precognitions 4.64 (1.68) .39

Accurate intuitions 5.19 (1.60) .35

Accurate waking precognitions 4.64 (1.68) .32

Accurate fortune teller predictions 2.42 (1.64) .33

Accurate fortune teller profiles 2.31 (1.56) .31

Successful spiritual healing 1.89 (1.40) .13

Range: From 1 strongly disagree to 7 strongly agree; sig. at

p< .001 level (two-tailed) (n 200).


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cognitive processing (French, 1992; French & Wilson, 2007; Irwin, 1993, 2008; Irwin &

Watt, 2007). It also supports the view that believers are more likely to adopt an intuitive or

heuristical, rather than analytic, style of thinking (Aarnio & Lindeman, 2005; Irwin &

Young, 2002; Lester et al., 1987). As yet, it is still unclear whether believers heightened

susceptibility to the conjunction fallacy leads to, or conversely is caused by, their

endorsement of the paranormal. Given that the single biggest predictor of belief

in the paranormal is the reported experience of paranormal phenomena (Blackmore, 1984),

the latter seems more plausible. Either way, the generality of believers conjunction errors

(see below) renders it likely that conjunction biases will help maintain and reinforce their

paranormal beliefs.

Second, participants generally made fewer conjunction errors for paranormal than for

non-paranormal events. This illustrates that at least some contextual factors will influence

the strength of conjunction biases. Moreover, while believers produced some conjunction

errors for paranormal events this tendency was much less evident among non-believers. Atfirst glance, current findings seem to suggest believers are even more prone to violating the

conjunction rule for ostensibly paranormal phenomena and thus, as with other cognitive

biases (Alcock & Otis, 1980; Gray & Mill, 1990; Merla-Ramos, 2000; Wierzbicki, 1985),

that their susceptibility to the conjunction fallacy is domain specific. This apparent context

specificity supports the view that paranormal believers maintain a different internal

representation of paranormality and thus that they require less subjective evidence of

(temporal) relatedness before they misattribute causal relationships to objectively

(statistically) unrelated, constituent events (cf. Bressan, 2002; Brugger & Taylor, 2003;

Wiseman & Watt, 2006). But compared to sceptics, paranormal believers also made

more errors for non-paranormal conjunctions too, thereby weakening this argument(cf. Lawrence & Peters, 2004; Roe, 1999). In sum, it seems that paranormal believers are

especially susceptible to the conjunction fallacy. Further, whilst non-believers commit few

errors when conjunctions relate to ostensibly paranormal experiences, believers continue to

commit the conjunction fallacy given either context.

Third, contrary to expectations, paranormal believers made fewer conjunction errors

for paranormal events than they did for non-paranormal events. Interestingly, identical

trends were also found for non-believers. A possible explanation for this unexpected

finding is that the two constituent events within paranormal conjunctions differed markedly

in terms of their surprise values. Generally, the conjunction fallacy is highly prevalent in

contexts where a very surprising constituent event is combined with a non-surprising one;that is, where the surprise differential is large (Fisk, 2004; Shackle, 1969). Thus, the

finding that participants susceptibility to the conjunction fallacy differed across the two

scenario types may reflect the fact that the paranormal scenarios had large surprise

differentials whereas non-paranormal scenarios contained two constituent events that were

similar in terms of their surprise value. But subsequent analysis of individual SJQ items

offers only limited support for this notion.6 Thus, it seems participants heightened

6Specifically, a series of 16 separate 2 constituent events 2 paranormal beliefs 2 format type mixed ANCOVA

(controlling for maths, statistics and/or psychology qualification) revealed significant differences in meanjudgement ratings across first vs. second constituent events in four of the eight paranormal items (significantF1,195 values ranged from 8.36 to 18.98; all p< .005; all h

2! .04). However, similar significant, albeit smaller,

main effects were also found also for three of the eight non-paranormal items (significant F1,195 values rangedfrom 3.95 to 10.55; all p< .05; all h2! .02). In sum, overall trends offer little indication that paranormalconstituents had a greater potential surprise value (cf. Fisk, 2004) than corresponding non-paranormal constitu-ents. Further details of these data are available from the first author (PR).


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tendency to violate normative rules for non-paranormal over paranormal conjunctions does

not reflect differential surprise values across these two types of event.

Taken together these unexpected findings suggest violation of the conjunction rule is less

prominent for events with an obvious paranormal connotation and thus that all participants,

regardless of their a priori beliefs, had their own internal representations of what

constitutes a paranormal as opposed to chance experience (cf. Bressan, 2002; Marks, 2002;

Watt, 1990/1991; Wiseman & Watt, 2006). The additional finding that compared to

sceptics, believers also made more conjunction errors for non-paranormal events has two

consequences. First, it further illustrates the generality and robustness of believers

susceptibility to the conjunction fallacy (cf. Tversky & Kahneman, 1983). Second, by

implication, it reinforces the claim that believers have particularly strong views on what

represents paranormality which may, in turn, reflect their own personal experiences of

alleged paranormal phenomena (cf. Blackmore, 1984).

Fourth, and contrary to expectations, the format with which conjunction events werepresented had little impact on participants conjunction biases. Overall, paranormal

believers made more conjunction errors given both probability and frequency formatted

items than did non-believers. This was the case regardless of the type of event described

and suggests that conjunction format may not be as important as previous suggested

(Fielder, 1988; Fisk, 2004; Fisk & Pidgeon, 1996).

Finally, current trends suggest individuals who reported a greater number of paranormal

experiences (i.e. seemingly accurate dream, waking, intuitive and/or fortune telling

predictions) also made more conjunction errors. These data reinforce previous claims that

alleged paranormal, and in particular precognitive, experiences are more prevalent in

individuals with a poorer understanding of probability (e.g. Blagrove et al., 2006). It seemsthis may be especially true for probabilistic reasoning biases relating to conjunction events.

Such biases are likely to have a major impact on subjective perceptions of chance and

randomness, and thus on peoples meaningful coincidence experiences (cf. Bressan,

2002; Henry, 1993, 2005).

Methodological issues and general discussion

Several methodological issues in the present study are worthy of note. First, the vast

majority (90.0%) of participants were university students and of those that did

have qualifications in maths, statistics and/or psychology, only a tiny minority (2.0%)were qualified beyond A Level standard. This has two implications. First, the

predominance of students within the sample, means the generalisability of current

findings are diminished (although see Farha & Steward, 2006). Second, it remains possible

that those with a university level education in maths, statistics and/or psychology might

have performed better than the current sample. It would be interesting to see whether

current findings extend to members of the general public and/or to those who have

completed an undergraduate or higher degree in these subjects.

A second methodological issue relates to the content of SJQ scenarios. As noted above,

there was little difference in the total number of surprising constituents across paranormal

(n 4) vs. non-paranormal (n 3) events. However, noticeable differences in magnitude

were found, with surprise differentials generally larger for paranormal constituents (see

footnote 6). This may have important consequences for conjunction estimates (Fisk, 2004).

Based on participant response codes, the one very surprising non-paranormal constituent

related to student vs. builder usage of a cafe at lunchtime, with the latter judged less likely


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(i.e., more surprising) than the former (p .001). This may be a reflection of participants

own student status. By comparison, the four very surprising paranormal constituents

related to feeling anxious when witnessing a ghostly image (p .003), to a horoscope

correctly predicting a job promotion (p .004), to dreaming about a house fire which later

happens (p .004) and to accurately intuiting a small lottery win (p< .001). In each case,

the second constituent was judged less likely (more surprising) than the first.

It is noticeable that five of the eight paranormal events incorporated sequential rather

than technically co-occurring constituents. In the dream precognition item for instance, the

first constituent described Leanne dreaming of a house fire whereas the second described a

fire breaking out at her sisters home. Whilst the third conjunction statements described

these events as co-occurring, participants may have inferred a temporal sequence, with the

first event presumed to have occurred before the second. By comparison, only two of the

eight non-paranormal events incorporated this temporal element. It is possible this

presumed sequential relationship between each pair of paranormal constituents influencedratings above and beyond their stated paranormality. Of course, this temporal relationship

may instead reflect the very essence of their paranormality. Nevertheless, future work

should ensure such factors are consistent across all event types. One way to achieve this is

to compare the precognitive (paranormal) vs. inferential (non-paranormal) prediction of

the same future event (e.g. a job promotion).

A similar criticism is that some paranormal events such as the near-death experience

(SJQ item 14) may be highly surprising simply because participants are unfamiliar with

such terms and/or concepts. Future work could test for this possibility via piloting scenario

content beforehand.

Finally, some paranormal events may be judged unsurprising because participants have aconsiderable personal experience of them. Whilst a PEQ was included in the current study,

it failed to cover all paranormal events outlined in conjunction scenarios. Future versions of

the PEQ should attempt to do this.

So far, results from the present study have been framed within normative probability

theory and as such, implies optimally correct probability judgements are at least possible

(Baron, 1994; Fiske & Taylor, 1991). Some have debated whether probabilities can be

applied to single events such as those included in the present study. Researchers adopting

the frequentist perspective who define probability as the proportion of actual

occurrences relative to all possible occurrences of a given event (Manktelow, 1999)

claim that probabilities cannot be meaningfully assigned in the absence of a referenceclass. As such, frequentists believe judgements about the conjunction of single events are

not governed by the rules of normative probability theory (Gigerenzer, 1991). Whilst this

suggestion has been strongly criticised (Kahneman & Tversky, 1996), others suggest that

the conjunction rule is not necessarily the appropriate rule to apply for problems of the kind

reported here. One alternative is to take a Bayesian perspective (e.g., Wolford, Taylor &

Beck, 1990). According to this view, individuals faced with the aforementioned Linda

problem (Tversky and Kahneman, 1982) do not estimate the probability that Linda is a

feminist and a bank teller given her character description but instead, estimate the

probability of Lindas description given the possibility she actually is a feminist and a bank

teller. If individuals were indeed adopting this Bayseian approach then their judgements

would not necessarily be fallacious (Wolford et al., 1990). Overall, evidence for this

proposition is absent (e.g. Fisk, 1996). Nonetheless, whilst current findings reveal some

interesting group differences between paranormal believers vs. paranormal sceptics, it is

possible that the kind of judgements they make about conjunctive events do not in fact


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violate the rules of probability theory. Future studies need to examine this possibility more

closely.

Summary and conclusion

Findings suggest paranormal believers are more susceptible to the conjunction fallacy and

thus that they are especially prone to misperceiving the co-occurrence of two independent

events as being more likely than either constituent event alone. Surprisingly, believers

susceptibility to this fallacy is less pronounced when one constituent is portrayed as an

ostensibly paranormal event implying such biases are, at least in part, context specific. In

general, participants susceptibility was unaffected by the format of conjunction items.

Taken together, current findings add further weight to the claim that paranormal believers

have a particularly poor understanding of probability and that they are prone tovarious deficits in cognitive processing. Future research to overcome methodological

limitations and extend this line of work is recommended.

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