British Journal of Clinical Psychology (1998), 37, 285-302 0 1998 The British Psychological Society

Printed in Great Brituin 285

Reasoning biases in delusion-prone individuals

Yvonne M. Linney* Department of Psychological Medicine, Institute of Pychiatry, Kings College London, De Crespigny Park,

Denmark Hill, London SES 8 A F , UK

Emmanuelle R. Peters Sub- Department of Clinical Health Pyhology, University College London, I - 19 Torrington Place, London

W C I E 6BT

Peter Ayton Psychology Department, City University, Northampton Square, London ECI V OHB

Objectives. The objective was to test whether individuals high in delusional ideation exhibit a reasoning bias on tasks involving hypothesis testing and probability judgments. On the basis of previous findings (e.g. Garety, Hemsley & Wessely, 1991), it was predicted that individuals high in delusional ideation would exhibit a ' jump-to-conclusions' style of reasoning and would be less sensitive to the effects of random variation, in comparison to individuals low in delusional ideation.

Design. A non-randomized matched groups design was employed enabling the performance of the delusion prone individuals to be compared to that of a control group.

Method. Forty individuals, selected from the normal population, were divided into groups high and low in delusional ideation, according to their scores on the Peters et al. Delusions Inventory (Peters, Day & Garety, 1996), and were compared on two tasks involving probability judgment and two tasks involving hypothesis testing.

Results. Although no significant differences were found on tasks involving hypothesis testing and the aggregation of probabilistic information, it was found that individuals high in delusional ideation had a ' jump-to-conclusions ' style of data gathering and were less sensitive to the effects of random variation, in comparison to individuals low in delusional ideation.

Conclusions. In conclusion, although individuals high in delusional ideation were not found to have a general reasoning bias, some evidence of a more specific bias was found. It is thought that these aberrations may play some role in delusion formation in schizophrenia and paranoia.

* Requests for reprints.

286 Yvonne M. Limy et al.

Based on the notion of a continuity model of psychosis, schizotypy refers to individuals within the normal population who have a predisposition towards schizophrenia (Meehl, 1962, 1990). Numerous self-report scales of schizotypy have been developed, including measures which tap general schizotypal traits (e.g. Schizotypal Personality Scale (STA); Claridge & Broks, 1984), and those which tap attenuated psychotic symptoms (e.g. Perceptual Aberration Scale (PAS) ; Chapman, Chapman & Raulin, 1978). Following the development of questionnaires identifying individuals prone to schizotypy, there have been a number of studies showing that individuals scoring highly on such measures resemble schizophrenics on a number of experimental measures : neuropsychological (Lenzenweger & Korfine, 1994), psychophysiological (Kidd & Powell, 1993) and cognitive (Williams, 1995). Indeed, it has been pointed out that it may be preferable to study the healthy, schizotypal individual, as an alternative to the medicated, symptomatic patient who may suffer from generalized performance deficits (Claridge, 1988). Moreover, as with schizophrenia, it is now clear that schizotypy is multidimensional (Bentall, Claridge & Slade, 1989) and, as a consequence, other studies have gone on to look at experimental correlates of specific components of schizotypy (Peters, Pickering & Hemsley, 1994). The present study examined reasoning in relation to the delusional component of schizotypy.

There have been a number of studies showing that delusional patients, in the clinical population, suffer from reasoning abnormalities or biases. The original studies carried out in this area looked at reasoning on a probabilistic judgment task known as the ‘beads’ task; participants were told the proportion of coloured beads contained in two jars and they had to request beads from the experimenter until they were ready to make a judgment about which of the two jars the sequence of beads had been taken from. Deluded patients were found to exhibit a ‘ jump-to-conclusions’ style of reasoning, whereby they required less evidence before reaching a decision and expressed higher levels of certainty, in comparison to control groups (Garety et a/. , 1991 ; Huq, Garety & Hemsley, 1988).

Other reasoning abnormalities in deluded patients have been observed using a variety of tasks. For example, Kemp, Chua, McKenna & David (1997) investigated performance on a number of tasks based on formal logic and, although few differences were found, the deluded group had higher error rates and were more prone to making invalid inferences. Similarly, on an inductive reasoning task known as the ‘Twenty Questions Game’, deluded patients were found to request less information before making a decision, and produce poorer judgments (John & Dodgson, 1994). Furthermore, on a hypothesis testing task requiring participants to generate rules on the basis of positive and negative feedback, deluded patients were less inclined to stick to their hypotheses when given positive feedback, and showed less evidence of focusing down to a hypothesis in response to successive sets of feedback (Young & Bentall, 1995). The findings of this study are consistent with the view that deluded individuals pay more attention to immediate environmental stimuli compared with the effects of prior learning (Hemsley, 1987). The authors proposed, on the basis of these findings, that deluded patients may have a basic deficit in the ability to make use of sequential information, which may lead them to ‘jump to conclusions ’. Young & Bentall further stipulate that a ‘ jump-to-conclusions ’ style

Reasoning biases in delusion-prone individuals 287

of reasoning is only likely to be observed if they are allowed to respond early, i.e. if the timing of response is participant-determined rather than experimenter- determined.

Indeed, recent studies have attempted to specify this reasoning bias further. Dudley, John, Young & Over (1997~) have proposed that deluded individuals do not have a general reasoning deficit, but rather a more specific deficit in data gathering. In accordance with previous findings, Dudley e t al. (1997~) found that deluded individuals requested fewer beads, in comparison to depressed and normal controls, before making a decision on a computer version of the ‘beads ’ task used by Garety e t al. (1991). Fewer beads were requested whether the ratio of beads was 85 : 15 or 60: 40, although more beads were requested when task difficulty increased (i.e. with the 60 : 40 ratio), suggesting that the ‘ jump-to-conclusions ’ reasoning style did not merely represent impulsiveness. Furthermore, reminding participants which beads had been drawn did not influence the results, indicating that the deluded patients’ performance was not caused by a memory deficit.

However, it was also reported that deluded individuals reasoned similarly to controls when estimating the probability that a coin was biased, and on the ‘beads ’ task when they were given a predetermined set of beads, i.e. when the amount of evidence viewed was determined by the experimenter rather than the participant. It was concluded from these findings that deluded individuals have a tendency to ‘ jump to conclusions’ in data gathering, rather than a deficit in reasoning per se (i.e. how they use the data gathered). Dudley e t al. (1997~) therefore aver that probability judgments remain intact in this population, whereas data gathering (i.e. deciding how much evidence is needed before being able to make an informed decision, where information is not predetermined) is dysfunctional.

A number of studies support Dudley e t al.’s proposal that deluded individuals have a specific, rather than general, reasoning deficit. For example, Bentall & Young (1996) investigated ‘ sensible hypothesis testing’, where participants were asked to prove which one of three variables was responsible for a specified outcome in a typical everyday situation ; they found that deluded participants showed no evidence of abnormal hypothesis testing. Similarly, Young & Bentall (1997) found that deluded individuals performed similarly to controls on a modified version of the ‘beads’ task in which participants were presented with a predetermined set of beads.

There are, however, some contradictory findings in the literature. For instance, Young & Bentall’s (1995) suggestion that deluded individuals may have a deficit in the ability to make use of sequential information, in fact, predicts that deluded individuals will perform less accurately when the amount of information is predetermined, since they are forced to make use of sequential processing, at which they are presumed poor. In contrast, Dudley e t al. (1997~) would predict the opposite, since they propose that deluded patients will perform normally if the experimenter decides when the task terminates, but will ‘jump to conclusions ’ if allowed to end the task themselves.

It is also unclear whether the lack of differences between the groups found by Young & Bentall (1997) on the ‘beads’ task was due to the information being predetermined, or whether it was in fact due to the scoring procedures (where blocks of five responses to the bead presentations were evaluated, thus possibly obscuring

288 Yvonne M. Linney et al.

differences in the reactions to individual beads). Furthermore, the distinction between data-gathering (where information is not predetermined) and probability judgments (where information is predetermined) made by Dudley and his colleagues is somewhat unclear. They maintain that deluded patients’ probability judgments are normal because they choose the right jar when the number of beads shown is predetermined (by the experimenter); however, it should be pointed out that in the ‘beads’ studies reported so far, deluded individuals have almost always chosen the right jar, even though the information is not predetermined, i.e. the search is terminated by the participants. Therefore performance, at least measured by the criterion of correct choice, is the same regardless of whether the information is participant- or experimenter-determined. Thus, although Dudley e t a/. seem to be correct in concluding that deluded individuals’ probability judgments are intact, and that the ‘ jump-to-conclusions’ bias is limited to data-gathering, it should be emphasized that what is important is what is being assessed: i.e. whether it is the probability judgment (which jar is chosen) or how they get to the judgment (the data- gathering), rather than whether or not the information is predetermined.

This review reveals that the exact nature of the reasoning bias involved in delusions remains unclear. In order to examine this relationship further, normal participants low and high in delusional ideation were tested on two tasks involving hypothesis testing and two tasks involving probability judgments. The ‘beads’ task used by Garety e t a/. (1991) was not used in the present study, first, because human judgment under these conditions is not well described by Bayes’ theorem (individuals taken from the normal population tend not to revise their opinions sufficiently in the light of the evidence (Fischoff & Beyth-Marom, 1983)), and, second, because several studies have already been carried out looking at deluded individuals’ reasoning on this task. Instead, four different tasks were selected in order to build on previous findings. The tasks involving hypothesis testing were a revised version of Wason’s 2-4-6 problem (Gorman, Stafford & Gorman, 1987) and a revised version of Wason’s selection task (Platt & Griggs, 1993), and the tasks involving probability judgments were the coin tossing task (Blackmore & Troscianko, 1985) and the book/suicide problem (Bar-Hillel, 1980; Tversky & Kahneman, 1980).

EXPERIMENT 1

The revised version of the 2-4-6 problem examines an individual’s ability to gather feedback in order to form hypotheses. Participants are told that they are looking for two rules that accept some number triples and reject others: the Dax rule (‘three different numbers’) and the Med rule, which is the opposite (i.e. ‘two or more numbers the same’). Participants are given an example of a triple following the Dax rule and are then asked to generate their own number triples. The experimenter indicates which rule each triple follows and the task ends when the individual believes s/he knows the two rules. Gorman e t a/. (1987) found that 88 per cent of normal individuals were able to correctly solve the Dax rule. This task is similar to the hypothesis testing task used by Young & Bentall (1995), although Young & Bentall gave the participants predetermined feedback, whereas this task requires the participants to gather their own feedback.

Reasoning biases in delusion-prone individuals 289

It is predicted that individuals high in delusional ideation, in comparison to individuals low in delusional ideation, will perform less accurately as they will be more likely to predict the two rules without fully attempting to establish the boundaries of the Med rule (i.e. ‘jump to conclusions’), and will be more likely not to use all the feedback in making their judgment. On the basis of previous research indicating that deluded individuals pay more attention to stimuli in the immediate environment (Hemsley, 1987), it is also predicted that individuals high in delusional ideation will be more likely to make decisions on the basis of feedback presented in the trials immediately preceding their decision.

Method Participants and questionnaires Twenty-one male participants and 19 female participants were recruited from the non-psychology population of University College London. All participants spoke English as their first language. Participants were divided into two groups on the basis of their scores on the Peters e t al. Delusions Inventory (PDI; Peters e t a/., 1996). The PDI is a 21-item questionnaire which is designed to measure delusional ideation in the normal population (it originated from the 40-item version of the questionnaire; Peters, Joseph & Garety, in press). For each item, the participant scores 1 if the belief is endorsed, and 0 if the belief is not endorsed. If the belief is endorsed, the participant is asked to rate on a scale of 1 to 5 the degree of distress, preoccupation and conviction with which the belief is held. The final score is the sum of the scores for each item, including the ratings on the three flanking scales. The range of possible scores is 0 to 336, where higher scores are associated with greater delusional ideation. Individuals scoring below the median score (61) on the PDI made up the control group, and individuals scoring above the median score made up the experimental group (although the scores on the PDI were slightly skewed, the kurtosis was within acceptable limits: - 1 < + 1). The PDI was chosen over other more general measures of proneness to psychoticism because the delusional component of schizotypy was of specific interest.

Participants also completed the Magical Ideation Scale (MIS; Eckblad & Chapman, 1983), the Social Desirability Scale of the Eysenck Personality Questionnaire (EPQ; Eysenck & Eysenck, 1976), and an adapted version of the Quick Test (Ammons & Ammons, 1962; Mortimer, 1995). The MIS is a 30-item truefalse scale developed for measuring magical ideation (defined as ‘belief in forms of causation that by conventional standards are invalid’) and it was used as a backup measure for the PDI to check that high PDI scorers also scored highly on this measure. The range of possible scores is 0 to 30 and higher scores are associated with greater magical ideation. The Social Desirability Scale of the EPQ is a 21- item scale which measures the tendency to give socially desirable answers in questionnaires. The range of possible scores is 0 to 21 and higher scores are associated with a greater tendency to give socially desirable answers. The Quick Test is a rapid measure of IQ which relies on verbal and perceptual skills. The individual is shown four line drawings and given 50 test words which must be related to one of the pictures. This version of the Quick Test differs from the original version in that the pictures are larger, clearer and updated, and the American word ‘bleachers’ has been replaced with the nearest English equivalent ‘benches ’ (Mortimer, 1995). The questionnaires were given to participants after they had completed the reasoning tasks, and the order in which the questionnaires were completed was counterbalanced across participants.

Participants’ characteristics can be seen in Table 1. As would be expected, the experimental group had significantly higher scores on the MIS than did the control group (438) = - 2 . 2 , ~ = .015, one-tailed). Analyses revealed no significant differences between the two groups in terms of age, years in full-time education, scores on the Quick Test and scores on the Social Desirability Scale of the EPQ.

Procedure Participants were tested individually by the experimenter in a quiet room. As the same individuals were used in each of the experiments, all individuals completed four reasoning tasks. The Quick Test was

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Table 1. Participant characteristics : Means and standard deviations (in parentheses)

Sex Years in Age ~ full-time Quick

G r o u p N (years) M F education PDI Test SD MIS

Control 20 27.5 11 9 15.75 31.9 105.6 4.35 6.35 (1 1.03) (2.31) (18.34) (6.4) (2.91) (0.97)

(9.15) (1.76) (29.84) (9.6) (2.75) (1.05) Experimental 20 25.0 10 10 16.55 93.35 104.8 5.0 9.5

Key. PDI = Peters e t a/. Delusions Inventory (Peters e t al., 1996); Quick Test (Ammons & Ammons, 1968); Social Desirability Scale of the EPQ (SD) (Eysenck & Eysenck, 1976); MIS = Magical Ideation Scale (Eckblad & Chapman, 1983).

presented with the problem-solving tasks in order to disguise the fact that it was an IQ test. The order in which the problem-solving tasks and the Quick Test were presented was counterbalanced across participants. The procedure for individual reasoning tasks will be described separately within each experiment. For the modified version of Wason’s 2-4-6 problem participants were presented with a set of standardized instructions (identical to those used by Gorman e t a/., 1987). These stated that the object of the task was to work out two rules which accept some number triples and reject others: the Dax rule (‘three different numbers’) and the Med rule (‘at least two numbers the same’).

Participants were also given a chart headed by the columns ‘Triple’, ‘Your Prediction?’, ‘Dax’ and ‘Med’. The instructions gave an example of a triple following the Dax rule ( 2 4 6 ) and stated that participants should propose further number triples in the ‘Triple’ column and write Dax or Med in the ‘Your Prediction?’ column, according to which rule they thought the number triple would follow. The instructions then stated that, after each triple was proposed, the experimenter would put a tick in either the ‘Dax’ or ‘Med’ column, according to which rule the number followed. Participants were told to read through the instructions and to ask questions if they came across anything that they did not understand. When participants were satisfied that they understood the instructions they began the task. The task continued until participants were confident that they knew both of the rules; they then wrote the rules down and were then told whether or not they were correct.

Results

Two individuals were classified as being unable to do this task: one failed to come up with an example of a triple following the Med rule, and one proposed rules that were inconsistent with the triples they had proposed. These individuals were excluded from the analysis (both were from the experimental group). The remaining participants were classified into one of two categories ; those who successfully solved both of the rules, and those who failed to solve both of the rules because they exhibited a ‘ jump-to-conclusions ’ style of data-gathering. In the ‘ jump-to- conclusions ’ category, two different types of reasoning were observed. The first and most prominent involved proposing Dax and Med rules without fully attempting to establish the boundaries of the Med rule. The second involved being excessively influenced by feedback presented in the trials immediately preceding their decision, in comparison with previously acquired information. For these participants, at least one rule was consistent with the latest triples they had proposed, although it was inconsistent with previously proposed triples. These two types of data-gathering were combined to create one ‘ jump-to-conclusions ’ category ; first, because only three individuals exhibited the second type of data-gathering (one in the control

Reasoning biases in delusion-prone individuals 29 1

group and two in the experimental group), and, second, because these two types of data-gathering are conceptually the same in that they both involve making judgments based on a limited amount of information. Within the experimental group, 8 individuals were classified as having solved the problem correctly and 10 individuals were classified as having ‘jumped to conclusions’. Within the control group, 15 individuals were classified as having solved the problem correctly and 5 individuals were classified as having ‘ jumped to conclusions ’. Two-factor chi-square analyses revealed that performance on this task was significantly related to participant group, with the control group being more likely to correctly solve both rules and the experimental group being more likely to exhibit a ‘jump to conclusions’ style of data-gathering ( x2 = 3.70, p = .05).

Conclusion

The fact that individuals high in delusional ideation were significantly less successful at correctly solving the two rules on the modified version of the 2-4-6 problem, and were significantly more likely to ‘ jump to conclusions’, in comparison to individuals low in delusional ideation, supports findings of previous studies (Garety e t a/., 1991 ; Huq e t a/., 1988). The fact that this study involves gathering data, and enables participants to determine when they will terminate the task, supports Dudley e t a/.’s (1997~) proposal that deluded individuals have a tendency to exhibit a ‘ jump-to- conclusions ’ style of data-gathering. Additionally, these findings support Young & Bentall’s (1 995) finding that deluded individuals are less responsive to feedback and are less able to narrow hypotheses down, in comparison to control groups.

EXPERIMENT 2

The modified version of Wason’s selection task examines an individual’s ability to test a given hypothesis. In this task, the participant is presented with four cards (a vowel, a consonant, an even number and an odd number) and a rule that refers to these cards: a card with a vowel on it can only have an even number, but a card with a consonant on it can have either an even or an odd number. The participant can only see one side of each card and is asked to indicate only those cards that must be turned over in order to determine whether the rule is being violated (the correct choice is the vowel and the odd number). A further modification instructing participants to only select two cards was not used in the present study as the number of cards turned over was one of the factors of interest. For the modified version of Wason’s selection task there were four main dependent variables: the number of cards turned over (one, two, three or four), certainty about the decision (this was marked on a 10-cm long bipolar scale, ‘totally certain’ to ‘totally uncertain’, and was then measured and converted into a percentage), the time taken to decide which cards to turn over, and correct responses (1 for turning over the correct cards and 0 for turning over incorrect cards). Platt & Griggs (1993) found that 87 per cent of the participants turned over the correct cards when presented with this task. This task is similar to Bentall & Young’s (1996) ‘sensible hypothesis testing’ task, although Bentall & Young asked participants to test the hypothesis by choosing between confirming and disconfirming strategies, whereas with this task participants are only asked to use disconfirming strategies.

292 Yvonne M. Linney et al.

It is predicted that individuals high in delusional ideation, in comparison to individuals low in delusional ideation, will turn over fewer cards in order to decide whether or not the rule has been violated, will take less time to decide which cards to turn over, and will express higher levels of certainty as to whether their decision is correct.

Method Participants

The participants were the same as those for Expt 1.

Procedure

For the modified version of Wason’s selection task, participants were told that they were being timed but that there was no time limit. They were then given the problem which began with a set of standardized instructions. The cards were presented below the instructions, and ‘ Turn over-? ’ was printed below each of the cards. Timing began as soon as the participant had begun reading the instructions and ended when the participant had decided which cards to turn over. Following this, participants were asked the reasons for their decisions and were given two lines on which to write their answers (this was one of the modifications made by Platt & Griggs, 1993, which was found to improve performance on the task). If they changed their minds about any of their decisions at this point then the time was altered. At the bottom of the page, participants were asked to indicate their certainty concerning their decision on a 10-cm long bipolar scale (totally certain to totally uncertain).

Results

Table 2 shows how participants performed in this task. Two-factor chi-square- analyses revealed that there were no significant relationships between group and the number of participants who turned over the correct cards, nor between group and the number of cards turned over. As the data were not normally distributed non-parametric statistics were used. Mann-Whitney tests revealed that there were no significant differences between the two groups in terms of time taken to decide which cards to turn over and certainty scores.

Table 2. Participants’ performance on the selection task (standard deviations in parentheses)

Number of participants turning over Number of Number of

Mean Time taken each number participants participants certainty to complete of cards turning over turning over

judgments task correct incorrect Group (”/I (min) 1 2 3 4 cards cards

Control group (N = 20) 86.25 (15.9) 2.61 (2.15) 4 11 2 3 9 11

(N = 20) 81.35 (22.51) 2.37 (1.54) 2 12 2 4 11 9

Experimental group

Reasoning biases in delusion-prone individuals 293

Conclusion

The finding that there were no significant differences between the two groups on the modified version of Wason’s selection task seems to contradict previous results (Huq e t al., 1988; Garety e t al., 1991). However, there are two possible explanations for this. First, it has been suggested that deluded individuals have a tendency towards a ‘ jump-to-conclusions ’ style of data-gathering, rather than a general reasoning deficit (Dudley e t al., 1 9 9 7 ~ ) . Since the modified version of the selection task involves the ability to test hypotheses (i.e. making a decision about whether each card could potentially disconfirm the rule), rather than the ability to gather data, then the present findings support Dudley and colleagues’ proposition. They are also in agreement with Bentall & Young (1996), where no group differences were found when using disconfirmatory strategies to test hypotheses. They do not, however, support the suggestion that deluded individuals will differ from normals on tasks which they are allowed to terminate, since this was a participant-determined task. Nevertheless, the second possible interpretation is that performance on this task is hitting a floor effect, with approximately 50 per cent of each group turning over the incorrect cards.

The fact that individuals high in delusional ideation did not express higher certainty levels on this task, in comparison to individuals low in delusional ideation, also contradicts previous findings (Huq e t al., 1988). However, it should be noted that the Huq e t al. study looked at initial certainty levels (after their first probability estimate), whereas in this study participants gave their certainty judgments after they had completed the task.

EXPERIMENT 3

The coin tossing task is a test of probability judgment which examines an individual’s sensitivity to varying sample sizes. In this task, the participant is presented with eight examples of coin tossing and asked to what extent the coin is biased; the proportion of heads is either 50 or 75 per cent, and the number of tosses is either 4, 12, 20 or 60. For example,

I toss a coin 12 times and get ‘heads’ 6 times. To what extent would you say this is not a fair coin? Please indicate how fair you think this coin is on a scale of 0 to 100, where 0 is totally fair and 100 is totally unfair.

This version differed from the original version in that the word fair has been used instead of biased, and, instead of using a rating scale of 1 to 5, a scale of 0 to 100 was used. The bias rating should decrease with an increasing number of tosses on examples with 50 per cent heads, and should increase with an increasing number of tosses on examples with 75 per cent heads (i.e. it is more likely that the distribution of heads and tails will be uneven if the coin has only been tossed a few times, but as the number of tosses increases the ratio should become closer to 50: 50). Blackmore & Troscianko (1985) showed that children who believe in the paranormal are significantly worse at responding to increasing sample size on this task (i.e. are less sensitive to random variation), when compared with children who do not believe in the paranormal. One possibility is that a lack of awareness that certain incidents occur due to randomness leads to an increased search for alternative (e.g. paranormal, or

294 Yvonne M. Linnty et al.

even delusional) explanations. It was therefore predicted that individuals high in delusional ideation would be less sensitive to the effects of varying sample size, and would be worse at the coin tossing task, in comparison to individuals low in delusional ideation.

Method Participants The participants were the same as those for Expts 1 and 2.

Procedure Participants were given eight examples of coin tossing (where the proportion of heads is either 50 or 75 per cent, and the number of tosses is either 4,12, 20 or 60) which were presented in a fixed pseudo- random order.

Results

Figure 1 shows the mean bias ratings for the groups for each of the sample sizes where the proportion of heads is 50 per cent. Figure 2 shows the mean bias ratings

60

50

.f 40

.j 20

.? 30 s

10

0

- - - - Control

4 12 20 60 Number of tosses

Figure 1. Performance on the coin tossing task where the proportion of heads is 50 per cent.

. .... .. .. . . . . . . .. . . . . . . . . . . . . . . . 60

50

.s 40 E .? 30

20 5: 10

M

.a

n

- - - - Control El 4 12 20 60

Number of tosses

Figure 2. Performance on the coin tossing task where the proportion of heads is 75 per cent.

Reasoning biases in delusion-prone individuals 295

for the groups for each of the sample sizes where the proportion of heads is 75%. The important variable in these figures is the slope of the line i.e. how the bias ratings change relative to the number of tosses (rather than whether the bias ratings are high or low); in other words, if a person is sensitive to sample size, their bias ratings should decrease with increasing sample size where the proportion of heads is 50% (i.e. in Figure 1 , ideal ratings should depict an inverse, approximately linear, relationship) and their bias ratings should increase with increasing sample size where the proportion of heads is 75% (i.e. in Figure 2, ideal ratings should depict an approximately linear relationship).

In order to analyse these data, the bias ratings were scored using the method employed by Blackmore & Troscianko (1985). This method of scoring takes account of an individual’s bias ratings relative to the number of tosses, for each category of strength (i.e. 50 per cent heads and 75 per cent heads). In cases where the proportion of heads is 50 per cent, scores were incremented by +1 where the rating decreased with increasing sample size, by 0 where the rating stayed the same with increasing sample size, and by - 1 where the rating increased with increasing sample size. In cases where the proportion of heads is 75 per cent, scores were incremented by +1 where the rating increased with increasing sample size, by 0 where the rating stayed the same with increasing sample size, and by - 1 where the rating decreased with increasing sample size (i.e. the opposite to 50 per cent). Using this method of scoring the possible range was -6 to +6. However, the score was normalized so that the total score was a percentage of the theoretical maximum, giving a range of -100 to +loo. A high score means a good ability to judge randomness (the higher, the better), and a low score means a poor ability to judge randomness (the lower, the poorer). This method of scoring is easy to interpret since it is obvious from the sign whether an individual’s performance is good or bad. The mean score for the experimental group was - 1.67 (SD = 14.21), and the mean score for the control group was 10.83 (SD = 18.95).

As the data were not normally distributed non-parametric statistics were used. As predicted, the control group scored significantly higher at this task than did the experimental group (Mann-Whitney test: U = - 1.81, p = .035, one-tailed), indicating that the experimental group was significantly less sensitive to random variation in comparison to the control group. However, it should be noted that the experimental group was not completely unaware of random variation since, similarly to the control group, their bias ratings were higher for the trials where the proportion of heads was 75 per cent, than for trials where it was 50 per cent.

Conclusion

The fact that individuals high in delusional ideation were significantly worse at the coin tossing task suggests that they are less sensitive to the effects of varying sample sizes, in comparison to individuals low in delusional ideation. These findings support implications of previous studies (Garety e t al., 1991 ; Huq e t al., 1988). This ‘jump to conclusions’ style of reasoning could itself be due to a lack of sensitivity to the effects of random variation (i.e. deluded individuals may make decisions on the basis of limited evidence because they are less aware that samples tend to become more representative as they increase in size). In turn, since randomness is not available as

296 Yvonne M. Linney et al.

an explanation for events, alternative (delusional) interpretations are more likely to be sought.

The present findings contradict those of Dudley e t a/. (1997a), in which deluded patients performed this task in a manner similar to controls. However, Dudley e t aL’s experiment differed from this one in that they investigated the dative effects of weight (i.e. sample size) and strength (i.e. proportion of heads to tails). They found that the effect of strength overrode that of weight for both groups. However, this does not necessarily mean that deluded individuals are equal to normals in how much notice they take of sample size, since the Dudley study only looked at relative differences between weight and strength, which may have obscured actual sensitivity to weight. It is possible that differences between the groups would have emerged if they had kept the strength constant, but manipulated the weight. In the present study, where there were only two different strengths, and where the method of scoring focused on sensitivity to weight, the findings indicate that individuals high in delusional ideation are less sensitive to sample size. However, the fact that both individuals high in delusional ideation and individuals low in delusional ideation had higher bias ratings when the proportion of heads was 75 per cent compared to when the proportion of heads was 50 per cent supports Dudley e t a/.’s finding that people generally tend to be overinfluenced by strength in comparison to weight.

A further contradiction between our results and those of the Dudley group concerns the fact that the coin tossing task involves making a decision about information which is, in fact, predetermined by the experimenter. This would suggest that whether or not the information supplied is predetermined is not predictive of performance. Secondly, the coin tossing task does not involve data- gathering either. However, as argued above, it is possible that a lack of sensitivity to random variation may in fact lead to a premature termination of data-gathering, and be causally implicated in the formation of a ‘ jump-to-conclusions’ style of data- gathering. We would therefore postulate that although abnormal performance in delusion-prone individuals is not restricted to tasks where the information is participant-determined, abnormalities do seem to centre around cognitive processes involved in data-gathering.

EXPERIMENT 4

The book/suicide problem involves giving individuals a problem containing information about prior probability and specific information which are inconsistent with each other. The original versions of these problems are referred to as the ‘specific’ type problem. The following is an example of the specific version of the suicide problem :

Consider the following assumptions regarding suicide. In a population of young adults, 80 per cent of the individuals are married and 20 per cent are single. The percentage of deaths by suicide is three times higher among single individuals than among married individuals. What is the probability that an individual, selected at random from those that had committed suicide, was single?

According to Macchi (1995), the wording of this question leads individuals to consider only a specific segment of the population and leads to base rate neglect

Reasoning biases in delusion-prone individuals 297

(where prior probabilities are neglected in favour of the specific information). Thus, most people will give a high probability estimate, since they ignore the fact that 80 per cent are married, and consider only the fact that single people are three times more likely to commit suicide. Macchi used adapted versions of these problems and demonstrated that by slightly changing the text, so that the entire population was explicitly referred to (i.e. ‘what is the probability that a suicide, selected at random from the population of young adults, was single?’), base rate neglect disappeared and individuals’ reasoning was more similar to Bayesian analysis (i.e. both the base rate and the specific information are used to calculate the answer). The adapted versions of these problems are referred to as ‘ population’ type problems. Participants received one ‘book’ and one ‘suicide’ problem, whereby one of the problems was the specific type problem and one of the problems was the population type problem (the ‘book ’ problem is similar to the ‘ suicide ’ problem, but instead refers to French and German books. The proportion of paperbacks among the French and German books are given, and the participant has to work out the probability that a paperback is French).

Based on previous research with the book/suicide problem (Macchi, 1995), it is predicted that all participants will exhibit base rate neglect on the specific type problem. This prediction is also supported by the findings of Dudley e t al. ( 1 9 9 7 ~ ) where, on the biased coin task, the factor of strength was such a powerful effect that it overrode the effect of sample size for both groups. However, on the population type problem, it is predicted that only individuals low in delusional ideation will use all of the given information to calculate their answer (i.e. individuals high in delusional ideation will ‘jump to conclusions’ and only use part of the information of the given information in calculating their answer). It is predicted that they will pay more attention to the latter part of the information (the specific information), first, because original versions of this task have shown that this part of the question is more salient and, second, because it has been proposed that deluded individuals pay more attention to immediate environmental stimuli (Hemsley, 1987).

Method Participants The participants were the same as those for Expts 1, 2 and 3.

Procedure For the book/suicide problem, one problem was presented at the top of the page and the other problem was presented half way down the page (to leave some space for calculations). As participants received two problems (one population type problem and one specific type problem), the values in one of the problems was changed by adding 10 per cent to the base rate percentages. Participants were told to work out approximate answers to the problems (without using a calculator). As the numerical value of an answer is not necessarily indicative of the underlying reasoning, participants were also asked to reason aloud so that the verbal protocols could be noted down and analysed. The order in which participants received the two problems was counterbalanced across subjects. Participants were told to do the problems in the order that they appeared, and not to look at the second problem until they had completed the first.

298 Yvonrre M. Linney et al.

Results

The numerical answers and verbal protocols for specific and population type questions were analysed by dividing them into two classes of answers: those based on only specific information, and those based on both prior probabilities and specific information. A third theoretical possibility of answer, based only on prior probabilities, was not produced. Answers to specific and population type questions which were based on specific information were classified as S1 and P1, respectively. Answers to specific and population type questions which were based on both the base rate and specific information were classified as S2 and P2, respectively. Figure 3 shows the proportion of individuals in the experimental and the control group who fell into each of these categories. Two-factor chi-square analyses revealed that there were no significant relationships between the participant group and the type of reasoning used on either type of problem.

0 Experimental group

Question type/reasoning style

Figure 3. Participants’ reasoning styles on specific and population type questions on the book/suicide problem.

Conclusion

On the specific version of the book/suicide problem, neither individuals high in delusional ideation nor individuals low in delusional ideation exhibited base rate neglect to the extent that it had been found in previous studies (e.g. Macchi, 1995). The reason for this difference in findings may be that half of the participants in this study attempted a population type question before attempting a specific type question, meaning that these individuals were less likely to misunderstand the specific question, or the specific information, when it was presented to them.

The fact that there was no significant difference between the groups in terms of the type of information used in the population type question seems to contradict previous findings that deluded individuals make judgments on the basis of a limited amount of evidence (Garety e t al., 1991 ; Huq et al., 1988). However, it should be noted that this task does not involve data-gathering, but a probability judgment, supporting Dudley et UPS (1997~) proposal that the bias may be limited to data- gathering.

Reasoning biases in delusion-prone individuals 299

GENERAL DISCUSSION

Individuals high in delusional ideation were significantly less likely to take account of varying sample sizes on the coin tossing task, and were significantly more likely to ‘jump to conclusions’ on the modified version of the 2-4-6 problem, in comparison to controls. However, there were no significant differences found between the two groups on the modified version of the selection task or on the book/suicide problem.

Overall, these findings support the proposal that the reasoning bias involved in delusional ideation is not a general one. However, the distinction advanced by Dudley e t al. ( 1 9 9 7 ~ ) that deluded individuals ‘jump to conclusions’ in tasks involving data- gathering (where the information is determined by the participant), but perform normally when probability judgments are required (where the information is predetermined by the experimenter), does not accommodate the present data. Thus, differences between the groups in the predicted direction were found on a task where information was participant-determined (the modified version of Wason’s 2-4-6 problem), but also where it was experimenter-determined (the coin tossing task). Similarly, on other tasks no differences were observed between the groups irrespective of whether the information was predetermined (the book/suicide problem) or not (the modified version of Wason’s selection task). Therefore, as argued in the introduction, whether or not information is predetermined by the experimenter is not predictive of performance.

Overall, our results do support the notion that only data-gathering abnormalities are involved in delusional ideation, although this is independent of whether or not the information is predetermined. The coin tossing results may, at first glance, indicate that the reasoning deficit is not limited to data-gathering, since the task does not require participants to gather any evidence or data. However, we suggest that a lack of sensitivity to random variation may in fact be linked to the data-gathering bias observed in other tasks. Thus, an individual who is insensitive to random variation may be less likely to realize that a larger sample is more representative, and this may lead them to ‘ jump to conclusions ’ and to terminate data-gathering early.

However, while insensitivity to random variation appears to be causally linked to some forms of data-gathering (such as gathering data on the ‘beads’ task), there seem to be other types of data-gathering which do not involve sensitivity to randomness, and may involve other cognitive processes. Thus, whereas the ‘beads’ task involves gathering a representative sample of beads so that a probability judgment can be made, the modified version of the 2-4-6 problem requires gathering feedback in order to generate and test hypotheses. The ‘jump to conclusions’ style of data-gathering on the ‘beads’ task is manifested by asking to view only a few beads, whereas on the 2-4-6 task it is illustrated by being more likely to propose hypotheses which have not been falsified and which are consistent with only some of the feedback. Although both types of performance are conceptually similar, in as much as they both involve making decisions on the basis of limited evidence, there are subtle differences in the underlying cognitive processes. Further research is therefore needed to specify the exact nature of the ‘ jump to conclusions ’ data-gathering bias exhibited by deluded individuals.

300 Yvonne M. Linney et al.

The findings of the present study have possible implications for understanding the formation of delusions. For example, Garety (1991) has proposed that the tendency to make judgments on the basis of limited information may be an important factor involved in the formation of delusions in schizophrenia and paranoia; thus, it is interesting to note that this reasoning bias is also present in normal individuals with high levels of delusional ideation. Although causal inferences can best be made with longitudinal data, the fact that there are biases in pre-delusional states would suggest that they are involved in delusion formation rather than just delusion maintenance. Thus, insensitivity to random variation may result in underestimating the likelihood that an event has occurred by chance, and this may, in turn, result in the individual searching for an alternative (i.e. delusional) explanation for the event. In addition, failure to gather adequate feedback (potentially confirming and disconfirming evidence), and failure to take account of all the feedback when searching for an explanation for an event, may result in the individual hastily accepting a false hypothesis.

There are, however, some notes of caution worth bearing in mind in interpreting the present data. First, the individuals tested were taken from the normal population, whereas the individuals tested in previous studies have been patients. It is therefore possible that the failure to find reasoning biases on the selection and book/suicide tasks is due to the bias being too subtle in normal individuals. Second, there may have been a floor effect in the Wason selection task, and lower rates of base rate neglect were observed in the book/suicide problem. It would be worthwhile replicating the present study with slightly modified versions of these tasks. Thirdly, some studies have shown that emotional salience affects people’s reasoning, and may affect people with delusions to a greater extent (Dudley, John, Young & Over, 1997 6 ; Kemp e t ai., 1997; Young & Bentall, 1997). Therefore, it is possible that more significant results might have been shown for emotionally salient material.

In conclusion, this study has found that individuals in the normal population who are high in delusional ideation may have a specific form of reasoning bias or abnormality. No significant differences were found on tasks involving hypothesis testing and the aggregation of probabilistic information, but individuals high in delusional ideation had a ‘ jump to conclusions ’ style of data-gathering and were less sensitive to the effects of random variation. These findings are thought to support the proposal that the bias exhibited by deluded individuals is limited to data-gathering, but not to the information being participant-determined. It is also proposed that there are different forms of data-gathering which may have different underlying cognitive processes. It is further suggested that these aberrations may play some role in delusion formation in psychosis and paranoia.

Acknowledgements

We would like to acknowledge The Wellcome Trust for their contribution to the second author. Thanks to University College London for providing the funds for this research project.

Reasoning biases in delusion-prone individuals

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Received 11 April 1997; revised version received 24 Februaty 1998