To further test people’s appreciation of probability Brugger (1990) conducted a study to test people’s ability to generate random sequences. Subjects were asked to imagine rolling a dice and respond with a number from one to six, this was repeated sixty-six times at a rate of one response per second. The subjects were asked to make the responses indistinguishable from that of a real dice. They were also asked to rate their belief in ESP on a scale of one to six where one is strong belief in ESP and six is a strong disbelief in ESP. People who believe in ESP are commonly referred to as sheep and disbelievers as goats.
The average number of repetitions in this sequence would be expected to total 10.8 for 66 throws of the dice. It was found that people who were rated as sheep (an ESP rating of 1 or 2) showed significantly less repetitions than goats (an ESP rating of 5 or 6). The mean number for sheep was 5.2, the mean for goats was 7.4 and the mean for people who were rated indifferent (an ESP of 3 or 4) was 5.9.
Brugger (1990) then designed an experiment to look for differences in repetition avoidance between sheep and goats in a context not involving ESP. He showed his subjects pairs of dice in six different sequences, one sequence always contained more repetitions than the other. The subjects were then asked which sequence was most likely to occur first or if they were both as likely to occur as each other. The mathematical probability of either occurring was the same. It was found that sheep were significantly less likely to answer correctly than goats. The mean number of correct answers for sheep was 2.2, for goats was 3.9 and for indifferent was 2.8.In none of the six pairs did sheep perform better than goats.
Brugger (1990) found that subjects who were rated as sheep avoided repetitions significantly more than subjects who were goats. This was true for both repetition avoidance and appreciation of randomness. He concluded that sheep have a more biased internal representation of randomness than goats, and this may explain why sheep are more likely to try and find an explanation for coincidences that occur in everyday life.
The results were different from Blackmore and Troscianko (1985) who first described the sheep-goat effect. They also found that people generally undersestimated the number of repetitions in a random sequence, and that sheep made more errors in probability tasks than goats, but contrary to Brugger’s findings that there was no significant difference between sheep and goats in repetition avoidance.
Other studies that examine the sheep-goat effect have studied illusion of control. Since sheep are more prone to believe that things do not occur by chance it was hypothesised that sheep will be more likely to believe that they can exert some kind of control over a task including illusionary control than goats. In a study by Blackmore and Troscianko (1985) subjects were asked to try and make a computer generated coin fall as either heads or tails. Real control was only made possible on one out of the two trails. The results showed that sheep were more likely to believe that they had exerted more control than goats. The subjects were then asked to estimate how many they had managed to get correct and it was found that sheep estimated that they had got fewer correct than they actually had.
They were then asked to estimate how many they would get correct due to chance i.e. with their eyes shut, this showed that sheep drastically underestimated the level of chance performance whereas goats did not. This made it appear to the sheep that their performance was better than chance even though it was not. Sheep seem to perceive themselves as more successful in tasks that involve the illusion of control.
Brugger (1990) also looked at the illusion of control and devised a test to see if sheep did believe they could influence a random event. He asked subjects to assess whether it was more likely that you could throw ten dice and get ten sixes or throw one dice ten times and get ten sixes. They probability of these things happening is mathematically the same. It was found that sheep thought that the second of the two was more likely as it allowed control.
The above research points to there being a difference between believers and disbelievers in ESP and indicates that sheep are more likely to underestimate the chance factor when asked to perform a task such as replicating a random dice roll or perceiving control on a chance coin toss.
This experiment will concentrate on one aspect of the research and replicate Brugger’s repetition avoidance study with the aim of finding a difference between believers in ESP and disbelievers in ESP. The independent variable will be whether the subjects classes themselves as a sheep or as a goat and the dependent variable will be the number of repetitions made in a string of sixty-six numbers. It is expected that sheep will be more likely to avoid repetitions than goats. This is because believers in ESP are more likely to look for an explanation for coincidences that occur in everyday life.
Method
Participants. One hundred and Sixty-five degree level psychology students from the University of Lincoln volunteered to participate in the experiment and ten other participants. The psychology students were an opportunity sample of students available at a single lecture, the other ten where randomly chosen. The sample comprised of both male & female participants.
Procedure. The participants were asked to imagine a dice being rolled sixty-six times and to say a random result for each throw. They were to make the resulting sequence as indistinguishable as possible from an actually rolled dice. These results were then checked for repetitions of the same number, and the amount of repetitions were counted and noted. The participants were also asked to state their belief in extra-sensory perception on a scale of one to six, where one is strong a strong belief in ESP and six is a strong disbelief in ESP.
Scoring. Participants who rated their belief as one or two were classed as sheep, ratings of three or four were classed as indifferent and ratings of five and six were classed as goats. The results were split into these three groups and the number of repetitions for each group was compared.
Results
It was found that all three groups underestimated the mean chance expectancy of repetitions, which for sixty-six rolls of the dice would be 10.8
The mean number of consecutive repetition for sheep was found to be 5.5, the mean for goats was 5.6 and the mean for indifferent was 5.36. The results are shown in a bar chart ( fig.1)
The standard deviation for sheep was found to be 4.45, for the goats was 3.9 and for the indifferent group was 3.8.
A t-test for an independent subjects design and a one-tailed hypothesis was carried out to test the results for significance. This found that the results were not significant at the 5%.
t (84)=0.11 p > 0.05
This results means that we reject the alternative hypothesis that sheep will be more likely to avoid repetitions than goats and accept the null hypothesis that there will be no difference between sheep and goat in repetition avoidance.
Discussion
The experiment failed to replicate Brugger’s finding that belief in ESP affects the amount of repetitions expected in a random generation of dice throws and that sheep were more likely to underestimate this than goats. It was found that there was no significant difference between sheep and goats in repetitions avoidance. This rejects the hypothesis that sheep will be more likely to avoid repetitions than goats.
There could have been improvements in the methodology of this experiment. The number of participants who were rated as sheep and as goats was not large enough, this could have been improved with a larger sample size. The experiments could have been conducted by one experimenter rather than many which would have allowed the use of a controlled environment and standardised instructions.
The experiment only looked at repetition avoidance which is only one area of differences between sheep and goat. The research by Blackmore and Troscianko (1985) indicated that the found no significant difference between repetition avoidance in sheep and goats but did find a difference in probability tasks. Further research could look into probability tasks or even devise another way of testing repetition avoidance and see if results were reliable and valid. Another area that could be improved is the way that people are judged on their belief in ESP, it may be that people are not entirely sure of the meaning of ESP or that they do not rate their belief accurately. This could be improved by devising a questionnaire that included different statements about factors that comprise ESP that could be rated separately and then an overall belief score could be obtained.
In finding the results of this experiment as not significant and accepting the null hypothesis we can assume that belief or disbelief in ESP is not the only factor that affects repetition avoidance or does not have any significant effect. Failure to replicate the sheep-goat effect could also be attributed to problems in the methodology of this experiment. Although we cannot be sure that this factors influence peoples ability to generate random number sequences.
References
Blackmore, S. and Troscianko, T. (1985). Belief in the paranormal: Probability judgements, illusory control, and the ‘chance baseline shift’. British Journal of Psychology, 76 (4), 459-468.
Brugger, P., Landis, T., and Regard, M. (1990). A ‘sheep- goat effect’ in repetition avoidance: Extra-sensory perception as an effect of subjective probability. British Journal of Psychology, 81 (4), 455-468.
French, C.C. (1992). Factors underlying belief in the paranormal: Do sheep and goats think differently? The Psychologist: Bulletin of the British Psychological Society, 5, 295-299.
Kahneman, D., Slovic, P. Tversky, A. (1982). Judgement Under Uncertainty:
Heuristics and Biases. Cambridge: Cambridge University Press