An Experimental Study of the Interrelationship between the Two Methods of Measuring the Sequence of Values of Subjective Inference, i.e. the Game-Method and the Guessing-Method

Abstract

The guessing-method has been widely employed to study the subjective inference of Ss who are observing a successive presentation of binary symbols. In applying the guessing-method, a sufficiently large number of Ss observing a series of symbols is asked at each presentation to predict which of the two possible symbols will occur the next time. The measure of guessing is defined as the ratio of the number of Ss who predicted the occurrence of a particular one of the two symbols to the whole number of Ss, and the value of the ratio is computed at each trial. Let F denote the guessing measure defined in this manner.
When a random series of binary symbols with a constant probability of occurrence p was used, many experiments showed that F usually started from 0.5 and gradually approached to a level fairly near p. This fact can not be ascribed simply to the Ss' probability learning as Jarvik has explained. As one of the present authors once pointed out, there is no direct correspondence between F and the mean value of Ss' intuitive probabilities, but F depends more directly on the distribution of intuitive probabilities. More precisely, F is to be interpreted as the ratio of the number of Ss whose intuitive probabilities of the occurrence of the particular symbol exceed 0.5 to the whole number of Ss, insofar as we can assume that each S predicts the occurrence of the symbol of which his intuitive probability exceeds 0.5. It can not be assumed unconditionally, however, that Ss follow such a type of response, though it may seem self-evident. One can claim the legitimacy of this assumption only when it is guaranteed, for instance, through instructions, that all the Ss have the aim to get the maximum number of correct hits, because the above type of response can be proved to be the good strategy to take for any S with the aim.
On the other hand, we can directly measure the intuitive probability by the game-method. Since the game-method provides us with the value of intuitive probability of each S, it also furnishes its distribution as well as the ratio of the number of Ss whose intuitive probabilities exceed 0.5 to the whole number of Ss. The ratio computed from the game-methgd data will be referred to as Fp. Then, as far as the above assumption holds good, F and Fp should be the same measure. Our experiments were designed for the purpose of testing this hypothesis.
Two groups of female college students were selected-one consisting of 28 Ss for the guessing experiment ; the other consisting of 58 Ss for the game experiment, among whom 29 Ss who played the role X of the game yielded the data. Since no S could be used in common for both of those experiments, we could only test whether the difference between the sample estimate of F and that of Fp was of a magnitude usually expected for two independent estimates of a population parameter.
Results are shown in Fig. 1. The x²-test established that the difference was not significant except for four trials. (Table 1) It should be tested, however, if there is any fixed tendency in the deviation between F and Fp, such as F>Fp or F<Fp, though the difference |F-Fp| may almost always be small. As long as we deal with the frequency measure defined over [0. 1], however, mere relation F>Fp or F<Fp is meaningless. We should ask whether F and Fp are on the same side of 0.5 and, further, which one of the inequalities, |F-0.5|_??_|Fp-0.5|, holds generally. The result of the non-parametric test on this matter is shown in Table 2.
Our third problem to be analysed is the the relationship between F (or Fp) and the mean value P of Ss' intuitive probabilities. Theoretically, it is expected that there should be the following relation between the population parameters P and F except for very special distributions : (1) P and F are on the same side of 0.5 and (2) the inequality |P-0.5|<|F-0.5| holds.