Effects of diagnosticity and prior odds on conservatism in a bookbag-and-pokerchip situation

Abstract

This bookbag-and-pokerchip experiment examined effects of prior odds (Ω 0), bag composition ( p r ), sample size ( r+ b), and the difference between red and blue chips in the sample ( r− b), on the deviation of the actual behavior from the prediction of Bayes' theorem. The responses of the Ss were transformed in such a way that if the Ss estimated as predicted by Bayes' theorem, their responses would equal 0.50. On these transformed responses — ψ ( T) — an analysis of variance was performed and the proportion of variance caused by each source was estimated. The results show (1) that the proportion of variance due to the Ss is small; (2) that ( r+ b) did not account for any variance; (3) that approximately 80 % of the variance can be ascribed to the sources ( r− b) and p r ×( r− b); (4) that the departure from the prediction, considered as conservatism, can be fitted well by log Φ( T)= A+ B( r− b), where Φ(T)= (ψ(T)) (1−ψ(T)) ; (5) that A is a function of Ω 0 and B a function of p r . It is suggested that the frequently found influence of ( r+ b) on the amount of conservatism is in fact a result of ( r− b). The results seem to support the misperception hypothesis and are incompatible with the misaggregation hypothesis and the response bias hypothesis.