Intuitive statistical inference: How pigeons categorize binomial samples

Abstract

Pigeons categorized binomial samples produced by two complementary random processes. Samples were 1, 2, 4, or 8 successively presented outcomes (vertical or horizontal lines) of, in effect, tossing one of two equally likely coins. One coin (A) was biased in favor of vertical, and the other coin (B) was similarly biased in favor of horizontal. Choosing red or green stimuli presented after each sample was reinforced with food if coin A or coin B had been tossed, respectively. In that sense, choosing red or green was logically analogous to inferring that the statistical evidence reflected tossing of coin A or coin B, respectively. The statistical diagnosticity of a sample, the relative likelihood of its having been produced by a particular coin, equaled, except for sampling fluctuation, the relative frequency of reinforcement of a particular color given that sample, and was experimentally varied by the bias on the coins and by sample size. All the variables that affect optimal, formal inference about binomial samples also affected intuitive inference. But inferences were very suboptimal: “undermatching” was obtained in part due to control of categorization by the sequential structure of binomial samples. These results reveal limitations of optimality theories for animal decision making in the face of uncertainty when observations in samples are presented successively. On the other hand, they are generally compatible with molecular analyses of instrumental learning which assign an important role to the local temporal organization of events preceding reinforcement. Most generally, they show that maladaptive control over intuitive statistical inference by a variable upon which optimal performance does not depend is neither a uniquely human phenomenon nor dependent upon linguistic strategies.