PURPOSE:In judgment and decision-making, people distort the probability or relative-frequency information in a stereotyped way: They overestimate small probabilities and underestimate large probabilities. Here we used a visual judgment task to investigate whether and how the distortion of relative-frequency may be influenced by the environmental statistics.
METHODS:The task was to report the relative-frequency of black (or white) dots in an array of black and white dots on a continuous scale from 0 to 1. In 693 trials, the values of the stimuli ranged from 0.01 to 0.99 with four possible distributions: the uniform distribution (“Uniform”), 50/99 of the relative-frequencies no larger than 0.1 (“Low”), 50/99 no less than 0.9 (“High”), or 30/99 low and 30/99 high (“Extreme”). Sixteen subjects were assigned to each condition. We performed two lines of analyses. First, we applied a smoothing algorithm to the deviation of the reported to the objective relative-frequency, obtaining a continuous function of how the deviation varied with the objective relative-frequency (“distortion function”). Second, we modeled the dependence of the present response on the stimuli and responses 1 to 5 trials back.
RESULTS: (1) The distortion functions had the shape of one sinusoid cycle, i.e. the typical pattern of overestimating small and underestimating large relative-frequencies. (2) Compared with the Uniform, the Low and Extreme conditions had a greater overestimation of small relative-frequencies, while the High and Extreme conditions had a greater underestimation of large relative-frequencies. That is, a higher concentration of the stimuli at the low or high end would be diluted in the responses, which agrees with Parducci’s (1965) range-frequency model. (3) A model based on non-linear sequential effects outperformed the range-frequency model in fitting subjects’ responses.
CONCLUSIONS: Human judgment of relative frequency adapts to the environmental statistics. The adaptation is the result of non-linear sequential effects.