Some Distribution Theory Related to the Analysis of Subjective Performance in Inferential Tasks

When inferences made by a subject differ from normative statistical inferences it is possible to define measures of this divergence which throw considerable light on the nature of the deficiencies in the subjective performance. These measures involve quantifying differences between distributions. For the analysis of a single subject performing a single task the paper generalizes previous work by replacing absolute measures by more meaningful relative measures and by extending the scope of the inferential tasks involved. For a single subject performing many tasks and for groups of different subjects statistical analysis requires a rich parametric class of distributions to describe patterns of variability of probabilistic data, and the use of logistic-normal distributions is advocated for this purpose. Simple illustrations are provided of the main analytical techniques.

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