Exact finite-sample significance and confidence regions for goodness-of-fit statistics in one-way multinomials.
As multinomial processing tree models become more popular in psychology, appropriate methods for statistical inference also become more necessary. Conventional methods are all based on the asymptotic chi-square approximation to the exact multinomial test, but the accuracy of this approximation has been shown to be poor in the usual small-sample situation. This paper describes an efficient algorithm that allows the exact multinomial test to be applied without incurring prohibitive computational costs. The algorithm is well suited to addressing three different aspects of statistical inference in one-way multinomials: (i) evaluating the exact significance of a multinomial test; (ii) determining significance at a given preset level; and (iii) enumerating exact confidence regions. Examples are given that illustrate how this algorithm accomplishes each of these tasks, and an analysis of its computational cost in some small-sample situations is also provided.
García-Pérez
M A
MA
Departamento de Metodología, Facultad de Psicología, Universidad Complutense, Madrid, Spain. miguel@psi.ucm.es
D000465:Algorithms; D006801:Humans; D008960:Models, Psychological