Massimiliano Pastore

Analysis of variance for binomial data. Is really necessary arcsine transformation?

  • Abstract

Informations and abstract

Keywords: ANOVA, Generalized Linear Models, Arcsine transformation

The arcsine transformation is typically applied in ANOVA context when data are proportions (for example the number of correct answers in dichotomous items). In order to assess whether this transformation is really necessary, a Monte Carlo experiment was performed with a fixed number of conditions in which each subject is assigned to a condition and required to respond to a set of items. Three ANOVA models were considered with three different dependent variables: the number of correct responses, the proportion of correct responses and the arcsine transformed proportion of correct responses. The number of correct responses was further analyzed by means of a Generalized Linear Model (GLM). The results showed that arcsine transformation does not increase control of Type I error. Furthermore, power rates were lower than for both non transformed proportions and number of correct responses analyzed by means of GLM.

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