Étude comparative de trois fonctions de transformation d'une proportion (Anscombe, 1948 -- Freeman-Tukey, 1950 -- Chanter 1975)

Abstract

This essay on proportions explores the statistical properties of three normalizing functions of a proportion based on Fisher's arcsine transformation (Anscombe, 1948; Freeman and Tukey, 1950; Chanter, 1975), namely their bias, variance and precision, quasi-normality. The use of these functions in statistical testing procedures is exemplified for the case of one proportion versus a given parametric value and that of the difference between two proportions, with a check on the procedures' accuracy and power. Conventional test procedures as well as exact calculation solutions are provided for comparison. An abundant graphic file accompanies the article, thanks to which the reader can make his own idea on the arguments and demonstrations here proposed.

Keywords

• proportions
• transformation arcsinus
• propriétés statistiques
• test sur une proportion
• test de différence entre deux proportions