A "rationalized" arcsine transform.

Abstract

Arcsine or angular transformations have been used for many years to transform proportions to make them more suitable for statistical analysis. A problem with such transformations is that the arcsines do not bear any obvious relationship to the original proportions. For this reason, results expressed in arcsine units are difficult to interpret. In this paper a simple linear transformation of the arcsine transform is suggested. This transformation produces values that are numerically close to the original percentage values over most of the percentage range while retaining all of the desirable statistical properties of the arcsine transform.