A Table of Values for the Freeman-Tukey Square-Root Transformation
Gerald M. Meredith, Connie G. W. Wong · Perceptual and Motor Skills · 1961
The presence of heterogeneity of variance in a set of data frequently necessitates a transformation of the raw scores. This is particularly illustrated when raw data are counts of rhe number of events occurring in a fixed exposure ( in space or time or both). Such distributions usually follow a Poisson distribution, and the best variance-stabilizing transformation is dx+ dx+ 1, where x is the observed count (Freeman & Tukey, 1950). The variance of Poisson data so transformed is approximately unity. Mosceller and Bush ( 1954) have presented a table for chis transformation for x berween 0 and 50. The purpose of the present table is to provide a rapid means of obtaining the Freeman-Tukey square-root cransformation for all integers between 0 and 1000. The observed count is x and the transformed values are d< + x + 1. The squares of the transformed values are also given for use in analysis of variance computations.