Data Transformation (statistics) - Variance Stabilizing Transformations

Variance Stabilizing Transformations

Many types of statistical data exhibit a "mean/variance relationship", meaning that the variability is different for data values with different expected values. As an example, in many parts of the world incomes follow an increasing mean/variance relationship. If we consider a number of small area units (e.g., counties in the United States) and obtain the mean and variance of incomes within each county, it is common that the counties with higher mean income also have higher variances.

A variance-stabilizing transformation aims to remove a mean/variance relationship, so that the variance becomes constant relative to the mean. Examples of variance-stabilizing transformations are the Fisher transformation for the sample correlation coefficient, the square root transformation or Anscombe transform for Poisson data (count data), the Box-Cox transformation for regression analysis and the arcsine square root transformation or angular transformation for proportions (binomial data).