The use of transformations.

1. Theoretical Discussion. The purpose of this note is to summarize the transformations which have been used on raw statistical data, with particular reference to analysis of variance. For any such analysis the usual purpose of the transformation is to change the scale of the measurements in order to make the analysis more valid. Thus the conditions required for assessing accuracy in the ordinary unweighted analysis of variance include the important one of a constant residual or error variance, and if the variance tends to change with the mean level of the measurements, the variance will only be stabilized by a suitable change of scale. If the form of the change of variance with mean level is known, this determines the type of transformation to use. Suppose we write