Transformations

Abstract

The transformation of data takes on great importance in statistical analysis, especially as one wishes to apply inferential procedures which are highly sensitive to deviations from their underlying assumptions to the data. In this chapter we discuss a number of such transformations, each focusing on a different ill. In Section 1 we describe the Glejser suggestions for searching for a deflator to apply to a regression equation, i.e., to each of the variables in the regression (including the constant), which will rid the regression residuals of their heteroscedasticity. In Section 2 we discuss the variance stabilizing transformation, a transformation procedure which produces a random variable whose variance is functionally independent of its expected value. Section 3 describes the Box—Cox transformations, power transformations which best transform data to normality. Section 4 is an exposition of Tukey’s “letter values” and “box plots”, which provide a quick graphic way of finding the appropriate power transformation. In Section 5, we describe the Box—Tidwell procedures for systematically determining the appropriate power transformation of an independent variable in a regression.

“The simple family often does quite well in transforming to normality!”

Tukey [1957]