# Variable Transformations

## Variance Stabilizing Transformations

Figure 32.13 shows the transformations that are available when you select Variance stabilizing from the Family list. Variance stabilizing transformations are often used to transform a variable whose variance depends on the value of the variable. For example, the variability of a variable Y might increase as Y increases. Equations for these transformations are given in Table 32.3.

Figure 32.13: Variance Stabilizing Transformations

Table 32.3: Description of Variance Stabilizing Transformations

 Default Name of Transformation log(Y+a) Log_Y log10(Y+a) Log10_Y sqrt(Y+a) Sqrt_Y 1 / Y Inv_Y arcsinh(Y) Arcsinh_Y generalized log(Y;a) GLog_Y log-linear hybrid(Y;a) LogLin_Y See text.

The log-linear hybrid transformation is defined for as follows:

The function is linear for , logarithmic for , and continuously differentiable.

The generalized log and the log-linear hybrid transformations were introduced in the context of gene-expression microarray data by Rocke and Durbin (2003).