Figure 32.13 shows the transformations that are available when you select from the 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 
Parameter 
New Variable 
Equation 
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 

loglinear hybrid(Y;a) 

LogLin_Y 
See text. 
The loglinear hybrid transformation is defined for as follows:
The function is linear for , logarithmic for , and continuously differentiable.
The generalized log and the loglinear hybrid transformations were introduced in the context of geneexpression microarray data by Rocke and Durbin (2003).