A variance-stabilizing transformation for gene-expression microarray data

Standard statistical techniques often assume that data are normally distributed, with constant variance not depending on the mean of the data. Data that violate these assumptions can often be brought in line with the assumptions by application of a transformation. Gene-expression microarray data have a complicated error structure, with a variance that changes with the mean in a non-linear fashion. Log transformations, which are often applied to microarray data, can inflate the variance of observations near background.

We introduce a transformation that stabilizes the variance of microarray data across the full range of expression. Simulation studies also suggest that this transformation approximately symmetrizes microarray data.