We introduce a model for measurement error in gene expression arrays as a function of the expression level. This model, together with analysis methods, data transformations, and weighting, allows much more precise comparisons of gene expression, and provides guidance for analysis of background, determination of confidence intervals, and preprocessing data for multivariate analysis.

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.

We demonstrate that the started-log and the log-linear-hybrid transformation families can produce approximate variance stabilizing transformations for microarray data that are nearly as good as the generalized logarithm (glog) transformation. These transformations may be more convenient in some applications.

R and Matlab code and test data are available from the authors on request.

We introduce a transformation within the generalized-log family which stabilizes, to the first order, the variance of the difference of transformed observations. We also introduce transformations from the 'started-log' and log-linear-hybrid families which provide good approximate variance stabilization of differences. Examples using control-control data show that any of these transformations may provide sufficient variance stabilization for practical applications, and all perform well compared to log ratios.