It has been shown that the generalized F-statistics can give satisfactory performances in identifying differentially expressed genes with microarray data. However, for some complex diseases, it is still possible to identify a high proportion of false positives because of the modest differential expressions of disease related genes and the systematic noises of microarrays. The main purpose of this study is to develop statistical methods for Affymetrix microarray gene expression data so that the impact on false positives from non-expressed genes can be reduced. I proposed two novel generalized F-statistics for identifying differentially expressed genes and a novel approach for estimating adjusting factors. The proposed statistical methods systematically combine filtering of non-expressed genes and identification of differentially expressed genes. For comparison, the discussed statistical methods were applied to an experimental data set for a type 2 diabetes study. In both two- and three-sample analyses, the proposed statistics showed improvement on the control of false positives.