Abstract
The concept of assumption adequacy averaging is introduced as a technique to develop more robust methods that incorporate assessments of assumption adequacy into the analysis. The concept is illustrated by using it to develop a method that averages results from the t-test and nonparametric rank-sum test with weights obtained from using the Shapiro-Wilk test to test the assumption of normality. Through this averaging process, the proposed method is able to rely more heavily on the statistical test that the data suggests is superior for each individual gene. Subsequently, this method developed by assumption adequacy averaging outperforms its two component methods (the t-test and rank-sum test) in a series of traditional and bootstrap-based simulation studies. The proposed method showed greater concordance in gene selection across two studies of gene expression in acute myeloid leukemia than did the t-test or rank-sum test. An R routine to implement the method is available upon request.