Detecting Relative Changes in Multiple Comparisons with an Overall Mean

Analysis of means (ANOM) is a procedure used for comparisons with the overall mean by taking the correlations between the comparisons into account. This procedure can be used, for example, in statistical process control to improve product quality. Our interest is to devise inference procedures when the aim is to detect percentage changes from the overall mean in a normal one-way layout. Like ANOM, the results can be presented graphically. Moreover, adjusted p-values and simultaneous confidence intervals for ratios to the overall mean can be constructed. Because ratio parameters are dimensionless, we demonstrate advantages of the proposed approach using examples for comparing several mutants using equal and unequal relative thresholds and for obtaining a set of comparable simultaneous confidence intervals in multiple endpoints.