Analysis of means approach in advanced designs

Analysis of means (ANOM), similar to Shewhart control chart that exhibits individual mean effects on a graphical display, is an attractive alternative mean testing procedure for the analysis of variance (ANOVA). The procedure is primarily used to analyze experimental data from designs with only fixed effects. Recently introduced, the ANOM procedure based on the q-distribution (ANOMQ procedure) generalizes the ANOM approach to random effects models. This article reveals that the application of ANOM and ANOMQ procedures in advanced designs such as hierarchically nested and split-plot designs with fixed, random, and mixed effects enhances the data visualization aspect in graphical testing. Data from two real-world experiments are used to illustrate the proposed procedure; furthermore, these experiments exhibit the ANOM procedures' visualization ability compared with ANOVA from the point of view of the practitioner.