A graphical alternative for multiple group comparisons in analysis of covariance

Analysis of means (ANOM) is a graphical alternative for the analysis of variance (ANOVA) that was primarily developed for multiple mean comparisons. The ANOM is a simple graphical display that provides a visualization of statistically significant results and it allows validating their practical significance without deep statistics knowledge. The classical ANOM has been developed to analyze fixed mean effects, and its recent developments allow testing random and mixed effects. On the other hand, analysis of covariance (ANCOVA) is an extension of ANOVA that applies to test means in the presence of uncontrollable concomitant/nuisance variables. To effectively communicate the statistical findings from ANCOVA to a general audience on some public interest issue areas such as COVID-19, visualization of statistically significant results is a practical approach. This paper provides a graphical alternative for multiple group comparisons in ANCOVA as an extension of the ANOM. The proposed graphical alternative is validated and compared with the ANCOVA using a Monte Carlo simulation study. The simulation results indicated that the proposed method stands strong for practical ANCOVA problems. In addition, a COVID-19 application and two additional applications related to toxicology and business are used to exhibit the value of the proposed graphical procedure in practice.