Enhanced Analysis of Means with Multiple Covariates: A Family of Ratio-Based ANOMC Tests

Abstract
The analysis of means (ANOM) is a statistical method and visualization tool mainly used in examining the equivalence of treatment means in experiments with fixed effects. On the other hand, in real-life situations, one often needs to consider covariates that are linearly related to the main variable. However, in these instances the standard ANOM approach neglects the role of these covariates when assessing group mean equivalence. A new proposal to counteract this lack, ANOM with Covariates (ANOMC), includes a regression estimator that adjusts for one covariate. The use of the ANOMC test is not sufficient; more investigations should be conducted on its utility in experiments where there are multi-covariates involved. Therefore, in this paper, we aim to find out the performance of the ANOMC test with two auxiliary variables with a family of ratio estimators. The proposed tests are ANOMC-MR1, ANOMC-MR2, ANOMC-MR3, ANOMC-MR4, and ANOMC-MR5 and will be evaluated in terms of Type I error rate and the power of the test. In order to evaluate and compare performance, a Monte Carlo simulation was conducted. Results nearly showed that ANOMC-MR2, ANOMC-MR3, ANOMC-MR4, and ANOMC-MR5 tests had higher performance than the ANOMC-MR1 test in most covariate case studied in the experimental simulation. Additionally, the proposed ANOMC tests are implemented on biomedical and mechanical engineering datasets to show practicality to the practitioners.