The analysis of means (ANOM) is a graphical method used to test whether the treatment means are different from grand mean as well as enables to declare exact treatment having significant mean. This technique is often used as an alternative to analysis of variance (ANOVA), for testing the significance of two or more treatment means. In practice, there might exist a linearly associated uncontrollable variable known as covariate or concomitant variable, along with the study variable. In such situations, it is important to incorporate the role of concomitant variable in our analysis, as otherwise ANOM will lead to misleading results. In this study, we have extended the ANOM in the presence of covariate named as ANOMC. It operates the same way as ANOM using adjusted means. We have investigated the effects normality, linearity, homogeneity, sample sizes (equal versus unequal), hypotheses (null vs nonnull) on ANOM and ANOMC. We have used type I error and power as performance measures. The findings reveal that ANOMC outperforms the ANOM technique under the above stated conditions. Finally, two illustrative examples are also presented using the data sets related to industry and medical.