In practice it is often of interest to compare the medians or means of several populations that are not assumed to have equal variances. A method is proposed that depends on the over-mean-rank function that is defined as the percentage of the ranks over the global mean rank in each group. Chi-square distribution is found to give a very good fit for this function. The main advantages for the proposed method are: stable in terms of Type I error; less affected by ties and can be shown graphically. Comparison with Kruskal-Wallis, Welch and ANOVA methods are given for unbalanced designs and not equal variances from normal and non-normal populations in terms of Type I error. The simulation results are shown that the proposed method improves the Type I error and its performance exhibits superior robustness over the studied methods.