The purpose of this paper is to compare Analysis of Variance with Contingency Table Analysis when the data being analyzed do not satisfy Analysis of Variance assumptions. The criteria for comparison are the powers of the Standard variance-ratio and the Chi-square test. The test statistic and powers were obtained by Monte Carlo. 1. Calculate test statistic for each of 100 trials, this process was repeated 12 times. Each time different combination of means and variances were used. 2. Powers were obtained for each of 12 combinations of means and variances. Whether Analysis of Variance or Contingency Table Analysis is a better alternative depends on if we are interested in equality of population means or differences of population variances.