In terms of the size and power of tests, the classical small sample F-statistic for testing the equality of means of k normal populations is sensitive to outliers. This paper suggests robust alternatives based on four M-estimators that are numerically standardized by similar levels of break-points, gross error sensitivities and similar rejection points. A Monte Carlo study for the case of three means (i.e., k=3) is conducted. The sizes and powers based on these estimates were computed using pure and contaminated samples. An empirical comparison of sizes and powers demonstrates that the performance of the robust test-statistic is better.