To test null hypothesis against umbrella alternative for scale parameters, a test statistic W-h based on a scale estimator is proposed in . In this study, W-h statistics based on different estimators of scale parameters are compared according to type I error, alpha, and power. For the nominal alpha=0.05 and given values of peak of umbrella, number of populations and sample sizes, the results are obtained using the data is generated from two-parameter exponential and normal distributions in simulation design. According to the simulation results, when the data generated from normal distribution, the power values of test statistics based on robust scale estimators are almost the same to the ones based on maximum likelihood estimator of scale parameters as the sample sizes increase. Moreover, the similar results are obtained when the data is generated from the two-parameter exponential distribution.