To test null hypothesis against umbrella alternative for scale parameters,  statistic based on scale estimator is proposed in [1]. In this study,  statistics based on different estimators of scale parameters are compared according to type I error ,  , and power. For  and given values of   , , , the results are obtained using the data is generated from exponential and normal distributions in simulation design. According to the simulation results, when the data generated from normal distribution, the power value of test statistics based on robust estimators is almost same to the ones based on parametric estimator as the sample size increases. Moreover, similar results are obtained when the data is generated from exponential distribution.