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Abstract

The purpose of this research was to study robustness of F – test in testing means when heterogeneity of population variances and bounds of variances that make F – test still robust. Robustness is considered from type I error rates based on Bradley criterion and power of the test under requirements of sample sizes were to equal (10,10,10), (30,30,30) and (80,80,80) and unequal (5,10,15), (20,30,40) and (60,80,100) with 3 variance ratios: small, moderate and high at .05 and .01 significant levels under normal distribution. Data are simulated by using Monte Carlo simulation technique from MATLAB with 5,000 repetitions for each case. Results could be summarized as follows: 1) When sample sizes are equal and homogeneity of population variances, F – test is robust in every cases at

.05 and .01. 2) When sample sizes are equal and heterogeneity of population variances,

F – test is robust in every cases at .05 and in large sample size at .01. 3) When sample sizes are unequal and homogeneity of population variances, F – test is robust in every cases at .05 and .01. 4) When sample sizes are unequal and heterogeneity of population variances, F – test is robust in every cases at .05 and .01. 5) When sample sizes are small both equal and unequal, power of the test decreases for the variance ratio of population increases but when sample sizes are moderate and high both equal and unequal sample size the variance ratio of are increases will effect on power of the test a little at the hypothesis testing are .05 and .01 population