# Impact of Homogeneity of Variances Violation in Single Factor Components of Variance Model when Sampling from Finite Population

### Abstract

This study aims to appraise the impact of heteroscedasticity on a single factor component of variance model when random effects are sampled from a finite population. Ten thousand data sets in each scenario of difference levels of variances, sample sizes per factor levels, choices of distributions, nominal α-levels, population sizes of random effects (*N*) and number of factor levels (*k*) are simulated to perform the assessment of the F-statistic in the one-way ANOVA via the type I error rate and power. Results show that when the null hypothesis is true, the F-test can generally keep the nominal α of 0.05 even though the homogeneity of variances is not satisfied. In contrast, for α = 0.01, its performance is very bad. Further, heterogeneity of variances still be a problem in the ANOVA for both terms, i.e., type I error rate and power even in medium heterogeneity cases. The power in the finite population situations is always greater than that of the standard F-test used in case of the infinite population under heteroscedasticity. Therefore, if the sampling fraction (*k*/*N*) exceeds 5 percent, a large value of the type II error rate is presented. Under this condition, one should avoid using the ordinary F-test in a single factor ANOVA.

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