# Impact of homogeneity of variances violation in single factor components of variance model when sampling from finite population

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## Abstract

This study aims to appraise the impact of heteroscedasticity in a single factor component of variance model when random effects are sampled from a finite population. Monte Carlo simulation was conducted to evaluate the performance of the F**-**statistic in the one**-**way ANOVA via the type I error rate and power. Results suggest that when the null hypothesis is true, the F*-*test can generally keep the nominal α of 0.05 even the homogeneity of variances is not satisfied, whereas the empirical type I error rates are far from α = 0.01. Further, the heterogeneity of variances is still a problem in the ANOVA for both terms, i.e., the type I error rate and power even for medium heterogeneity cases. The finite F**-**test always has greater power than the usual F**-**test in case in which the heteroscedasticity is presented and the random effects (*t** _{i}*) are sampled from a finite population. This suggests that a large value of a type II error rate may arise when the sampling fraction (

*k*/

*N*) exceeds five percent. Under this condition, one should avoid use of the ordinary F-test in a single factor ANOVA.

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