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

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Published: Apr 23, 2019
DOI: https://doi.org/10.14456/sehs.2019.4
Keywords:
ANOVA finite population heteroscedasticity Monte Carlo simulation variance components

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Teerawat Simmachan
Faculty of Science and Technology, Thammasat University, Thailand. Corresponding author's e-mail: [email protected]

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 (ti) 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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How to Cite
Simmachan, T. (2019). Impact of homogeneity of variances violation in single factor components of variance model when sampling from finite population. Science, Engineering and Health Studies, 13(1), 29–37. https://doi.org/10.14456/sehs.2019.4
Issue
Volume 13, Number 1 (January - April), 2019
Section
Research Articles

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