Effect Of Sample Sizes On The Empirical 
Power Of Some Tests Of Homogeneity Of 
Variances

Ogbonna; Chukwudi J.; Okenwe Idochi; Ifeanyichukwu Ogechukwu Sylvia

doi:https://doi.org/10.14445/22315373/IJMTT-V65I6P518

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 6 | Year 2019 | Article Id. IJMTT-V65I6P518 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I6P518

Effect Of Sample Sizes On The Empirical Power Of Some Tests Of Homogeneity Of Variances

Ogbonna, Chukwudi J., Okenwe Idochi, Ifeanyichukwu Ogechukwu Sylvia

Citation :

Ogbonna, Chukwudi J., Okenwe Idochi, Ifeanyichukwu Ogechukwu Sylvia, "Effect Of Sample Sizes On The Empirical Power Of Some Tests Of Homogeneity Of Variances," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 6, pp. 119-134, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I6P518

Abstract

This study compares the effect of sample sizes on the empirical power of some homogeneity of variance tests that have been proposed to assess the homogeneity of within-group variances, prior to ANOVA. The Tests of Homogeneity of Variance (THV) compared are: Bartlett (1937), Levene (1960), Cochran (1941) and Hartley Fmax (1950) tests. Homogeneity of variances occurs when variances are equal across groups. Homogeneity of variance testing is a statistical method designed to provide evidence that groups are comparable by demonstrating that the variations found between groups are small enough that they are considered practically insignificant.Few recommendations exist regarding the appropriate use of these tests under varying data conditions. Monte Carlo simulation methods were used to generate data to examine and compare the power rates of the tests under conditions of equal and unequal sample sizes when the underlying distribution is normal 1,000 times through the use of R software. It was found that Hartley Fmax test performs best (highest power) when the sample sizes are equal, while, Cochran test has the worst performance. Generally, when the sample sizes are both equal and unequal, Levene test has the highest power followed by Bartlett test, hence, Bartlett and Levene tests will be recommended for both equal and unequal sample sizes since they give higher power (above 0.8).Thus it is important for researchers to conduct an initial analysis of the data in order to determine the distribution of the population and is also advised to pay attention to the amount of sample size required to obtain a powerful test.

Keywords

Tests of Homogeneity of Variance, Empirical Power, Cochran Test, Levene Test, Hartley Fmax Test

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