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All Journal East Asian Journal of Multidisciplinary Research (EAJMR)
Egburonu O. D
Centre for Critical Thinking and Research, CLAPAI Orphanage High School, Jos, Nigeria
Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Industrial & Manufacturing Engineering

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On The Use of Analysis of Variance under Unequal group variances Adekunle Omotayo Abidoye; Egburonu O. D
East Asian Journal of Multidisciplinary Research Vol. 2 No. 3 (2023): March 2023
Publisher : PT FORMOSA CENDEKIA GLOBAL

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55927/eajmr.v2i3.3374

Abstract

In this study, we imposed Analysis of variances test (ANOVA) which use when we have more than two treatments or different levels of a single factors that we wish to compare then we assume homogeneity of variances across the groups being compared although most of the earlier works that have addressed the problem of testing equality of mean variance overestimates the appropriate variance and the test statistic becomes conservative. This is the well-known Behrens – Fisher problem. Then we are interested in comparing several treatments means in this work, we made use the analysis of variance under unequal variances when the groups variances differ. It will be very inappropriate to use the pooled sample variance as a single value for the variances, instead the sample harmonic mean of variances is proposed as an alternative to the pooled sample variance when there is heterogeneity of variances. The distribution theoretically and confirmed using simulation studies and this proposed harmonic mean of variance was , examined in this work and found useful for unequal variances. Data set from Kwara State Ministry of Health on the incidence of diabetes diseases for male patients was used to illustrate the relevance of our proposed test statistic.
Application of Minimum Bayes Factor to a Balanced Two-Way Anova with Random Effects Adekunle Omotayo Abidoye; Adewara A.A; Popoola J; Egburonu O. D
East Asian Journal of Multidisciplinary Research Vol. 2 No. 3 (2023): March 2023
Publisher : PT FORMOSA CENDEKIA GLOBAL

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55927/eajmr.v2i3.3375

Abstract

It is a common practice in statistical analysis to draw conclusions based on significance. P-values often reflect the probability of incorrectly concluding that a null hypothesized model is true; they do not provide information about other types of error that are also important for interpreting statistical results. Standard model selection criteria and test procedures are often inappropriate for comparing models with different numbers of random effects, due to constraints on the parameter space of the variance components. In this paper, we focused on a minimum Bayes factor proposed by Held and Ott (2018) and applied it to a balanced two way analysis of variance (ANOVA) with random effects under three cases namely: Case 1: both factors are fixed; Case 2: both factors are random; Case 3: factor A is fixed and factor B is random. We realized that in all the three cases, considered the Bayes factor indicates weak evidence against the null hypothesis of zero variability in the effects of the levels of the factors as well as the interactions. This result is due to the conservative nature of the minimum Bayes factor.
Co-Authors Adekunle Omotayo Abidoye Adewara A.A Popoola J