ANOVA and the variance homogeneity assumption: Exploring a better gatekeeper

Abstract

Valid use of the traditional independent samples ANOVA procedure requires that the population variances are equal. Previous research has investigated whether variance homogeneity tests, such as Levene's test, are satisfactory as gatekeepers for identifying when to use or not to use the ANOVA procedure. This research focuses on a novel homogeneity of variance test that incorporates an equivalence testing approach. Instead of testing the null hypothesis that the variances are equal against an alternative hypothesis that the variances are not equal, the equivalence-based test evaluates the null hypothesis that the difference in the variances falls outside or on the border of a predetermined interval against an alternative hypothesis that the difference in the variances falls within the predetermined interval. Thus, with the equivalence-based procedure, the alternative hypothesis is aligned with the research hypothesis (variance equality). A simulation study demonstrated that the equivalence-based test of population variance homogeneity is a better gatekeeper for the ANOVA than traditional homogeneity of variance tests.

Accuracy of different digital scanning techniques and scan bodies for complete-arch implant-supported prostheses

“…Precision was defined as the degree of variance within groups of scans, whereas trueness was defined as the amount of average distance and average angular deviation between the corresponding scan bodies in the test scan and the MRM. In terms of precision, 4 tests (Levene, O'Brien, Brown and Forsythe, and Bartlett) 34 were used to evaluate the homogeneity of the variances among the scan body and technique subgroups. The overall reliability of the study method was evaluated by using intraclass correlation according to Shrout and Fleiss.…”

The gamma generalized linear model, log transformation, and the robust Yuen-Welch test for analyzing group means with skewed and heteroscedastic data

“…As sample size increases, these tests have increased power for detecting even minute departures, though researchers may consider such departures less consequential. Even if formal tests are used in practice, stringency could be imposed with a more logically-aligned equivalence test, such as one for detecting evidence of homoscedasticity (Kim and Cribbie 2017;Mara and Cribbie 2017) or with conservative alpha levels (Schucany and Ng 2006). In practice, we recommend neither reliance on assumptions tests nor conditional approaches for method selection.…”

lncRNA Mediated Hijacking of T-cell Hypoxia Response Pathway byMycobacterium tuberculosisPredicts Latent to Active Progression in Humans

“…4). ANOVA was applied across all the samples (both class wise and sample wise) for calculation of differentially expressed elements [27]. For higher confidence false discovery rate (FDR) cut-off of <0.01 was applied.…”

“…ANOVA was applied on three classes ("Mtb Infected", "Ag85 Stimulated", and "ESAT Stimulated"), with all the 340 samples with the false discovery rate (FDR) of <0.01 26 . Differential expression analysis for lncRNA is done using lncDIFF, as the lncRNAs show very low expression as compared to mRNA 27 .…”

“…Differential expression analysis for lncRNA is done using lncDIFF, as the lncRNAs show very low expression as compared to mRNA 27 . Similarly, ANOVA was applied on all the 340 samples of mRNA with three classes with the FDR cut-off of <0.0.1 26 . Differentially expressed genes were calculated using EdgeR 28 .…”