Consequences of Failure to Meet Assumptions Underlying the Fixed Effects Analyses of Variance and Covariance

Glass, Gene V.; Peckham, Percy D.; Sanders, James R.

doi:10.2307/1169991

Cited by 171 publications

(186 citation statements)

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“…Violations of the HOV assumption will cause the nominal Type I error rates to be inflated or deflated, depending on the combinations of the unequal sample sizes and unequal variances. This phenomenon was demonstrated in this study and by numerous other researchers (e.g., Boneau, 1960;Glass et al, 1972).…”

Section: Discussionsupporting

confidence: 87%

“…For example, a researcher may want to know if the number of words recalled from a list differs depending on the nature of the lists (e.g., happy, sad, or neutral words). It is widely known that the ANOVA F test is biased when the assumptions of normality, homogeneity of variance (HOV), or independence of errors are violated (Choi, 2005;Cochran, 1947;Cribbie, Fiksenbaum, Wilcox, & Keselman, 2012;Glass, Peckham, & Sanders, 1972;Hoekstra, Kiers, & Johnson, 2012;Olsen, 2003). In this paper, we explore the HOV assumption of the ANOVA F test.…”

Section: Introductionmentioning

confidence: 99%

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ANOVA and the variance homogeneity assumption: Exploring a better gatekeeper

Kim

Cribbie

2017

Brit J Math & Statis

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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.

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Section: Discussionsupporting

confidence: 87%

Section: Introductionmentioning

confidence: 99%

ANOVA and the variance homogeneity assumption: Exploring a better gatekeeper

Kim

Cribbie

2017

Brit J Math & Statis

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“…Data were also subjected to analysis of variance (SAS 1999), and the Shapiro-Wilk test was performed to test for normality (Shapiro and Wilk 1965). In cases where deviations from normality were due to kurtosis and not skewness, the data were accepted as reliable and the results were interpreted without transformation (Glass et al 1972). The Student's t-Least Significant Difference was calculated at the 5% confidence level to compare treatment means.…”

Section: Pathogenicity Assaysmentioning

confidence: 99%

Characterization of fungi (Fusarium and Rhizoctonia) and oomycetes (Phytophthora and Pythium) associated with apple orchards in South Africa

et al. 2011

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“…Data were also subjected to analysis of variance (SAS 1999), and the Shapiro-Wilk test was performed to test for normality (Shapiro and Wilk 1965). In cases where deviations from normality were due to kurtosis and not skewness, the data was accepted as reliable and the results were interpreted without transformation (Glass et al 1972). The student's t-Least Significant Difference was calculated at the 5% confidence level to compare treatment means.…”

Section: Pathogenicity Assaysmentioning

confidence: 99%

Cylindrocarpon species associated with apple tree roots in South Africa and their quantification using real-time PCR

et al. 2010

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Cylindrocarpon species are known to be a component of the pathogen/pest complex that incites apple replant disease. In South Africa, no information is available on apple associated Cylindrocarpon species and their pathogenicity. Therefore, these aspects were investigated. Among the isolates recovered from apple roots in South Africa, four species (C. destructans, C. liriodendri, C. macrodidymum and C. pauciseptatum) were identified using β-tubulin gene sequencing and phylogenetic analysis. This is the first report of C. liriodendri, C. macrodidymum and C. pauciseptatum on apple trees. Cylindrocarpon macrodidymum was the most prevalent. Isolates within each of the four species were pathogenic towards apple seedlings, but varied in their virulence. With a single exception, all isolates were able to induce lesion development on seedling roots. Only 57% of the isolates, which represented all four species, were able to cause a significant reduction in seedling weight and/or height. The greatest seedling growth reductions were caused by two isolates of C. destructans, and one isolate each of C. liriodendri and C. macrodidymum. A quantitative real-time polymerase chain reaction (qPCR) method was developed for simultaneous detection of all four Cylindrocarpon species. qPCR analyses of Cylindrocarpon from the roots of inoculated seedlings showed that the amount of Cylindrocarpon DNA in roots was not correlated to seedling growth reductions (weight and height) or root rot. The qPCR method is, however, very useful for the rapid identification of apple associated Cylindrocarpon species in roots. The technique may also hold potential for being indicative of Cylindrocarpon disease potential if rhizosphere soil rather than roots are used.

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Consequences of Failure to Meet Assumptions Underlying the Fixed Effects Analyses of Variance and Covariance

Cited by 171 publications

References 0 publications

ANOVA and the variance homogeneity assumption: Exploring a better gatekeeper

ANOVA and the variance homogeneity assumption: Exploring a better gatekeeper

Characterization of fungi (Fusarium and Rhizoctonia) and oomycetes (Phytophthora and Pythium) associated with apple orchards in South Africa

Cylindrocarpon species associated with apple tree roots in South Africa and their quantification using real-time PCR

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