Consequences of Assumption Violations Revisited: A Quantitative Review of Alternatives to the One-Way Analysis of Variance "F" Test

Environmental influence on urban rodent bait consumption

“…Considering that, in accordance with McDonald (2009), the samples were large enough to ensure that the means of those samples were approximately normally distributed, and that several simulation studies, using a variety of nonnormal distributions have clearly tested that both the t-test and the ANOVA are very robust to several kinds of deviations from normality (Boneau 1960;Glass et al 1972;Harwell et al 1992;Lix et al 1996), before the proceeding of the t-test and the ANOVA, only the homogeneity of variances was verified by means of the Levene's test. Subsequently, percentages of bait consumption were dichotomized for the multiple logistic regression: value equal to 1 was assigned when there was bait consumption and value equal to 0 otherwise.…”

Effects of brain mechanical properties on child head responses under linear load

“…However, an ANOVA method is not very sensitive to moderate deviations from normality. Simulation studies, using a variety of nonnormal distributions, have shown that the false positive rate is not affected very much by this violation of the assumption [19][20][21]. This is another result of the central limit theorem, which says that when you take a large number of random samples from a population, the means of those samples are approximately normally distributed even when the population is not normal.…”

Application of Robust Statistical Methods for Sensitivity Analysis of Health-Related Quality of Life Outcomes

“…These include approximate degrees of freedom test statistics which do not assume equality of variances, permutation tests, nonparametric tests based on rank scores, parametric tests applied to transformed data, and parametric tests applied to robust estimators. Theoretical and empirical methods have demonstrated that no single method or test procedure is best under all circumstances -the choice of one procedure over competing alternatives is a function of the distribution of the data, group sizes, magnitude of variance heterogeneity, and the hypothesis of interest [4].…”

“…One approach is to adopt either a non-parametric procedure based on rank scores or a rank transform test in which a parametric procedure is applied to rank scores. A limitation of the former is that nonparametric procedures are sensitive to the presence of heterogeneous variances because they test equality of distributions as opposed to equality of means [4]. Only when the population distributions are equivalent will the two procedures test approximately the same hypothesis [5].…”