The impact of sample non‐normality on ANOVA and alternative methods

Abstract

In this journal, Zimmerman (2004, 2011) has discussed preliminary tests that researchers often use to choose an appropriate method for comparing locations when the assumption of normality is doubtful. The conceptual problem with this approach is that such a two-stage process makes both the power and the significance of the entire procedure uncertain, as type I and type II errors are possible at both stages. A type I error at the first stage, for example, will obviously increase the probability of a type II error at the second stage. Based on the idea of Schmider et al. (2010), which proposes that simulated sets of sample data be ranked with respect to their degree of normality, this paper investigates the relationship between population non-normality and sample non-normality with respect to the performance of the ANOVA, Brown-Forsythe test, Welch test, and Kruskal-Wallis test when used with different distributions, sample sizes, and effect sizes. The overall conclusion is that the Kruskal-Wallis test is considerably less sensitive to the degree of sample normality when populations are distinctly non-normal and should therefore be the primary tool used to compare locations when it is known that populations are not at least approximately normal.

The identity of belowground herbivores, not herbivore diversity, mediates impacts on plant productivity

“…This allowed us to determine whether wireworms impacted plant productivity across all levels of composition and diversity. We then used non-parametric Kruskal-Wallis tests31, followed by posthoc Dunn’s tests, to assess whether wireworm richness (1, 2, or 3 species) impacted each plant productivity metric except seed viability. To analyze impacts of wireworm presence and biodiversity on seed viability we used logistic regression models, where seed germination (yes or no) was the binary response.…”

Normal enough? Tools to aid decision making

“…This concerned the potential for non-parametric tests to be more powerful than parametric tests in the presence of non-Normality. Moving to the current century, Khan and Rayner (2003) and Lantz (2013) also demonstrate the contrasting effects of non-Normality on the performance of parametric and non-parametric tests, but now using simulated data.…”

Preliminary Tests of Normality When Comparing Three Independent Samples

“…The Shapiro-Wilk test has recently been found to have the best power among the tests commonly used for normality screening (Marmolejo-Ramos & González-Burgos, 2013;Razali & Wah, 2011), even though other researchers recommend other tests, such as the Anderson-Darling test (see Keselman et al, 2013), for normality screening.…”