2010
DOI: 10.1027/1614-2241/a000016
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Is It Really Robust?

Abstract: Empirical evidence to the robustness of the analysis of variance (ANOVA) concerning violation of the normality assumption is presented by means of Monte Carlo methods. High-quality samples underlying normally, rectangularly, and exponentially distributed basic populations are created by drawing samples which consist of random numbers from respective generators, checking their goodness of fit, and allowing only the best 10% to take part in the investigation. A one-way fixed-effect design with three groups of 25… Show more

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Cited by 878 publications
(358 citation statements)
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“…However, when considered separately, the data within each pH level were normally distributed. Furthermore, ANOVA is known to be very robust with respect to violations of this assumption (Schmider et al, 2010), and therefore we proceeded with the analysis as planned.…”
Section: Discussionmentioning
confidence: 99%
“…However, when considered separately, the data within each pH level were normally distributed. Furthermore, ANOVA is known to be very robust with respect to violations of this assumption (Schmider et al, 2010), and therefore we proceeded with the analysis as planned.…”
Section: Discussionmentioning
confidence: 99%
“…In that case, many studies have shown that for ANOVAs and t tests, departures from normality are not critical (e.g., Glass, Peckham, & Sanders, 1972;Harwell, Rubinstein, Hayes, & Olds, 1992;Lix, Keselman, & Keselman, 1996;Schmider, Ziegler, Danay, Beyer, & Bühner, 2010). For t tests, the Type I errors still meet Bradley's liberal criterion even with extreme deviations from normality, at least if the sample size is higher than about 20, if there are (approximately) equal numbers of observations per group (balanced design) and if two-tailed tests are conducted (Kubinger, Rasch, & Moder, 2009;Sawilowsky & Blair, 1992).…”
Section: Discussionmentioning
confidence: 99%
“…As these data are not normally distributed, we did not conduct any further pairwise comparisons. Since ANOVAs have shown to be robust against violations of normal distribution (Schmider et al, 2010), we do not anticipate any problems when interpreting the reported effects. Figure 8 shows the participants' flight paths and the 3.8 nm circle around the MDF VOR.…”
Section: Eye-trackingmentioning
confidence: 99%