Tests for Normality and Measures of Skewness and Kurtosis: Their Place in Research Reporting

Hopkins, Kenneth D.; Weeks, Douglas L.

doi:10.1177/0013164490504001

Cited by 215 publications

(117 citation statements)

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“…KR was also robust for the interaction effect, although with a total sample size of 30, it was mainly liberal, but again independently of the degree of kurtosis or violation of the sphericity assumption. These findings are partially consistent with research that has reported the effect of kurtosis on the robustness of other statistical tests (Harwell et al, 1992;Hopkins & Weeks, 1990). Although the present results show an effect of kurtosis on empirical type I error rates with small samples and in relation to the interaction effect, taken together they support previous studies Chafin & Rhiel, 1993;Scheffé, 1959) that have suggested that skewness effects are greater than those of kurtosis.…”

Section: Discussionsupporting

confidence: 93%

“…However, the effect of kurtosis and skewness on the KR procedure has yet to be specifically explored. Some studies focusing on other statistical procedures have found that the effects of kurtosis are greater than those of skewness (Harwell, Rubinstein, Hayes & Olds, 1992;Hopkins & Weeks, 1990), whereas others have reported that the effects of skewness are greater than those of kurtosis Chafin & Rhiel, 1993;Scheffé, 1959).…”

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confidence: 99%

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The effect of skewness and kurtosis on the robustness of linear mixed models

et al. 2013

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This study analyzes the robustness of the linear mixed model (LMM) with the Kenward-Roger (KR) procedure to violations of normality and sphericity when used in split-plot designs with small sample sizes. Specifically, it explores the independent effect of skewness and kurtosis on KR robustness for the values of skewness and kurtosis coefficients that are most frequently found in psychological and educational research data. To this end, a Monte Carlo simulation study was designed, considering a split-plot design with three levels of the between-subjects grouping factor and four levels of the within-subjects factor. Robustness is assessed in terms of the probability of type I error. The results showed that (1) the robustness of the KR procedure does not differ as a function of the violation or satisfaction of the sphericity assumption when small samples are used; (2) the LMM with KR can be a good option for analyzing total sample sizes of 45 or larger when their distributions are normal, slightly or moderately skewed, and with different degrees of kurtosis violation; (3) the effect of skewness on the robustness of the LMM with KR is greater than the corresponding effect of kurtosis for common values; and (4) when data are not normal and the total sample size is 30, the procedure is not robust. Alternative analyses should be performed when the total sample size is 30.Keywords Linear mixed model . Kenward-Roger procedure . Skewness . Kurtosis . RobustnessLongitudinal studies, which can be broadly defined as those studies in which the response of each individual is observed on two or more occasions, play a prominent role in the behavioral sciences. The empirical evidence obtained by considering the changes in psychological and educational variables over time can be used to establish predictive relationships that sometimes cannot be detected when cross-sectional studies are used. One of the most popular longitudinal designs is the split-plot design, in which individuals are measured repeatedly on two or more occasions in relation to one or more grouping factors. Data from this design are frequently analyzed with an analysis of variance (ANOVA) with within-subjects and between-subjects factors. This approach is valid under certain assumptions, such as normality, sphericity, and independence of the observations. However, when these assumptions are not satisfied, as is often the case in psychological and educational research

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Section: Discussionsupporting

confidence: 93%

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confidence: 99%

The effect of skewness and kurtosis on the robustness of linear mixed models

et al. 2013

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“…We identified deviations from normality for all four regressions and examined the mental health measures to evaluate whether problems with skewness might be accounting for the lack of normality. Variables were considered skewed if the variable's skewness statistic exceeded twice its standard error (Hopkins & Weeks, 1990). This was the case for all four measures.…”

Section: Weighting and Analysesmentioning

confidence: 99%

Gender differences in combat-related stressors and their association with postdeployment mental health in a nationally representative sample of U.S. OEF/OIF veterans.

Vogt

Vaughn

Glickman

et al. 2011

Journal of Abnormal Psychology

205

157

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Though the broader literature suggests that women may be more vulnerable to the effects of trauma exposure, most available studies on combat trauma have relied on samples in which women's combat exposure is limited and analyses that do not directly address gender differences in associations between combat exposure and postdeployment mental health. Female service members' increased exposure to combat in Afghanistan and Iraq provides a unique opportunity to evaluate gender differences in different dimensions of combatrelated stress and associated consequence for postdeployment mental health. The current study addressed these research questions in a representative sample of female and male U.S. veterans who had returned from deployment to Afghanistan or Iraq within the previous year. As expected, women reported slightly less exposure than men to most combat-related stressors, but higher exposure to other stressors (i.e., prior life stress, deployment sexual harassment). No gender differences were observed in reports of perceived threat in the war zone. Though it was hypothesized that combat-related stressors would demonstrate stronger negative associations with postdeployment mental health for women, only one of 16 stressor ϫ gender interactions achieved statistical significance and an evaluation of the clinical significance of these interactions revealed that effects were trivial. Results suggest that female Operation Enduring Freedom/Operation Iraqi Freedom service members may be as resilient to combat-related stress as men. Future research is needed to evaluate gender differences in the longer-term effects of combat exposure.

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“…Platykurtic (flat) distributions have a flatter top and shorter and thinner tails while leptokurtic (sharp) distributions have a sharp top but longer and wider tails. Skewed distributions are always sleptokurtic (Hopkins and Weeks, 1990). An unbiased estimator of underlying kurtosis that works well for any n can be calculated as (Joanne and Gill, 1998) (…”

Section: Skew and Kurtosismentioning

confidence: 99%

Auditory Spatial Perception: Auditory Localization

Łȩtowski¹,

Letowski²

2012

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Tests for Normality and Measures of Skewness and Kurtosis: Their Place in Research Reporting

Cited by 215 publications

References 11 publications

The effect of skewness and kurtosis on the robustness of linear mixed models

The effect of skewness and kurtosis on the robustness of linear mixed models

Gender differences in combat-related stressors and their association with postdeployment mental health in a nationally representative sample of U.S. OEF/OIF veterans.

Auditory Spatial Perception: Auditory Localization

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