Univariate and multivariate skewness and kurtosis for measuring nonnormality: Prevalence, influence and estimation

Nonnormality of univariate data has been extensively examined previously (Blanca et al., Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 9 (2), 78–84, 2013 ; Miceeri, Psychological Bulletin, 105 (1), 156, 1989 ). However, less is known of the potential nonno...

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Vydané v:Behavior research methods Ročník 49; číslo 5; s. 1716 - 1735
Hlavní autori: Cain, Meghan K., Zhang, Zhiyong, Yuan, Ke-Hai
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.10.2017
Springer Nature B.V
Predmet:
Behavioral Research - statistics & numerical data
Behavioral Science and Psychology
Cognitive Psychology
Data processing
Education
Educational research
Factor analysis
Humans
Kurtosis
Multivariate Analysis
Normal Distribution
Psychological research
Psychology
Research methodology
Simulation
Skewness
Social factors
Social sciences
Software
Statistical analysis
Statistics
Nonnormality
Kurtosis
Software
Skewness
ISSN:1554-3528, 1554-3528
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Shrnutí:Nonnormality of univariate data has been extensively examined previously (Blanca et al., Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 9 (2), 78–84, 2013 ; Miceeri, Psychological Bulletin, 105 (1), 156, 1989 ). However, less is known of the potential nonnormality of multivariate data although multivariate analysis is commonly used in psychological and educational research. Using univariate and multivariate skewness and kurtosis as measures of nonnormality, this study examined 1,567 univariate distriubtions and 254 multivariate distributions collected from authors of articles published in Psychological Science and the American Education Research Journal. We found that 74 % of univariate distributions and 68 % multivariate distributions deviated from normal distributions. In a simulation study using typical values of skewness and kurtosis that we collected, we found that the resulting type I error rates were 17 % in a t -test and 30 % in a factor analysis under some conditions. Hence, we argue that it is time to routinely report skewness and kurtosis along with other summary statistics such as means and variances. To facilitate future report of skewness and kurtosis, we provide a tutorial on how to compute univariate and multivariate skewness and kurtosis by SAS, SPSS, R and a newly developed Web application.
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ISSN:1554-3528
1554-3528
DOI:10.3758/s13428-016-0814-1