Univariate and multivariate skewness and kurtosis for measuring nonnormality: Prevalence, influence and estimation.
Behav Res Methods
; 49(5): 1716-1735, 2017 10.
Article
in En
| MEDLINE
| ID: mdl-27752968
ABSTRACT
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.Key words
Full text:
1
Collection:
01-internacional
Database:
MEDLINE
Main subject:
Normal Distribution
/
Multivariate Analysis
/
Behavioral Research
Type of study:
Prevalence_studies
/
Risk_factors_studies
Limits:
Humans
Language:
En
Journal:
Behav Res Methods
Journal subject:
CIENCIAS DO COMPORTAMENTO
Year:
2017
Document type:
Article
Affiliation country:
United States