Skewness and Kurtosis in Real Data Samples

By M. Blanca, J. Arnau, Dolores López-Montiel, Roser Bono, R. Bendayan. 2013

461 citations recorded by the source corpus.

Parametric statistics are based on the assumption of normality. Recent findings suggest that Type I error and power can be adversely affected when data are non-normal. This paper aims to assess the distributional shape of real data by examining the values of the third and fourth central moments as a measurement of skewness and kurtosis in small samples. The analysis concerned 693 distributions with a sample size ranging from 10 to 30. Measures of cognitive ability and of other psychological variables were included. The results showed that skewness ranged between −2.49 and 2.33. The values of kurtosis ranged between −1.92 and 7.41. Considering skewness and kurtosis together the results indicated that only 5.5% of distributions were close to expected values under normality. Although extreme contamination does not seem to be very frequent, the findings are consistent with previous research suggesting that normality is not the rule with real data.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/123d9449fe6e51709ea2c53ec427470ec3a38315

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Management Science and Operations Research

1. J. D. de Winter
2. Fatih Orçan
3. Marley W. Watkins
4. Matt C. Howard

In Statistics and Probability

1. J. D. de Winter
2. J. Potter
3. Samuel D. Gosling
4. Fatih Orçan
5. Marley W. Watkins
6. Matt C. Howard

Citations in the corpus

• Parametric or Non-parametric: Skewness to Test Normality for Mean Comparison (2020, background): “Blanca et al. (2013) examined 693 data sets with sample sizes, ranging between 10 and 30, in terms of skewness and kurtosis.”
• Comparing the Pearson and Spearman correlation coefficients across distributions and sample sizes: A tutorial using simulations and empirical data. (2016, background): “However, in psychological research, heavy-tailed distributions are common (Blanca et al., 2013; Micceri, 1989).”