Statistical notes for clinical researchers: assessing normal distribution (2) using skewness and kurtosis

By Hae-Young Kim. Restorative Dentistry & Endodontics, 2013

3,679 citations recorded by the source corpus.

As discussed in the previous statistical notes, although many statistical methods have been proposed to test normality of data in various ways, there is no current gold standard method. The eyeball test may be useful for medium to large sized (e.g., n > 50) samples, however may not useful for small samples. The formal normality tests including Shapiro-Wilk test and Kolmogorov-Smirnov test may be used from small to medium sized samples (e.g., n < 300), but may be unreliable for large samples. Moreover we may be confused because ‘eyeball test’ and ‘formal normality test’ may show incompatible results for the same data. To resolve the problem, another method of assessing normality using skewness and kurtosis of the distribution may be used, which may be relatively correct in both small samples and large samples. 1) Skewness and kurtosis Skewness is a measure of the asymmetry and kurtosis is a measure of ’peakedness’ of a distribution. Most statistical packages give you values of skewness and kurtosis as well as their standard errors.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5af949b9277c1ea39848101c3f21cdd9ed37b180

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Citations in the corpus

Adolescent gaming and social media usage before and during the COVID-19 pandemic (2021, methodology): “Absolute values of skewness > 2.0 and kurtosis > 7.0 were used to check for substantial deviation of normality distribution (Kim, 2013).”
Validity of the trait emotional intelligence questionnaire in sports and its links with performance satisfaction (2014, background): “It is recommended for samples larger than 300 to judge normality based on the skewness and kurtosis values (Kim, 2013).”
Descriptive Statistics and Normality Tests for Statistical Data (2019, background): “Either an absolute skewness value ≤2 or an absolute kurtosis (excess) ≤4 may be used as reference values for determining considerable normality.[11] A histogram is an estimate of the probability distribution of a continuous variable.”
Parametric or Non-parametric: Skewness to Test Normality for Mean Comparison (2020, background): “Besides, for larger sample sizes it was suggested to increase the z-score from 1.96 up to 3.29 (Kim, 2013).”
The roles of absorptive capacity and cultural balance for exploratory and exploitative innovation in SMEs (2017, methodology): “We examined skewness and kurtosis using SPSS to determine data distributions (Kim, 2013).”
Students’ Psychological Perceptions Toward Online Learning Engagement and Outcomes during the COVID-19 Pandemic: A Comparative Analysis of Students in Three Different Countries (2021, background): “The skewness ranged from −1.09 to .68 and kurtosis ranged from −1.07 to 1.31, indicating the normality of the distribution (Kim, 2013).”