The Complete Guide: How to Report Skewness & Kurtosis


In statistics, skewness and kurtosis are two ways to measure the shape of a distribution.

Skewness is a measure of the asymmetry of a distribution. This value can be positive or negative.

  • Negative skew indicates that the tail is on the left side of the distribution, which extends towards more negative values.
  • Positive skew indicates that the tail is on the right side of the distribution, which extends towards more positive values.
  • A value of zero indicates that there is no skewness in the distribution at all, meaning the distribution is perfectly symmetrical.

Kurtosis is a measure of whether or not a distribution is heavy-tailed or light-tailed relative to a normal distribution.

  • The kurtosis of a normal distribution is 3.
  • If a given distribution has a kurtosis less than 3, it is said to be playkurtic, which means it tends to produce fewer and less extreme outliers than the normal distribution.
  • If a given distribution has a kurtosis greater than 3, it is said to be leptokurtic, which means it tends to produce more outliers than the normal distribution.

Note: Some formulas (Fisher’s definition) subtract 3 from the kurtosis to make it easier to compare with the normal distribution. Using this definition, a distribution would have kurtosis greater than a normal distribution if it had a kurtosis value greater than 0.

When reporting the skewness and kurtosis of a given distribution in a formal write-up, we generally use the following format:

The skewness of [variable name] was found to be -.89, indicating that the distribution was left-skewed.

 

The kurtosis of [variable name] was found to be 4.26, indicating that the distribution was more heavy-tailed compared to the normal distribution.

Keep in mind the following when reporting the results:

  • Round the values for skewness and kurtosis to two decimal places.
  • Drop the leading 0 when reporting the values (e.g. use .79, not 0.79)

The following example shows how to use this format in practice.

Example: Reporting Skewness & Kurtosis

Suppose we’re analyzing the distribution of exam scores among students at a certain university.

Using statistical software, we calculate the values for the skewness and kurtosis of the distribution to be:

  • Skewness: -1.391777
  • Kurtosis: 4.170865

We would report these values as follows:

The skewness of the exam scores was found to be -1.39, indicating that the distribution was left-skewed.

 

The kurtosis of the exam scores was found to be 4.17, indicating that the distribution was more heavy-tailed compared to the normal distribution.

Along with reporting these values for skewness and kurtosis, we generally include some chart to visualize the distribution of values such as a histogram or boxplot so the reader can get a visual understanding of the distribution as well.

Additional Resources

The following tutorials explain how to calculate skewness and kurtosis in different statistical software:

How to Calculate Skewness & Kurtosis in R
How to Calculate Skewness & Kurtosis in Python
How to Calculate Skewness & Kurtosis in Google Sheets

The following tutorials explain how to report other statistical results:

How to Report Confidence Intervals
How to Report ANOVA Results
How to Report Regression Results
How to Report Pearson’s Correlation

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