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 .

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.

Additional Resources

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

The following tutorials explain how to report other statistical results: