How to Calculate Skewness & Kurtosis in SPSS


In statistics, we use skewness and kurtosis to measure the shape of a distribution.

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

  • A negative skew indicates that the tail is on the left side of the distribution, which extends towards more negative values.
  • A 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 0.
  • If a given distribution has a kurtosis less than 0, then it tends to produce fewer and less extreme outliers than the normal distribution.
  • If a given distribution has a kurtosis greater than 0, then it tends to produce more outliers than the normal distribution.

The following example shows how to calculate skewness and kurtosis for a given dataset in SPSS.

Example: How to Calculate Skewness & Kurtosis in SPSS

Suppose we have the following dataset in SPSS that shows the exam scores received by various students in some class:

To calculate the skewness and kurtosis for the distribution of exam scores, click the Analyze tab, then click Descriptive Statistics, then click Descriptives:

In the new window that appears, drag Exam_Score to the Variables panel:

Then click the Options button. In the new window that appears, check the boxes next to Kurtosis and Skewness:

Then click Continue. Then click OK.

The following output will appear:

skewness and kurtosis in SPSS

From the output we can see the values for the skewness and kurtosis of the distribution:

  • The skewness is -1.551. Since this value is negative, it indicates that the distribution is left-skewed.
  • The kurtosis is 2.230. Since this value is greater than zero, it indicates that the distribution has heavier “tails” than a normal distribution.

In addition to calculating these metrics, it can be helpful to create a histogram to visualize the distribution.

To do so, click the Graphs tab, then click Histogram:

In the new window that appears, drag Exam_Score into the Variable panel:

Once you click OK, a histogram will be generated that shows the distribution of exam scores:

We can see that the distribution is indeed left-skewed (the “tail” extends to the left side of the distribution), which matches the fact that we calculated the skewness to be negative.

Related: Left Skewed vs. Right Skewed Distributions

By calculating the skewness and kurtosis along with creating a histogram, we now have a pretty good understanding of the distribution of exam scores in this dataset.

Additional Resources

The following tutorials explain how to perform other common tasks in SPSS:

How to Calculate a Five Number Summary in SPSS
How to Create a Frequency Table in SPSS
How to Calculate Percentiles in SPSS

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