How to Perform a Kolmogorov-Smirnov Test in SPSS


The Kolmogorov-Smirnov (K-S) test is a statistical that is used to determine whether or not a sample comes from a certain distribution.

In most cases, the K-S test is used to check if a given distribution follows a normal distribution.

The K-S test uses the following hypotheses:

  • H0: The data is normally distributed.
  • HA: The data is not normally distributed.

If the p-value that results from the test is less than your chosen significance level (e.g. 0.05) then you can reject the null hypothesis and conclude that the data is not normally distributed.

The easiest way to perform a Kolmogorov-Smirnov test in SPSS is by using Analyze > Descriptive Statistics > Explore.

The following example shows how to perform this test in practice.

Example: How to Perform a Kolmogorov-Smirnov Test in SPSS

Suppose we have the following dataset in SPSS that contains information about the final exam scores received by 25 different students in some class:

Suppose that we would like to perform a Kolmogorov-Smirnov test to determine if the exam scores are normally distributed.

To do so, click the Analyze tab, then click Descriptive Statistics, then click Explore:

In the new window that appears, drag the Score variable into the Dependent List panel: 

Then click the Plots button.

Check the box next to Histogram and Normality plots with tests:

Then click Continue. Then click OK.

The following output will be generated that shows the results of the Kolmogorov-Smirnov test along with a histogram to help us visualize the distribution of exam scores:

Kolmogorov-Smirnov test in SPSS

From the output we can see that the p-value of the K-S test is .036.

Recall that the K-S test uses the following hypotheses:

  • H0: The data is normally distributed.
  • HA: The data is not normally distributed.

Since the p-value of the test is less than .05, we have sufficient evidence to reject the null hypothesis.

We would conclude that the distribution of exam scores is not normally distributed.

The histogram seems to agree with this conclusion. 

The distribution of exam scores in the histogram do not follow a “bell curve” that is typical of a normal distribution.

Additional Resources

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

How to Perform a Correlation Test in SPSS
How to Calculate Spearman Rank Correlation in SPSS
How to Calculate Percentiles in SPSS

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