The **Kolmogorov-Smirnov test** is used to determine whether or not or not a sample is normally distributed.

This test is widely used because many statistical tests and procedures make the assumption that the data is normally distributed.

The following step-by-step example shows how to perform a Kolmogorov-Smirnov test on a sample dataset in SAS.

**Example: Kolmogorov-Smirnov Test in SAS**

First, let’s create a dataset in SAS with a sample size of n = 20:

/*create dataset*/ data my_data; input Values; datalines; 5.57 8.32 8.35 8.74 8.75 9.38 9.91 9.96 10.36 10.65 10.77 10.97 11.15 11.18 11.47 11.64 11.88 12.24 13.02 13.19 ; run;

Next, we’ll use **proc univariate** to perform a Kolmogorov-Smirnov test to determine if the sample is normally distributed:

/*perform Kolmogorov-Smirnov test*/ proc univariate data=my_data; histogram Values / normal(mu=est sigma=est); run;

At the bottom of the output we can see the test statistic and corresponding p-value of the Kolmogorov-Smirnov test:

The test statistic is **0.1098** and the corresponding p-value is **>0.150**.

Recall that a Kolmogorov-Smirnov test uses the following null and alternative hypotheses:

**H**: The data is normally distributed._{0}**H**: The data is not normally distributed._{A}

Since the p-value from the test is not less than .05, we fail to reject the null hypothesis.

This means we can assume that the dataset is normally distributed.

**Additional Resources**

The following tutorials explain how to perform a Kolmogorov-Smirnov test in other statistical software:

How to Perform a Kolmogorov-Smirnov Test in Excel

How to Perform a Kolmogorov-Smirnov Test in R

How to Perform a Kolmogorov-Smirnov Test in Python