# How to Perform a Kolmogorov-Smirnov Test in SAS

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:

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

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.