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 Excel.

**Step 1: Enter the Data**

First, let’s enter the values for a dataset with a sample size of n = 20:

**Step 2: Calculate Actual vs. Expected Values from Normal Distribution**

Next, we’ll calculate the actual values vs. the expected values from the normal distribution:

Here is the formula we used in various cells:

**B2**: =ROW() – 1**C2**: =B2/COUNT($A$2:$A$21)**D2**: =(B2-1)/COUNT($A$2:$A$21)**E2**: =IF(C2<1, NORM.S.INV(C2),””)**F2**: =NORM.DIST(A2, $J$1, $J$2, TRUE)**G2**: =ABS(F2–D2)**J1**: =AVERAGE(A2:A21)**J2**: =STDEV.S(A2:A21)**J4**: =MAX(G2:G21)

**Step 3: Interpret the Results**

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}

To determine if we should reject or fail to reject the null hypothesis we must refer to the **Maximum** value in the output, which turns out to be **0.10983**.

This represents the maximum absolute difference between the actual values of our sample and the expected values from a normal distribution.

To determine if this maximum value is statistically significant, we must refer to a Kolmogorov-Smirnov Table of critical values and find the number equal to n = 20 and α = .05.

The critical value turns out to be **0.190**.

Since our maximum value is not greater than this critical value, we fail to reject the null hypothesis.

This means we can assume that our sample data is normally distributed.

**Additional Resources**

The following tutorials explain how to perform other common statistical tests in Excel:

How to Perform a Correlation Test in Excel

How to Perform a Durbin-Watson Test in Excel

How to Perform a Jarque-Bera Test in Excel

How to Perform Levene’s Test in Excel