A **variance ratio test** is used to test whether or not two population variances are equal.

This test uses the following null and alternative hypotheses:

**H**: The population variances are equal_{0}**H**: The population variances are not equal_{A}

To perform this test, we calculate the following test statistic:

**F** = s_{1}^{2} / s_{2}^{2}

where:

**s**: The sample variance of the first group_{1}^{2}**s**: The sample variance of the second group_{2}^{2}

If the p-value that corresponds to this F test-statistic is less than a certain threshold (e.g. 0.05) then we reject the null hypothesis and conclude that the population variance are not equal.

The following step-by-step example shows how to perform a variance ratio test in Excel.

**Step 1: Enter the Data**

Suppose we want to know if two different species of plants have the same variance in height.

To test this, we collect a simple random sample of 15 plants from each species.

First, we’ll enter the heights for each species:

**Step 2: Calculate the F Test Statistic**

Next, we’ll type the following formula into cell **E1** to calculate the F test-statistic:

=VAR.S(A2:A16)/VAR.S(B2:B16)

The F test-statistic turns out to be **0.437178**.

**Step 3: Calculate the P-Value**

Next, we’ll type the following formula into cell **E2 **to calculate the p-value that corresponds to the F test-statistic:

=F.DIST(E1, COUNT(A2:A16)-1, COUNT(B2:B16)-1, TRUE)*2

**Note**: In the formula, we multiplied by 2 at the end to produce a two-tailed p-value.

The p-value turns out to be **0.133596**.

Recall the null and alternative hypotheses for this test:

**H**: The population variances are equal_{0}**H**: The population variances are not equal_{A}

Because the p-value of our test** (.133596) **is not less than 0.05, we fail to reject the null hypothesis.

This means we do not have sufficient evidence to conclude that the variance in plant height between the two species is unequal.

**Additional Resources**

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

How to Perform a Correlation Test in Excel

How to Perform Welch’s t-test in Excel

How to Perform a Kolmogorov-Smirnov Test in Excel