The **F-test** is used to determine whether or not two population variances are equal.

The F-test uses the following null and alternative hypotheses:

- H
_{0}: The population variances are equal (σ_{1}^{2}= σ_{2}^{2}) - H
_{A}: The population variances are not equal (σ_{1}^{2}≠ σ_{2}^{2})

If the p-value of the test is less than some significance level (e.g. α = .05) then we can reject the null hypothesis and conclude that the population variances are not equal.

The following step-by-step example shows how to perform the F-test in Google Sheets.

**Step 1: Enter the Data**

First, let’s enter the data values for two samples:

**Note:** The sample sizes do not have to be equal between the two groups to perform the F-test.

**Step 2: Perform the F-Test**

Next, we will use the **=FTEST(sample1, sample2)** function to perform the F-test:

The p-value of the test turns out to be **.0367**. Since this p-value is less than α = .05, we will reject the null hypothesis.

This means we have sufficient evidence to say that the variances between the two populations that the samples came from are not equal.

**Note:** The p-value returned by the FTEST() function represents the two-tailed p-value. Thus, if you were performing a one-tailed test (H_{A}: σ_{1}^{2} < σ_{2}^{2} or H_{A}: σ_{1}^{2} > σ_{2}^{2}) then you could simply multiply the resulting p-value by two to get the one-tailed p-value.

**Additional Resources**

How to Perform t-Tests in Google Sheets

How to Calculate Critical Values in Google Sheets

How to Find P-Values in Google Sheets