F-Test Calculator

F-test for equality of two variances with p-value and APA write-up.

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About this tool

Paste two samples and the F-test returns the ratio of their variances, the degrees of freedom and the p-value for the chosen tail.

How to use

1
Step 1
Enter sample 1 and sample 2.
2
Step 2
Pick two-tailed, left or right.
3
Step 3
Press Calculate to read F, df, p and both variances.

How it works

The F statistic is the variance of sample 1 divided by the variance of sample 2, with df n₁ − 1 and n₂ − 1. It is used to check the equal-variance assumption before a pooled t-test. The test is sensitive to non-normality.

F = s₁² ÷ s₂²      df = (n₁ − 1, n₂ − 1)

Worked example

Two samples of seven

Input
12,15,14,10,13,16,11 vs 13,14,13,12,14,13,15
Output
F(6, 6) = 4.90, p = .074
Walkthrough
Sample variances 4.667 and 0.952, so F = 4.667 ÷ 0.952 = 4.90.

Limitations

  • Sensitive to departures from normality.
  • Order matters for a one-tailed test.

Questions

Why test variances?
To decide between pooled and Welch t-tests, though Welch is generally safe without it.
Is F = 4.90 significant?
Not at 5% here: p =.074 two-tailed for df (6, 6).
What df does the F-test use?
n₁ − 1 for the numerator and n₂ − 1 for the denominator.

Features

  • Variances shown
  • Any tail
  • Runs in your browser

Related resources

Guides and videos from around the web—opens on YouTube or the publisher’s site.

  • Hypothesis testing and p-values

    StatQuest with Josh Starmer

    Intuition for t/z/χ² decision rules.

    Watch on YouTube

  • Mean, Variance and Standard Deviation

    StatQuest with Josh Starmer

    Descriptive stats behind table and test tools.

    Watch on YouTube

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