F-Test Calculator

Q: What is the F-test used for?

The F-test compares two sample variances to determine if the populations have the same variability. It is a prerequisite for the two-sample t-test and forms the basis of ANOVA.

Q: Why is F always greater than or equal to 1?

By convention, the larger variance goes in the numerator. Since variance is always positive, dividing a larger number by a smaller one gives at least 1.

Q: What are the assumptions of the F-test?

Both samples must be independent, drawn from normally distributed populations. The F-test is quite sensitive to the normality assumption. Consider Levene's test as a more robust alternative.

Q: How does the F-test relate to ANOVA?

ANOVA uses the F-test to compare variance between groups to variance within groups. If between-group variance is significantly larger (large F), at least one group mean differs.

Q: What if my F-value is close to 1?

An F near 1 means the two sample variances are similar. You would fail to reject the null hypothesis and conclude the variances are not significantly different.

Q: How do I add this F-Test Calculator to my site?

Absolutely. Use the "Embed" option above to tailor the dimensions, color scheme, and styling to match your site. Copy the generated iframe snippet and drop it into your HTML, WordPress editor, or any CMS. There is no cost and no account required. See calculory.com/services/embed-calculators for a step-by-step walkthrough.

Use this free online F-test calculator to compare two sample variances and test whether they are significantly different. Enter the variances and sample sizes from both groups to get the F-statistic, degrees of freedom, and hypothesis test decision.

Enter Values

Sample 1 Variance (s1 squared)

The variance of the first sample

Sample 1 Size (n1)

Number of observations in the first sample

Sample 2 Variance (s2 squared)

The variance of the second sample

Sample 2 Size (n2)

Number of observations in the second sample

Significance Level (alpha)

The threshold for statistical significance

Result

Enter values above and click Calculate to see your result.

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Formula

Core Formula

F = \frac{s_1^2}{s_2^2}

How it works: Divide the larger sample variance by the smaller sample variance. The F-statistic follows an F-distribution with (n1 - 1) numerator and (n2 - 1) denominator degrees of freedom under the null hypothesis of equal variances.

Review and Methodology

Updated Mar 26, 2026

This calculator runs locally in your browser. Inputs are converted into the units required by the formula, and the result is paired with supporting references so you can verify the method before using it for planning or estimates.

Worked Example

Variance 1 = 25 (n1 = 20), Variance 2 = 10 (n2 = 18), alpha = 0.05

1Step 1: F = 25 / 10 = 2.50

2Step 2: Numerator df = 20 - 1 = 19

3Step 3: Denominator df = 18 - 1 = 17

4Step 4: For F(19, 17), approximate p-value is around 0.04

5Step 5: Since p < 0.05, reject H0

Result: F = 2.50, p = 0.04. Evidence that the two population variances are not equal.

What Is an F-Test for Variance Equality?

The F-test for equality of variances determines whether two populations have the same variance. It is a prerequisite for choosing between the pooled t-test (equal variances) and Welch's t-test (unequal variances). The F-test is also the foundation of ANOVA.

The F-statistic is always the ratio of the larger variance to the smaller variance, so F is always at least 1
Under H0, the F-statistic follows an F-distribution with (n1-1, n2-1) degrees of freedom
The F-test is sensitive to departures from normality, more so than the t-test
Levene's test is a more robust alternative when normality is questionable
The F-distribution is used in ANOVA, regression analysis, and comparing nested models

The F-test is commonly used as a preliminary test before running a two-sample t-test. If variances are equal, use the pooled t-test. If unequal, use Welch's t-test.

You can also calculate changes using our T-Test Calculator, Chi-Square Calculator, Degrees of Freedom Calculator or Test Statistic Calculator.

Frequently Asked Questions

What is the F-test used for?

The F-test compares two sample variances to determine if the populations have the same variability. It is a prerequisite for the two-sample t-test and forms the basis of ANOVA.

Why is F always greater than or equal to 1?

By convention, the larger variance goes in the numerator. Since variance is always positive, dividing a larger number by a smaller one gives at least 1.

What are the assumptions of the F-test?

Both samples must be independent, drawn from normally distributed populations. The F-test is quite sensitive to the normality assumption. Consider Levene's test as a more robust alternative.

How does the F-test relate to ANOVA?

ANOVA uses the F-test to compare variance between groups to variance within groups. If between-group variance is significantly larger (large F), at least one group mean differs.

What if my F-value is close to 1?

An F near 1 means the two sample variances are similar. You would fail to reject the null hypothesis and conclude the variances are not significantly different.

How do I add this F-Test Calculator to my site?

Absolutely. Use the "Embed" option above to tailor the dimensions, color scheme, and styling to match your site. Copy the generated iframe snippet and drop it into your HTML, WordPress editor, or any CMS. There is no cost and no account required. See calculory.com/services/embed-calculators for a step-by-step walkthrough.

AI Assistant

Ask about this calculator

I can help you understand the f-test calculator formula, interpret your results, and answer follow-up questions.

Try asking

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