F-Test Calculator
Compare two sample variances with an F-test, returning the F statistic and p-value.
About F-Test Calculator
The F-test for equality of variances compares two sample variances. The F statistic is the ratio of the larger to the smaller variance. A significant result (small p-value) indicates the population variances are likely unequal.
Formula
F = s₁² / s₂² (larger variance in numerator)
- s₁²
- Larger sample variance
- s₂²
- Smaller sample variance
Worked example
With the default values below, F-Test Calculator returns F Statistic of 1.3392. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Sample 1 (comma separated)
- 6, 7, 9, 15, 21
- Sample 2 (comma separated)
- 20, 28, 31, 33, 40
Results
- F Statistic
- 1.3392
- P-value (two-tailed)
- 0.784016
- Variance of Sample 1
- 39.8000
- Variance of Sample 2
- 53.3000
Step by step
- 1Values used
- 2Formula applied
- 3F Statistic= 1.3392
- 4P-value (two-tailed)= 0.784016
- 5Variance of Sample 1= 39.8000
- 6Variance of Sample 2= 53.3000
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What are the assumptions of the F-test?
Both samples must be independent and drawn from normally distributed populations. The F-test is sensitive to non-normality.
How does this relate to ANOVA?
ANOVA uses the F distribution to compare means across groups. This F-test specifically compares two variances rather than means.