F-Test Calculator
Are Two Groups Equally Variable, or Not?
Before comparing two groups' means with a standard t-test, it's often worth asking a different question first: do the two groups vary by roughly the same amount, or is one far noisier than the other? The F-test compares two variances directly, and the result matters beyond curiosity — unequal variances affect which version of other tests, like the two-sample t-test, is appropriate.
The Formula
By convention the larger of the two sample variances always goes in the numerator, which keeps F ≥ 1 and makes the corresponding two-tailed p-value straightforward to compute from the F-distribution using each sample's degrees of freedom (n−1).
Worked Example: Comparing Two Production Lines
Line A (n=15) shows a standard deviation of 5 units; Line B (n=12) shows a standard deviation of 3 units in the same measurement:
| F-statistic | df1 | df2 | Two-tailed p-value |
|---|---|---|---|
| 2.778 | 14 | 11 | 0.0955 |
A p-value of 0.0955 is above the conventional 0.05 threshold, so this sample doesn't provide strong enough evidence to conclude the two lines have genuinely different variability — even though Line A's variance is nearly three times larger.
Where This Matters
- Manufacturing consistency — comparing whether two machines, shifts, or suppliers produce equally consistent output.
- Choosing a t-test variant — historically used to decide between a pooled-variance and a Welch's (unequal-variance) t-test.
- ANOVA foundations — the F-test is the same statistical machinery that powers one-way ANOVA across more than two groups.
- Financial volatility comparison — testing whether one asset or portfolio is meaningfully more volatile than another over the same period.
How to Use This Calculator
- Enter the standard deviation and sample size for Sample 1.
- Enter the standard deviation and sample size for Sample 2.
- Select Calculate to get the F-statistic, degrees of freedom, and two-tailed p-value.
Related Calculations
To compare more than two groups' means at once using the same F-distribution machinery, see the ANOVA Calculator. For comparing two group means directly, use the T-Test Calculator.