Use this F test calculator to compare two population variances from independent samples.
What this F test calculator does
The F test compares two sample variances to evaluate whether the underlying population variances are likely equal. This is a common step before choosing methods that assume equal variance, such as the pooled two-sample t-test.
Enter the two sample variances and sample sizes, pick your hypothesis direction, and the calculator returns:
- F statistic
- Degrees of freedom for numerator and denominator
- p-value
- Critical value(s) for your selected α
- A decision to reject or fail to reject the null hypothesis
Formula used
The test statistic is:
Under the null hypothesis H₀: σ₁² = σ₂², this statistic follows an F distribution with df₁ and df₂ degrees of freedom.
Hypothesis options
- Two-sided: H₁: σ₁² ≠ σ₂²
- Right-tailed: H₁: σ₁² > σ₂²
- Left-tailed: H₁: σ₁² < σ₂²
How to interpret results
The p-value is the probability of observing a test statistic as extreme as yours, assuming the null hypothesis is true. If p-value < α, the result is statistically significant and you reject H₀.
Critical values provide the same decision in threshold form. If your F statistic lands in the rejection region, reject H₀; otherwise, fail to reject H₀.
Practical assumptions
- The two samples are independent.
- Each population is approximately normally distributed.
- Variances are estimated from random samples.
The F test is sensitive to non-normality. If your data are heavily skewed or contain extreme outliers, consider robust alternatives such as Levene’s test or Brown–Forsythe.
Quick example
Suppose sample 1 has variance 25 with n = 20, and sample 2 has variance 16 with n = 18. Then F = 25/16 = 1.5625, with df₁ = 19 and df₂ = 17. Using α = 0.05, the calculator computes the p-value and tells you whether evidence supports unequal variances.