Hypothesis Tests

F-Test (Variance Equality)

Tests whether two normally distributed populations have equal variances.

Statusvalidated

Version1.0.0

Minitab equivalentStat > Basic Statistics > 2 Variances

Description

The F-test compares the variances of two independent, normally distributed samples. The test statistic F = s₁²/s₂² follows an F-distribution with (n₁−1, n₂−1) degrees of freedom. The test is sensitive to departures from normality — for non-normal data, the Levene test should be preferred.

Formulas

F = \frac{s _{1}^{2}}{s _{2}^{2}}

Test statistic: ratio of sample variances

H₀

H_{0} : σ_{1}^{2} = σ_{2}^{2}

Null hypothesis: The population variances are equal

Assumptions

Both samples are normally distributed
Samples are independent
Continuous data

Limitations

Very sensitive to departures from normality
Use Levene test for non-normal data

References

Snedecor, G. W. & Cochran, W. G. (1989), Statistical Methods, 8th Ed.
NIST/SEMATECH e-Handbook of Statistical Methods, Section 7.3.1.2