Two-Sample F-Test for Variances

The Two-Sample F-Test is used to test whether the two samples are from normal populations with equal variances. The null hypothesis is that the variances for the two samples are equal. This F-test is very sensitive to non-normality, so it is recommended to check the normality of data.

# Assumptions

Samples arise from normal populations with homogeneous variances.

# How To

Run:
Statistics→Basic Statistics→**Two-Sample
F-Test for Variances...**

Select two variables.

(v6.3+) Optionally, specify the test ratio other than 1 (variances are equal).

**Listwise**
deletion is used for missing values removal.

# Results

Sample Size, Mean, Variance, Standard Deviation, Mean Standard Error are calculated for each input variable. See the Descriptive Statistics procedure for more information.

F – test statistic, is the ratio of variances from both samples, has an F-distribution under the null hypothesis.

F Critical Value () – critical values of the F distribution: one-tailed critical value , and two‑tailed critical value .

p-level values are provided
for the two-tailed test (alternative hypothesis H_{1}: ), lower one-tailed test (H_{1}: ) and for the upper one-tailed test (H_{1}: ).

F [larger/smaller] section

Many authors suggest using the sample with the largest variance for the numerator.

When using the sample with the largest variance for the numerator F is always greater than one, and we can simply compare the observed value with the two-tailed critical value to determine whether the null hypothesis (variances are equal: ) should be accepted. If the observed value is greater than the two-tailed critical value, the null hypothesis is rejected and the conclusion is that the two variances differ significantly.

# References

Snedecor, George W. and Cochran, William G. (1989), Statistical Methods, Eighth Edition, Iowa State University Press.