Variance Equality Test Calculator

Calculator Inputs

Input mode

Significance level

Alternative hypothesis

Dataset 1

Dataset 2

Sample 1 size

Sample 1 variance

Sample 2 size

Sample 2 variance

Use raw datasets for automatic means and sample variances, or enter summary values when only sample size and variance are available.

Example Data Table

Observation	Dataset 1	Dataset 2
1	12	18
2	15	21
3	14	20
4	11	24
5	13	17
6	16	23
7	12	19
8	14	22

Formula Used

Sample variance: s² = Σ(x − x̄)² / (n − 1)

F statistic: F = s₁² / s₂²

Decision rule: Compare the F statistic with critical F values, or compare the p value with α.

This calculator applies the classic F test for equality of two independent population variances. The F distribution uses degrees of freedom n₁ − 1 and n₂ − 1.

For a two-sided test, the calculator checks both tails. For one-sided tests, it evaluates whether variance 1 is greater than or less than variance 2.

How to Use This Calculator

Choose raw datasets if you have observations, or summary values if you already know sample sizes and variances.
Enter the significance level. Common choices are 0.10, 0.05, and 0.01.
Select the alternative hypothesis that matches your analysis goal.
Run the test to display the F statistic, p value, critical values, and final interpretation above the form.
Export the displayed results as CSV, or use the PDF button to save a print-ready copy.

Frequently Asked Questions

1. What does this test measure?

It tests whether two independent populations have equal variances. The calculator compares sample spread using the F distribution and reports whether the difference looks statistically meaningful.

2. When should I use raw data mode?

Use raw mode when you have the original observations. The calculator then computes each sample mean and unbiased sample variance automatically before running the F test.

3. When is summary mode helpful?

Use summary mode when a report already gives sample sizes and sample variances. It saves time and avoids re-entering long datasets when only summary statistics are available.

4. What assumptions matter most?

The F test assumes independent samples and roughly normal population distributions. Strong departures from normality can distort p values and make conclusions less reliable.

5. What does a small p value mean?

A small p value suggests the observed variance ratio would be unusual if the population variances were truly equal. That supports rejecting the null hypothesis.

6. Why can one-sided and two-sided results differ?

They answer different questions. A two-sided test checks for any variance difference, while one-sided tests look only for variance 1 being larger or smaller.

7. Can I export the results?

Yes. The result panel includes CSV export for spreadsheet use and a PDF-style print button for saving or sharing a formatted summary.

8. What if my datasets are not normal?

Interpret carefully. Non-normal data can weaken the F test. In applied work, analysts often consider robust or nonparametric alternatives before final decisions.