Two Sample Variance Test Calculator

Test variance equality using sample sizes and deviations. Review F score, p value, and decisions. Plan robust comparisons with readable tables, charts, and exports.

Calculator Inputs

Sample 1 Label

Sample 2 Label

Alternative Hypothesis

Sample 1 Size

Sample 1 Variance

Sample 2 Size

Sample 2 Variance

Significance Level (α)

Displayed Decimals

Reset

Formula Used

F statistic: F = s₁² / s₂²

Degrees of freedom: df1 = n₁ - 1 and df2 = n₂ - 1

Two-sided p value: 2 × min(F-CDF(F), 1 − F-CDF(F))

Confidence interval for σ₁² / σ₂²: ratio divided by appropriate F critical values.

This calculator uses the F distribution to compare two independent sample variances and determine whether the population variances can be treated as equal.

How to Use This Calculator

Enter labels for both samples to keep the output readable.
Provide each sample size and its sample variance.
Choose a significance level such as 0.05 or 0.01.
Select the correct hypothesis direction: two-sided, greater, or less.
Press Run Variance Test to view the result summary above the form.
Review the p value, critical values, confidence interval, and decision statement.
Use the CSV and PDF buttons to export the result table.

Example Data Table

Sample	Size	Variance	Standard Deviation	Degrees of Freedom
Machine A Output	25	18.40	4.2895	24
Machine B Output	20	11.20	3.3466	19

Using these values gives an F statistic of approximately 1.6429, which can be checked against the F distribution using the selected alternative hypothesis.

Frequently Asked Questions

1. What does this calculator test?

It compares two independent sample variances using an F test. The goal is to assess whether the underlying population variances appear equal or significantly different.

2. When should I use a two-sided test?

Use a two-sided test when you only want to know whether the variances differ, without assuming which sample should have the larger variance.

3. What does the p value mean here?

The p value measures how unusual your observed variance ratio is under the null hypothesis of equal population variances. Smaller values provide stronger evidence against equality.

4. Why are sample sizes important?

Sample sizes determine the test’s degrees of freedom. Those degrees of freedom shape the F distribution and directly affect critical values and p value calculations.

5. Can I enter standard deviations instead of variances?

This page expects variances. If you have standard deviations, square them first. For example, a standard deviation of 3 becomes a variance of 9.

6. What assumptions should hold for the F test?

The samples should be independent, and each population should be approximately normal. Strong non-normality can make the F test sensitive and less reliable.

7. What does the confidence interval show?

It estimates a plausible range for the population variance ratio. If the interval includes 1, that often supports no meaningful variance difference at the same confidence level.

8. Why might equal-variance testing matter?

Many later procedures, such as pooled t tests and process comparisons, depend on whether equal-variance assumptions are reasonable for the data.