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Enter the variance and sample size of two datasets to quickly calculate the F-statistic and p-value, and determine if the variances are significantly different.
Both samples require at least 2 valid numbers.
Enter at least 2 numbers per sample. F-statistic = Sample 1 Variance ÷ Sample 2 Variance. Supports comma, space, newline, or semicolon as separators; non-numeric content will be ignored.
Enter two sets of sample data to see F-test results
Overview
Understand what the tool solves, how it works, and the boundaries of its data.
Paste two groups of raw observations to compare spread. Values may be separated by commas, spaces, semicolons, tabs, or line breaks; each group needs at least two numeric values. The calculator computes each sample mean and sample variance, then uses F = s₁² / s₂², preserving input order. Numerator and denominator degrees of freedom are n₁ − 1 and n₂ − 1.
This is the classical two-sample variance-ratio test. “F-test” can also refer to ANOVA or regression tests, which answer different questions. This calculator does not test whether group means differ.
Sample variance: s² = Σ(xᵢ − x̄)² / (n − 1)
Test statistic: F = s₁² / s₂²
Select two-sided to test for a difference in either direction, or left/right when the question specified that sample 1’s variance is lower/higher than sample 2’s. Set α, the significance threshold; the initial value is 0.05. If p is below α, the result rejects equal population variances under the assumptions. If p is at least α, evidence is insufficient to reject equality; that does not prove the variances identical.
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Put group 1 and group 2 values in their boxes. Non-numeric text is ignored, so ensure labels or stray numbers are not treated as observations.
Use two-sided when either direction matters. Choose left or right only when the research question specified direction beforehand.
Enter a value greater than 0 and less than 1, then compare p with α. Review F, degrees of freedom, sample sizes, means, variances, and standard deviations. Worked steps show how the summaries and ratio were formed.
Use cases
See how the tool fits into real work and everyday tasks.
Enter independent measurement readings from two processes to examine whether observed variability differs. Interpret results alongside measurement conditions and study design.
Paste both lists, then compare displayed sample variances and degrees of freedom with hand calculations before interpreting p.
Q&A
Find concise answers to common questions and confusing cases.
The tool divides sample 1 variance by sample 2 variance without reordering. If sample 1 is smaller, F is below 1. Keep order consistent for one-sided tests.
No. This calculator accepts raw observation lists, not summary statistics. Enter original values in each sample box.
If all sample 2 values are identical, the denominator is zero and the ratio cannot be calculated. Check the selected data; do not add artificial values.
No. This test evaluates variance or spread. A mean comparison needs a suitable separate method.
Notes
Review scope, result limitations, and important precautions before use.
The classical F test assumes independent samples from approximately normal populations and is sensitive to non-normality. Skew, outliers, dependence, or unsuitable sampling can make the p-value misleading. Examine data and study design; for non-normal data, consider a robust variance comparison method suited to the question.
The test describes evidence about population variances under its assumptions; a non-significant result does not establish equality and the test does not explain a difference. For consequential analysis, confirm the method with a statistician.
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