Understand the hypothesis test
Read the test as a model-based comparison
F-Test for Two Variances. The observed effect is scaled by its null-model uncertainty and located on a reference distribution selected before looking at the result.
1State H₀, the effect, and direction2Calculate the statistic under H₀3Report p-value with effect and interval
Test statistic and reference model
F=s₁²/s₂² with df₁=n₁−1 and df₂=n₂−1.
Variance evidence is highly sensitive to nonnormality; pair the result with distribution checks.
Responsible interpretation
A p-value is not the probability that the null is true, the chance the result occurred ‘by luck,’ or a measure of effect size, importance, replication, bias, or causation.
Required assumption: Samples must be independent and drawn from normal populations; the entered order determines one-sided direction.
Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the f-test for two variances calculator works
F=s₁²/s₂² with df₁=n₁−1 and df₂=n₂−1.
Variance evidence is highly sensitive to nonnormality; pair the result with distribution checks.
Worked example
F-Test for Two Variances example
Variance 25 from 20 observations versus variance 9 from 18 observations gives F=2.778.
F=s₁²/s₂² with df₁=n₁−1 and df₂=n₂−1.
Supported inputs
Precision and limits
Model and design
Samples must be independent and drawn from normal populations; the entered order determines one-sided direction.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
Variance evidence is highly sensitive to nonnormality; pair the result with distribution checks.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
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