Check if two processes have equal variability today. Flexible inputs, clear steps, and exportable reports. Built for students, analysts, and lab quality checks everywhere.
| # | Sample 1 | Sample 2 |
|---|---|---|
| 1 | 12 | 10 |
| 2 | 15 | 11 |
| 3 | 14 | 9 |
| 4 | 16 | 12 |
| 5 | 13 | 10 |
| 6 | 18 | 8 |
| 7 | 17 | 11 |
| 8 | 15 | 9 |
n-1).
For two independent samples with variances s1^2 and s2^2,
the variance ratio test statistic is:
F = s1^2 / s2^2df1 = n1 - 1, df2 = n2 - 1
The p-value is computed from the F distribution. Two-tailed tests use
2 × min(P(F≤f), P(F≥f)).
F = variance1/variance2 as entered.sigma1^2/sigma2^2.Comparing variability is often as important as comparing averages. In manufacturing, a small drift in variance can signal tool wear before the mean shifts. In education or sports analytics, a higher variance can reflect inconsistent performance, even when the average looks stable. This calculator focuses on the variance ratio framework where the key output is an F statistic built from two sample variances.
The input data are converted to unbiased sample variances, using n−1 in the denominator. The ratio
F = s1² / s2² follows an F distribution under the equal-variance assumption, with
degrees of freedom (n1−1, n2−1). Larger degrees of freedom tighten the distribution, so the same observed ratio
typically produces smaller p-values when samples are larger.
Use a two-tailed test when you want to detect any difference in variability. Use right-tailed when your question is specifically whether Sample 1 is more variable than Sample 2, and left-tailed for the opposite direction. Alpha is the false-alarm budget; common choices are 0.10 for exploratory checks, 0.05 for routine inference, and 0.01 for tighter quality controls.
The p-value summarizes how extreme the observed ratio is under equal variances. The critical values are threshold ratios: if F falls beyond them, the test rejects. For two-tailed tests, the calculator uses symmetric tail areas, reporting both lower and upper cutoffs. This makes the decision transparent even when the ratio is below 1.
Beyond a yes/no decision, the interval estimates the plausible range of the true variance ratio. A wide interval often indicates limited data or noisy measurements. If the interval includes 1, the data are compatible with equal variances at the chosen confidence level. If it sits entirely above 1, Sample 1 likely has higher variability.
Variance tests are sensitive to departures from normality. If values are heavily skewed or contain outliers, consider cleaning rules, transformations, or robust alternatives. Always confirm independence: repeated measures on the same unit can artificially reduce variance. When reporting results, include sample sizes, df, F, p-value, and the ratio interval for a complete, auditable summary.
It tests whether two populations have equal variances by comparing sample variances through an F statistic under an equal-variance assumption.
Use two-tailed when any variance difference matters. Use one-tailed only when your question is directional, such as “Sample 1 is more variable.”
Non-normality, especially outliers and heavy tails, can distort F-test results. Consider transformations, outlier rules, or robust variance tests when distributions look irregular.
The statistic uses F = s1²/s2². Swapping samples inverts the ratio and swaps degrees of freedom, which changes tail probabilities and critical values.
It estimates a plausible range for the true variance ratio σ1²/σ2². If the interval excludes 1, variability likely differs at the chosen confidence level.
Use summary mode when you already know sample sizes and unbiased variances from another system, or when you cannot share raw data but can share aggregate statistics.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.