F-Test for Equality of Variances
Computes the F-test for comparing the variances of two independent groups, checking whether they have the same spread. It's a common step before choosing between the classic t-test (which assumes equal variances) and Welch's (which doesn't). The statistic is the ratio of the two sample variances, and the F distribution, with its two degrees of freedom, provides the p-value. The tool takes the two samples and computes F, the degrees of freedom and the two-sided p-value. Enter the two groups of values.
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F-Test for Equality of Variances
Computes the F-test for comparing the variances of two independent groups, checking whether they have the same spread. It's a common step before choosing between the classic t-test (which assumes equal variances) and Welch's (which doesn't). The statistic is the ratio of the two sample variances, and the F distribution, with its two degrees of freedom, provides the p-value. The tool takes the two samples and computes F, the degrees of freedom and the two-sided p-value. Enter the two groups of values.
Do two groups have the same spread?
Before comparing two groups' means with a t-test, there's a hidden decision: are the groups' variances similar? The answer changes which version of the t-test to use. The F-test for equality of variances answers that question directly, comparing how much each group spreads around its own mean.
The statistic is simply the ratio of the two sample variances. If the groups had the same spread, that ratio would sit near 1; the further it strays from 1, in either direction, the stronger the evidence that the variances differ. The reference distribution is the F, which depends on two degrees of freedom, one per sample, and the p-value comes from the two tails.
Enter the two samples and the tool returns the F statistic, the degrees of freedom and the two-sided p-value. A practical warning: the F-test is sensitive to non-normality, more so than the very t-test it usually precedes. When the shape of the distribution is in doubt, Levene's or Bartlett's tests are more robust alternatives.
Related Tools
Levene's Test (Equality of Variances)
Computes Levene's test, which checks whether several groups share the same variance — the homogeneity assumption that ANOVA and the t-test rely on. Instead of working with the original values, it transforms each data point into the absolute deviation from its group mean and runs an ANOVA on those deviations, gauging whether the spread differs across groups. It's more robust to non-normality than Bartlett's test. Enter the groups: values by comma, groups by semicolon.
Bartlett's Test (Equality of Variances)
Computes Bartlett's test, the classic test for checking whether several groups share the same variance. It compares the pooled variance of all groups against the individual variances through a statistic that approximately follows a chi-square distribution, with a bias correction that improves the approximation in small samples. It's more powerful than Levene's test when the data are genuinely normal, but more sensitive to departures from normality. Enter the groups: values by comma, groups by semicolon.
Brown-Forsythe Test (Variances)
Computes the Brown-Forsythe test, a robust version of Levene's test for checking whether several groups share the same variance. The difference lies in one decisive detail: instead of measuring how far each point sits from the group mean, it uses the distance from the median. Because the median resists extreme values and skewed distributions, the test becomes much more reliable when the data aren't normal. Enter the groups: values by comma, groups by semicolon.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.