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.
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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.
Equal variances, even with rebellious data
Testing whether several groups share the same variance is a common ANOVA prerequisite, and Levene's test is the usual tool. But classic Levene measures each point's distance from the group mean, and the mean is fragile against outliers and skewed distributions. When the data misbehave, that fragility contaminates the test.
Brown and Forsythe proposed a simple, powerful swap: use the group median, instead of the mean, as the reference point for measuring distance. The median barely moves in the face of extreme values, so the deviations computed from it are far more stable. On those deviations, you run the same analysis of variance as Levene, producing an F statistic with the usual degrees of freedom.
Enter the groups, with values separated by commas and groups by semicolons. The tool returns the W statistic, the degrees of freedom and the p-value. Because of its robustness, Brown-Forsythe is often the default recommendation whenever there's any doubt about the normality of the data, ranking ahead of both mean-based Levene and Bartlett's test.
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.
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.
Welch's t-test
Computes the Welch's t-test statistic, the two-sample t-test version that does NOT assume equal variances. Unlike the classic Student's t-test, it doesn't pool the variances into a single value, which makes it more reliable when the two groups have different spreads — the default recommendation in modern statistics. The degrees of freedom come from the Welch-Satterthwaite equation, usually fractional. Enter the mean, standard deviation and size of each of the two groups.
Paired t-Test
Computes the paired t-test, used when you measure the same subjects twice — before and after a treatment, or by two methods. It works with the differences of each pair and tests whether the mean difference is compatible with zero. By removing the variability between subjects, it's usually far more powerful than comparing two independent groups. The tool returns the t statistic, the degrees of freedom and the two-sided p-value. Enter the two paired series.
D'Agostino-Pearson Normality Test (K²)
Computes the D'Agostino-Pearson omnibus normality test, which combines two clues of non-normality into a single verdict: skewness (do the data lean to one side?) and kurtosis (are the tails too heavy or too light?). Each becomes a standardized z score, and the sum of their squares, the K² statistic, follows a chi-square with 2 degrees of freedom. It's more informative than looking at skewness and kurtosis separately. Enter the sample (at least 8 values).
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