Compare spread across multiple samples with median-based robustness. Review deviations, F statistic, p-value, interpretation, exports, and clear graph outputs instantly.
| Observation | Group A | Group B | Group C |
|---|---|---|---|
| 1 | 11 | 10 | 9 |
| 2 | 12 | 11 | 10 |
| 3 | 12 | 12 | 10 |
| 4 | 13 | 12 | 11 |
| 5 | 14 | 12 | 11 |
| 6 | 15 | 13 | 12 |
| 7 | 15 | 25 | 12 |
This example shows three groups, with Group B containing an outlier. The test checks whether dispersion differs after centering each group by its median.
The Brown-Forsythe test is a robust variance homogeneity test. It replaces each original observation with its absolute deviation from the group median.
Step 1: For group i and observation j, compute:
Zij = |Xij - Median(Xi)|
Step 2: Run a one-way ANOVA on the transformed values Zij.
Between-group sum of squares:
SSB = Σ ni(Z̄i - Z̄)2
Within-group sum of squares:
SSW = ΣΣ(Zij - Z̄i)2
Mean squares:
MSB = SSB / (k - 1)
MSW = SSW / (N - k)
Test statistic:
F = MSB / MSW
The p-value comes from the F distribution with k - 1 and N - k degrees of freedom.
It tests whether multiple groups have equal variability. It does this by comparing absolute deviations from each group median, then applying an ANOVA framework.
Levene’s test often uses deviations from the group mean. Brown-Forsythe uses the group median, making it more resistant to outliers and skewed data.
Use it before comparing group means when you want to assess homogeneity of variance, especially if your samples may contain outliers or non-normal distributions.
The null hypothesis states that all compared groups have equal variances. A small p-value suggests at least one group differs in spread.
This page supports two to six groups in one run. Each group should contain at least two valid numeric observations.
No. The Brown-Forsythe procedure works with unequal group sizes, although very small groups can reduce statistical reliability and interpretability.
A significant result means the data provide evidence that dispersion is not equal across groups. It does not identify which group differs most by itself.
Yes. That is one reason this method is popular. Median-based centering makes it more robust than mean-based variance tests under skewness and outliers.