An ANOVA on distances
Levene's test checks whether groups share a common variance, by a manoeuvre worth learning in its own right: transform the data into spread data, then test means as usual. Replace each value by its absolute distance from its group's centre, and groups with wider spreads now have larger transformed values. An ordinary one-way ANOVA on those distances does the rest. The null hypothesis is equal variances; a small p-value says the spreads differ more than chance explains.
Three filling machines, five bottles each: A reads 10, 11, 12, 13, 14 (SD 1.58); B reads 2, 8, 14, 20, 26 (SD 9.49); C reads 9, 11, 13, 15, 17 (SD 3.16). The means are close; the spreads are obviously not. Distances from group medians, then ANOVA: the calculator reports the F and p for these groups directly above. Brown-Forsythe centring on medians is doing the work, so machine B's extreme bottles inflate its distances without hijacking the centre the distances are measured from.
Median or mean centring
Levene's original 1960 test centres on group means. The Brown-Forsythe variant centres on medians, and it is the version to use by default: spread questions arise exactly where data are skewed or heavy-tailed, and a mean centre gets dragged by the same extremes whose spread you are measuring, corrupting the distances. The calculator offers both so you can see the difference on your own data; on clean symmetric data they nearly agree, and on messy data the gap is the lesson.
Treating a non-significant Levene test as proof the variances are equal, then proceeding as if certified. With small samples the test has little power; it fails to detect differences that matter. Use it as a smoke alarm, not a structural inspection, and prefer designs and tests that tolerate unequal variances when in doubt.
Frequently asked questions
What is the difference between Levene and Brown-Forsythe?
The centre. Levene measures distances from group means; Brown-Forsythe from group medians. The median version holds up far better on skewed data and is the recommended default.
What do I do when Levene's test is significant?
It tells you variances differ; it does not fix anything. Switch to procedures that allow it: Welch's t-test or Welch ANOVA, a transformation, or a nonparametric route, depending on the question.
Is Bartlett's test better?
Only when the data are close to normal, where it is more powerful. It is notoriously sensitive to non-normality itself, which is why Levene-type tests are the routine choice.