Levene Test Calculator — Equal Variances

The Levene Test. Levene's test asks whether two or more independent groups show the same population spread. It turns that question into a familiar one-way ANOVA. Keep each observation in its original group. This page accepts two to twelve groups, at least two finite values per group, and a pre-specified alpha. For every group, compute its own arithmetic mean. Then replace each observation by its absolute distance from that group mean. Large absolute deviations mean wide spread; small deviations mean tight spread. Location differences disappear because every group is centered separately. Run ordinary one-way ANOVA on the deviation groups. The resulting F statistic is conventionally called W, with degrees of freedom k minus one and N minus k. Only the upper F tail matters. The omnibus alternative is that at least one spread differs, not a choice between numerical left and right directions. A rejection says spread differs somewhere. It does not identify which pair differs, and this calculator offers no post-hoc spread comparisons or variance-ratio interval.

This calculator uses the arithmetic mean center and suits roughly symmetric, moderate tailed groups. The default setting in Sci Py uses the median instead. For skewed or outlier-prone data, use the separate Brown-Forsythe test. Its median center is usually less sensitive to a single extreme value. A nonsignificant result does not prove equal variances. Small groups may miss important spread differences, so read the sample standard deviations and raw shapes too. Variance equality is not distribution equality. Groups can share a variance while differing in skew, tails, mixtures, or other features of shape. Levene also cannot repair dependent observations, clusters, repeated measures, wrong group labels, selection bias, or measurements recorded on incomparable scales. Do not use a preliminary p-value as an automatic switch between pooled and Welch mean tests. Pre-specifying Welch often avoids that unstable two-stage ritual. Use Levene when spread itself matters scientifically or when a documented symmetric-data diagnostic is wanted. Keep practical magnitude separate from significance.

Now compare three machines with seven, six, and eight measurements, twenty-one observations total, using alpha point zero five. The group means are thirteen point two seven one, eighteen point three eight three, and fifteen point three three eight. Each machine gets its own center. Their sample standard deviations are about one point one nine three, one point four zero eight, and point seven four six. Machine three looks tightest. After taking absolute deviations, the transformed group means are point nine one zero, one point zero two two, and point six one three. ANOVA on those deviations gives W equal to point seven nine eight five, with numerator degrees of freedom two and denominator degrees of freedom eighteen. The point zero five upper-tail critical value is three point five five five. The observed W remains well below that boundary. The p-value is point four six five, above alpha. Fail to reject a common population spread; do not rewrite that conclusion as proof of equality.

Add one hundred to every Machine One value and nothing changes. Group-specific shifts preserve every absolute deviation, W, and p-value. Multiply Machine Two by two and its spread doubles. Here W becomes three point seven zero nine and p falls to point zero four four eight. Replace one Machine One value by forty and mean-centered Levene rejects at p point zero two nine nine, while Brown-Forsythe remains nonsignificant at point three four three. Give three groups the identical shape but shift their locations far apart. W becomes essentially zero and p equals one because spread, not mean, is the target. Validation stops fewer than two or more than twelve groups, undersized groups, nonfinite values, invalid alpha, and zero within-group variability among deviations. Report the independent-group design, center choice, group sizes and standard deviations, W, both degrees of freedom, upper-tail p, alpha, and shape or power cautions. Use Brown-Forsythe for skew, the two-group F test only under strong normality, and Welch for unequal-variance mean comparisons. Run the Levene Test free at Distri Scope dot com.