Bartlett's Test Calculator

Test variances, not group means

Bartlett’s test evaluates the null that independent groups have equal population variances. Enter at least two finite observations per group and at least two groups. The test requires positive group variances and is sensitive to non-normal distributions.

The tool reports each group size, variance and SD, the pooled variance, a corrected log-variance statistic, df=k−1, and the approximate chi-square upper-tail p-value. Group labels and entered observations are not included in analytics.

A reproducible small example

For groups 1,2,3, 2,4,6, 3,6,9, sample variances are 1,4,9 and the pooled variance is 4.6667. Bartlett’s statistic is approximately 1.6982, df=2, and p≈0.4278.

With three observations per group the test has limited information. Non-rejection does not prove equal variances or verify an ANOVA assumption. Likewise, rejection can reflect departures from normality as well as variance differences.

Choose the analysis for the substantive question

Do not make a preliminary variance test the sole gatekeeper between pooled and Welch t-tests. For unequal-variance mean comparisons, consider a suitable Welch method directly. Robust variance tests such as Levene or Brown–Forsythe answer a variance question using a different procedure; this calculator does not implement them.

For a group-mean question, inspect the collection design, distributions and purpose of the analysis. A clean variance-test result cannot establish independent observations or causal identification.

Continue

Read ANOVA or use the one-way ANOVA calculator. NIST documents Bartlett’s statistic and its sensitivity.