Test whether multiple normally distributed groups have equal population variances, with detailed calculations and exportable results.
For k independent groups, Bartlett's test combines the sample variances into a pooled variance.
The corrected test statistic is:
Under the null hypothesis, the statistic is approximated by a chi-square distribution with k − 1 degrees of freedom.
Bartlett's test evaluates whether several independent populations can reasonably be treated as having equal variances. Equal variance is an important assumption for many classical procedures, including some versions of analysis of variance and pooled-variance methods. The null hypothesis states that all population variances are equal. The alternative states that at least one population variance differs.
The calculation starts with each group's sample size and sample variance. Those variances are combined into a pooled estimate. The procedure then compares the logarithm of that pooled variance with a weighted combination of the logarithms of each group variance. A correction factor adjusts the statistic for finite sample sizes. The resulting Bartlett statistic is compared with a chi-square distribution using one fewer degree of freedom than the number of groups.
A small p-value indicates that the observed variance differences would be unusual if all population variances were truly equal. When the p-value is lower than the selected significance level, the null hypothesis is rejected. A larger p-value does not prove equal variances. It means the available sample does not provide enough evidence to conclude that the variances differ.
Bartlett's test is especially sensitive to departures from normality. Skewed distributions, heavy tails, or strong outliers can produce significant results even when variance equality is not the main issue. Samples should also be independent, and every group needs at least two observations with positive sample variance. When normality is doubtful, Levene's test or the Brown–Forsythe test is often more robust.
Use the result alongside graphs, descriptive statistics, and subject-matter knowledge. A statistically significant result may reflect a small variance difference in very large samples. Conversely, small samples can miss important differences. Report the Bartlett statistic, degrees of freedom, p-value, sample sizes, and the chosen significance level. This gives readers enough information to understand the decision and reproduce the analysis.
| Group | Example values | What is compared |
|---|---|---|
| Group A | 10, 12, 9, 11, 13 | Sample variance |
| Group B | 8, 7, 9, 10, 6 | Sample variance |
| Group C | 15, 14, 16, 13, 17 | Sample variance |
It tests whether independent populations have equal variances using sample variance information.
The null hypothesis states that every population represented by the groups has the same variance.
Reject it when the calculated p-value is lower than your selected significance level.
You can calculate it, but interpretation may be unreliable because Bartlett's test is sensitive to non-normality. Levene's or Brown–Forsythe tests may be preferable.
Yes. Choose the summary statistics mode and select sample standard deviation.
No. It only indicates insufficient evidence to reject the equal-variance null hypothesis.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.