Bartlett's Test (Equality of Variances)
Computes Bartlett's test, the classic test for checking whether several groups share the same variance. It compares the pooled variance of all groups against the individual variances through a statistic that approximately follows a chi-square distribution, with a bias correction that improves the approximation in small samples. It's more powerful than Levene's test when the data are genuinely normal, but more sensitive to departures from normality. Enter the groups: values by comma, groups by semicolon.
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Bartlett's Test (Equality of Variances)
Computes Bartlett's test, the classic test for checking whether several groups share the same variance. It compares the pooled variance of all groups against the individual variances through a statistic that approximately follows a chi-square distribution, with a bias correction that improves the approximation in small samples. It's more powerful than Levene's test when the data are genuinely normal, but more sensitive to departures from normality. Enter the groups: values by comma, groups by semicolon.
The classic test of variance homogeneity
When you need to decide whether several groups share the same variance and you have good reason to believe the data are normal, Bartlett's test is the historical tool for the job. It predates Levene's test and is still the most powerful in that specific scenario: genuinely well-behaved data.
The statistic combines the variances of all groups into a pooled variance and measures how far the individual variances depart from it, on the logarithmic scale. There's also a correction factor, the constant C, that adjusts the approximation's bias in small samples. The result approximately follows a chi-square with degrees of freedom equal to the number of groups minus one.
Enter the groups with values by comma and groups by semicolon; each group needs at least two values and a positive variance. The tool returns the chi-square statistic and the degrees of freedom. A practical warning: Bartlett is sensitive to non-normality, so if the shape of the data is in doubt, prefer Levene's test.
Related Tools
Levene's Test (Equality of Variances)
Computes Levene's test, which checks whether several groups share the same variance — the homogeneity assumption that ANOVA and the t-test rely on. Instead of working with the original values, it transforms each data point into the absolute deviation from its group mean and runs an ANOVA on those deviations, gauging whether the spread differs across groups. It's more robust to non-normality than Bartlett's test. Enter the groups: values by comma, groups by semicolon.
F-Test for Equality of Variances
Computes the F-test for comparing the variances of two independent groups, checking whether they have the same spread. It's a common step before choosing between the classic t-test (which assumes equal variances) and Welch's (which doesn't). The statistic is the ratio of the two sample variances, and the F distribution, with its two degrees of freedom, provides the p-value. The tool takes the two samples and computes F, the degrees of freedom and the two-sided p-value. Enter the two groups of values.
Chi-Square Test of Independence
Computes the chi-square test of independence for a contingency table, checking whether two categorical variables are associated or independent. For example: does preference for a product depend on age group? The test compares the observed frequencies with those that would be expected if there were no relationship at all, and the chi-square statistic measures the size of that mismatch. The tool returns the statistic, the degrees of freedom and the p-value. Enter the table: columns by comma, rows by semicolon.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.