Bartlett's Test

Bartlett's Test — check the equal-variance assumption behind ANOVA and the pooled t-test, right on your phone.

Many classic tests assume every group has the same spread (variance). Bartlett's test is the normal-theory way to check it: do your groups really share one common variance, or is one of them far more erratic than the rest? Enter your data and get a clear verdict in seconds.

WHAT YOU CAN DO
• Enter 2 to 6 groups of values and run Bartlett's test instantly.
• Read the verdict in plain language: variances look equal, or the assumption fails.
• See each group's mean, variance and standard deviation in a clean table.
• Get the full numbers: Bartlett's chi-square statistic, degrees of freedom, the p-value, the pooled variance, the Bartlett correction C and the max/min SD ratio.

SEE IT, DON'T JUST READ IT
• Per-group variance bars compared against the pooled variance line.
• Spread bands that show each group on a shared axis.
• The chi-square curve with the 5% rejection tail and your statistic marked on it.

EXPLORE AND LEARN
• Idea — why equal variances matter, with the pooled-variance formula and the statistic, rendered with offline KaTeX (no internet needed for the math).
• Simulate — keep every group's mean identical and stretch just one group's spread. Type a value, tap the − / + steppers, or drag the slider, and watch the test light up on variance alone.
• Cases — worked, real-world style examples: erratic filling machines, well-behaved labs, and one wildly variable group.

THE MATH
• Pooled variance: Sp² = Σ(nᵢ−1)·sᵢ² / (N−k)
• Statistic: χ² = [(N−k)·ln Sp² − Σ(nᵢ−1)·ln sᵢ²] / C, with the Bartlett correction C
• Degrees of freedom k−1, with the p-value from the chi-square distribution

WHO IT'S FOR
Students, teachers, researchers, QA and quality-control engineers, data analysts — anyone who needs to justify (or question) the equal-variance assumption before running ANOVA or a t-test. Tip: Bartlett's test assumes roughly normal data; Levene's test is the robust alternative for non-normal data.

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