Bartlett's Test

Bartlett's test is a hypothesis test of whether two or more groups have equal population variances, comparing the pooled variance with the group variances under the assumption of normally distributed data.

바틀렛 검정은 자료가 정규분포를 따른다는 가정 아래 합동분산과 집단별 분산을 비교하여, 둘 이상의 집단의 모분산이 같은지를 검정하는 가설검정이다.

How do I test whether several normally distributed groups have the same variance?

정규분포를 따르는 여러 집단의 분산이 같은지 어떻게 검정하나요?

Bartlett's test checks the equal-variance assumption across two or more independent groups and has good power when each group is normally distributed. Because it is sensitive to non-normality, a significant result may reflect skewed data rather than unequal variances, in which case Levene's test is safer.

When to use Bartlett's Test

• Checking homogeneity of variance before ANOVA when groups are approximately normal
• Comparing variability itself, such as the precision of instruments or processes
• Two or more independent groups with a continuous outcome

When to use something else

• Skewed or heavy-tailed data: use Levene's test or the Brown-Forsythe test
• When the goal is only a robust mean comparison: use Welch's ANOVA or Welch's t-test without a variance pretest

Assumptions and requirements

• Normal distribution within each group
• Independent observations and independent groups
• Continuous outcome

What the analysis reports

• Bartlett's chi-square statistic
• p-value (df = k − 1)
• Number of groups k
• Normality check for each group
• Box plot of the outcome by group

How to report it

Bartlett's test indicated that variances did not differ significantly across groups, χ²([df]) = [value], p = [value].

Related methods

• Levene's Test
• Welch's ANOVA
• Shapiro-Wilk Test

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