MANOVA

MANOVA (multivariate analysis of variance) is a test of whether group means differ on two or more correlated continuous outcomes considered jointly.

다변량분산분석(MANOVA)은 서로 상관된 두 개 이상의 연속형 결과변수를 함께 고려하여 집단 간 평균이 다른지를 검정하는 방법이다.

How do I test whether groups differ on several outcome variables at once?

여러 결과변수에서 집단 간 차이가 있는지 한 번에 어떻게 검정하나요?

MANOVA tests whether groups differ on a combination of two or more continuous outcomes while accounting for their correlation, giving a single omnibus test of the overall null hypothesis. It fits when the outcomes are conceptually related, and a significant result is best followed by descriptive discriminant analysis or by univariate ANOVAs with their own multiplicity adjustment, because a significant MANOVA does not by itself control the error rate of those follow-up tests.

When to use MANOVA

• Two or more related continuous outcomes compared across groups
• Outcomes that are moderately correlated, such as subscales of one construct
• Wanting one overall test before examining individual outcomes

When to use something else

• A single outcome; use one-way ANOVA
• Strongly non-normal outcomes or very unequal covariance matrices in small samples; consider PERMANOVA

Assumptions and requirements

• Independent observations
• Multivariate normality of outcomes within groups
• Homogeneity of covariance matrices (Box's M test)
• No severe multicollinearity among outcomes

What the analysis reports

• Pillai's trace, Wilks' lambda, Hotelling's trace and Roy's largest root
• Approximate F, degrees of freedom and p-value
• Partial eta-squared
• Follow-up univariate ANOVAs

How to report it

There was a significant multivariate effect of [group] on the combined outcomes, Pillai's trace = [value], F([df1], [df2]) = [value], p = [value], partial η² = [value].

Related methods

• One-Way ANOVA
• Discriminant Analysis
• PERMANOVA

Run MANOVA on Quorant