MANCOVA

MANCOVA is a multivariate general linear model that tests whether groups differ on several dependent variables jointly after adjusting for one or more continuous covariates.

MANCOVA는 하나 이상의 연속형 공변량을 통제한 뒤 여러 종속변수에서 집단 차이가 함께 나타나는지를 검정하는 다변량 일반선형모형입니다.

Do my groups differ on several outcomes together once I control for a baseline covariate?

기저 공변량을 통제했을 때 여러 결과변수에서 집단 간 차이가 있나요?

MANCOVA fits all dependent variables at once with group effects and covariates and tests the adjusted group effect with Wilks' lambda, Pillai's trace, the Hotelling-Lawley trace and Roy's largest root. Covariate-adjusted means, univariate ANCOVA follow-ups and a test of homogeneous regression slopes help interpret the result.

When to use MANCOVA

• Comparing groups on two or more correlated continuous outcomes
• A continuous covariate such as a baseline score should be controlled
• You want a single multivariate test before univariate follow-ups

When to use something else

• There is only one outcome: use ANCOVA
• Regression slopes clearly differ by group: model the group-by-covariate interaction instead

Assumptions and requirements

• Multivariate normal residuals and independent observations
• Homogeneous covariance matrices across groups (Box's M on residuals is reported)
• Homogeneous regression slopes (group-by-covariate test is reported)
• Linear relationships between covariates and outcomes

What the analysis reports

• Wilks' lambda, Pillai's trace, Hotelling-Lawley trace and Roy's root with F approximations
• Multivariate tests for each covariate
• Partial eta squared from Wilks' lambda
• Univariate ANCOVA F for each outcome and covariate-adjusted group means

How to report it

A one-way MANCOVA on [p] dependent variables controlling for [covariate] (N = [n]) showed a significant multivariate effect of group, Wilks' Λ = [value], F([df1], [df2]) = [value], p = [value], partial η² = [value].

Related methods

• MANOVA
• ANCOVA
• Profile Analysis (Repeated-Measures MANOVA)

Run MANCOVA on Quorant