Estimated Marginal Means and Simple Effects

Estimated marginal means are model-based cell and factor-level means from a factorial or ANCOVA model, averaged with equal weights over the other factors, used to test simple effects and pairwise contrasts.

추정 주변평균은 요인설계나 공분산분석 모형이 추정한 칸평균을 다른 요인 수준에 같은 가중치로 평균한 값으로, 단순효과와 짝 비교 검정에 쓰입니다.

My two-way ANOVA shows an interaction; how do I test the effect of one factor at each level of the other?

이원분산분석에서 상호작용이 유의한데, 한 요인의 효과를 다른 요인의 수준별로 어떻게 검정하나요?

Fit the full factorial model, compute the model-based mean of every cell, and test the effect of one factor separately within each level of the conditioning factor using the pooled error from the whole model. Pairwise differences within each level are then adjusted for multiplicity, and interaction contrasts show which differences of differences drive the interaction.

When to use Estimated Marginal Means and Simple Effects

• A two-way or three-way factorial ANOVA has a significant interaction and you need to break it down.
• Cell sizes are unequal and you want means that are not weighted by cell size.
• You want group means adjusted for a covariate (ANCOVA) and their pairwise comparisons.

When to use something else

• There is a single factor without covariates; use one-way ANOVA with Tukey HSD.
• Variances differ strongly across cells; use Games-Howell comparisons or a robust model.

Assumptions and requirements

• Residuals are normally distributed with equal variance across cells.
• Observations are independent.
• Every combination of factor levels has at least one observation.
• Covariates have a linear, common-slope relation with the outcome.

What the analysis reports

• Model-based cell means and factor-level marginal means with standard errors and confidence intervals
• Simple-effect F test of the effect factor at each level of the by factor
• Pairwise comparisons within each level with Holm, Bonferroni or Tukey adjustment
• Interaction contrasts (differences of differences) and the omnibus interaction F test

How to report it

The [A] × [B] interaction was significant, F([df1], [df2]) = [value], p = [value]. At [A] = [level], the simple effect of [B] was significant, F([df1], [df2]) = [value], p = [value]; [level 1] exceeded [level 2] by [value] (SE = [value]), adjusted p = [value].

Related methods

• Two-way ANOVA
• ANCOVA
• Tukey HSD Post Hoc Test

Run Estimated Marginal Means and Simple Effects on Quorant