Robust Factorial ANOVA on Trimmed Means

Robust factorial ANOVA on trimmed means tests main effects and interactions in two- or three-way between-subjects designs using cell trimmed means, Winsorized variances and a heteroscedastic Johansen-type statistic.

절사평균 강건 요인 분산분석은 칸별 절사평균과 윈저화 분산, 이분산 Johansen 형 통계량으로 2·3원 피험자 간 설계의 주효과와 상호작용을 검정하는 방법입니다.

My two-way design has outliers and unequal variances across cells; is there a robust alternative to the factorial ANOVA?

이원 설계 자료에 이상치가 있고 칸마다 분산이 달라요. 요인 분산분석 대신 쓸 강건한 방법이 있나요?

Compute the 20% trimmed mean and Winsorized squared standard error in each cell and test each effect with a Johansen-type quadratic form that does not assume equal variances. Main-effect levels can then be compared with trimmed-mean contrasts using Welch degrees of freedom.

When to use Robust Factorial ANOVA on Trimmed Means

• You have a two- or three-way between-subjects design with outliers or heavy tails.
• Cell variances are unequal.
• You want tests of main effects and interactions on trimmed means rather than means.

When to use something else

• The design is one-way; use the robust ANOVA on trimmed means (one-way) instead.
• Factors are within-subject; a robust repeated-measures or mixed approach is needed instead.

Assumptions and requirements

• Independent observations.
• Every cell has enough cases (at least about 10 recommended) after trimming.
• Factors are fully crossed with no empty cells.

What the analysis reports

• Johansen Q statistic, df, adjustment term A, critical value and p for each main effect and interaction
• Pairwise trimmed-mean contrasts for main-effect levels with Welch df and Holm-adjusted p
• Cell sizes, trimmed means and squared standard errors

How to report it

A robust two-way ANOVA on 20% trimmed means showed a main effect of [factor], Q = [value], p = [value], and no [factor] x [factor] interaction, Q = [value], p = [value].

Related methods

• Robust ANOVA on Trimmed Means
• Two Way ANOVA
• Yuen's Trimmed Means t Test

Run Robust Factorial ANOVA on Trimmed Means on Quorant