Scheffé's Test

Scheffé's test is a post hoc procedure following a significant ANOVA that tests all possible contrasts among group means, including complex contrasts, while controlling the familywise error rate.

Scheffé 검정은 분산분석이 유의한 뒤 집단 평균 간 복합 대비를 포함한 모든 가능한 대비를 검정하면서 전체 1종 오류율을 통제하는 사후검정이다.

Which post hoc test should I use after ANOVA if I want to test complex comparisons between group means?

분산분석 후 집단 평균 간 복합 비교를 검정하려면 어떤 사후검정을 써야 하나요?

Scheffé's test is a post hoc method that controls the familywise error rate for every possible linear contrast among group means, not just pairwise differences. It fits when you want to compare combinations of groups, such as the average of two treatments against a control, after a significant ANOVA.

When to use Scheffé's Test

• After a significant one-way ANOVA with three or more groups
• Testing complex contrasts such as (A + B)/2 versus C
• Unplanned comparisons chosen after looking at the data

When to use something else

• Only pairwise comparisons are needed: use Tukey's HSD, which has more power
• Group variances are unequal: use Welch-type (Brown–Forsythe) contrasts with separate variance estimates, or the Games–Howell test if only pairwise comparisons are needed

Assumptions and requirements

• Assumptions of the preceding ANOVA (independence, normality, equal variances)
• Independent groups
• Continuous outcome

What the analysis reports

• Mean differences or contrast estimates
• Scheffé-adjusted p-values
• Simultaneous confidence intervals
• Homogeneous subsets of groups

How to report it

Scheffé post hoc tests showed that [group A] (M = [value], SD = [value]) scored significantly higher than [group B] (M = [value], SD = [value]), p = [value].

Related methods

• Tukey's HSD Test
• Bonferroni Correction
• Games-Howell Test

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