Analysis of Means (ANOM)

Analysis of means (ANOM) compares each group mean with the grand mean using decision limits, showing which specific groups are significantly above or below the overall average.

평균분석(ANOM)은 판정한계를 써서 각 집단 평균을 전체 평균과 비교하여, 어느 집단이 전체 평균보다 유의하게 높거나 낮은지 보여 주는 방법입니다.

Which of my production lines has a mean that differs from the overall average?

여러 생산 라인 중 어느 라인의 평균이 전체 평균과 다른지 알고 싶어요.

ANOM draws decision limits around the grand mean at h · s_p · √((N − n_i)/(N n_i)), where h is a critical value that accounts for the correlation among the group deviations from the grand mean. A group whose mean falls outside its limits differs from the overall average, which answers a different question from ANOVA's test that all means are equal.

When to use Analysis of Means (ANOM)

• You want to know which groups differ from the overall average rather than from each other.
• Quality or process data from several machines, lines or sites must be screened against the grand mean.
• You want a chart that presents the comparison graphically.

When to use something else

• You need all pairwise group comparisons; use Tukey HSD.
• Variances differ strongly between groups; use Welch's ANOVA followed by Games-Howell.

Assumptions and requirements

• Residuals are normally distributed.
• Variances are equal across groups.
• Observations are independent.

What the analysis reports

• Grand mean, pooled standard deviation and critical value h
• Lower and upper decision limits for each group
• Signal for each group (above, below or within)
• Chart of group deviations from the grand mean

How to report it

An analysis of means (α = .05, h = [value]) showed that [group] ([value]) fell [above/below] the decision limits around the grand mean of [value].

Related methods

• One-way ANOVA
• Dunnett's Test
• Tukey HSD Post Hoc Test

Run Analysis of Means (ANOM) on Quorant