Variance Components Analysis (Random-Effects ANOVA)

Variance components analysis splits the total variance of an outcome into a between-group part and a within-group part by treating the groups as a random sample from a larger population.

분산성분 분석은 집단을 더 큰 모집단에서 뽑은 무작위 표본으로 보고, 결과변수의 전체 분산을 집단 간 분산과 집단 내 분산으로 나누어 추정하는 방법입니다.

How much of the variation in my measurements comes from differences between batches rather than within batches?

측정값의 변동 중 로트(배치) 간 차이에서 오는 부분이 얼마나 되는지 알고 싶어요.

Variance components analysis fits a random-effects model in which each group adds its own random shift, and estimates the variance of those shifts and of the residual by REML or by ANOVA mean squares. The share of the group variance in the total, the intraclass correlation, says how strongly observations from the same group resemble each other.

When to use Variance Components Analysis (Random-Effects ANOVA)

• Groups such as batches, sites or raters are a sample from a larger set and you want to generalise to that set.
• You need to know which level of a nested design (for example plants within farms) contributes most variation.
• You want an intraclass correlation with a confidence interval from a one-way layout.

When to use something else

• The groups are the only ones of interest and you want to compare their means; use one-way ANOVA.
• You have repeated measures with predictors at several levels; use a linear mixed model.

Assumptions and requirements

• Random group effects and residuals are independent and normally distributed.
• The residual variance is the same in every group.
• Groups are sampled independently of each other.

What the analysis reports

• Variance of each random component with its percentage of the total (REML and ANOVA estimates side by side)
• ANOVA table with F test of a zero group variance
• Intraclass correlation with F-based confidence interval (one-way design)
• Satterthwaite interval for the group variance and chi-square interval for the residual variance (one-way design)
• Two-stage nested design: variance of the upper level, the nested level and the residual

How to report it

A one-way random-effects model attributed [value]% of the variance to [group] (σ²_group = [value], σ²_error = [value]; ICC = [value], 95% CI [[value], [value]]), F([df1], [df2]) = [value], p = [value].

Related methods

• Intraclass Correlation (ICC)
• Nested ANOVA
• Hierarchical Linear Modeling (HLM)

Run Variance Components Analysis (Random-Effects ANOVA) on Quorant