Nested ANOVA

Nested ANOVA is an analysis of variance for hierarchical designs in which clusters belong to only one group, testing group effects against between-cluster variation rather than individual-level error.

내포 분산분석은 군집이 한 집단에만 속하는 위계적 설계에서, 집단 효과를 개인 수준 오차가 아니라 군집 간 변동과 비교해 검정하는 분산분석이다.

Students are nested in classrooms and classrooms in teaching methods; how do I compare the methods correctly?

학생은 학급에, 학급은 교수법에 속해 있는데 교수법 효과를 어떻게 제대로 비교하나요?

Nested ANOVA splits the variation into differences among groups, among clusters within groups, and among individuals within clusters. The group effect is tested against the cluster-within-group mean square, so the number of clusters, not individuals, drives the effective sample size.

When to use Nested ANOVA

• Units such as patients, pupils or plants are measured within clusters assigned to one group each.
• Clusters are a random sample whose variability must be accounted for.
• The design is balanced or close to balanced.

When to use something else

• Clusters are crossed with groups so each cluster appears in several groups; use a two-way or mixed ANOVA.
• The design is strongly unbalanced or has covariates; use a linear mixed model with REML.

Assumptions and requirements

• Observations within clusters are independent.
• Cluster effects and residuals are normally distributed.
• Variances are equal across clusters.
• Each group contains at least two clusters.

What the analysis reports

• ANOVA table with group, cluster-within-group and residual rows
• F test of groups over the cluster-within-group mean square
• F test of clusters within groups
• Variance components for balanced designs

How to report it

A nested ANOVA showed a significant group effect, F([df_group], [df_cluster]) = [F], p = [p], and significant variation among clusters within groups, F([df_cluster], [df_error]) = [F2], p = [p2].

Related methods

• Hierarchical Linear Modeling (HLM)
• One way ANOVA
• Intraclass Correlation (ICC)

Run Nested ANOVA on Quorant