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Nested one-way ANOVA (mixed model)

Nested ANOVA extends the nested t-test to k ≥ 2 groups, fitting the mixed model y ~ group + (1 | subject).

What is Nested one-way ANOVA (mixed model)?

When experimental units (subjects, dishes, classrooms) each contribute multiple observations and you want to compare k groups, ordinary one-way ANOVA on the pooled data has inflated type-I error. The nested ANOVA partitions variance into between-subject and within-subject components and tests the group effect at the appropriate level.

The LRT compares the full model (with group effect) to a null model (group dropped). The fixed-effect table reports k − 1 Wald-z rows for the group contrasts; pair with emmeans for full pairwise comparisons if needed.

When should I use Nested one-way ANOVA (mixed model)?

k-group comparison with replicate measurements per subject.
Classroom-level interventions with student-level outcomes.
Animal experiments with multiple readings per animal across treatment groups.

What data does it need?

Response + group (k ≥ 2 levels) + subject (random factor).

What does it report?

LRT χ² + (k − 1) Wald-z rows + variance components + ICC.

How do I interpret the result?

Significant omnibus LRT ⇒ at least one group differs; use post-hoc pairwise on the fixed effects for the comparisons of interest.