intraklustkorrelation

Intraklustkorrelation, often abbreviated ICC, is a statistic used to describe how strongly units within the same cluster resemble each other. It measures the proportion of total variance in an outcome that is attributable to differences between clusters rather than within clusters. ICC is central to clustered study designs, multilevel models, and meta-analytic approaches, as it informs the degree of similarity of observations inside the same group.

In a simple random-intercept model, Var(Y) can be decomposed into between-cluster and within-cluster components: Var(Y) = σ²_between + σ²_within. The intraklustkorrelation is defined as ICC = σ²_between / (σ²_between + σ²_within). Different forms of ICC arise under various modeling assumptions (for example, one-way or two-way models) and can be estimated from variance components in mixed-effects models or from ANOVA.

Estimation methods include linear mixed-effects models for continuous outcomes and generalized linear mixed models for non-normal outcomes. The ICC has practical interpretations: it describes how similar outcomes are within clusters and helps quantify the expected similarity in repeated measures or grouped data.

A key implication of the ICC is its effect on study design. The design effect is DEFF = 1 + (m − 1) × ICC, where m is the average cluster size. A higher ICC increases the required sample size to achieve a given precision and reduces the effective sample size due to clustering.

Applications of intraklustkorrelation include education (students within schools), healthcare (patients within clinics), and survey research with clustered sampling. Values of ICC vary by context and outcome, with higher values indicating stronger clustering and greater impact on statistical inference.