nonindependence

Nonindependence refers to a situation in which observations are correlated or otherwise related, so they cannot be treated as independent draws. It is a property of the data structure, not of any single observation. Common contexts include repeated measurements on the same subject, individuals within families or classrooms, spatially proximate measurements, and observations linked by social networks or dyadic relationships.

Because many statistical methods assume independence, nonindependence can bias standard errors and test statistics, leading to inflated or deflated type I or type II error rates and unreliable inference. It can also affect parameter estimates when the correlation is related to covariates.

Approaches to analysis include mixed-effects or multilevel models with random effects to model clustering, generalized estimating equations with robust standard errors, and explicit correlation structures. Other options include Bayesian hierarchical models, spatial econometric methods, dyadic or network models, block bootstrap, or permutation tests designed to preserve dependence.

Design strategies such as proper randomization, blocking, or clustering at the data collection stage can mitigate nonindependence. Understanding the source of dependence is essential for selecting an appropriate method.