Glossary

Independent and Identically Distributed (IID)

IID is a foundational assumption requiring that observations are mutually independent and drawn from the same probability distribution. When the IID assumption is violated, specialised techniques such as block bootstrapping or HAC standard errors are needed.

Definition

Why It Matters

The IID assumption underpins the validity of standard errors, confidence intervals, and hypothesis tests. If observations are correlated (as in time-series data) or come from different populations (as in stratified samples), treating them as IID leads to underestimated standard errors, inflated test statistics, and false discoveries. Recognising when IID holds and when it does not is one of the most important diagnostic judgments in applied research, guiding the choice between ordinary regression, panel methods, time-series models, or clustered inference.

Example

A researcher surveys 500 individuals selected randomly from a national population. If each person responds independently and the sampling frame ensures identical probabilities of selection, the observations are approximately IID, and standard t-tests and regression apply. However, if the survey is conducted in 20 schools and students within the same school share similar characteristics, the independence assumption is violated, requiring clustered standard errors or multilevel models.

Related Terms

Software Notes

SPSS: IID is assumed by default in most procedures; test independence using Analyze > Correlate > Autocorrelation for time-series data
R: IID is the default in lm() and t.test(); use vcovHC() from the sandwich package for non-IID standard errors, or lme4 for mixed-effects models
Stata: IID is assumed by default; use vce(cluster clustvar) for clustered standard errors, or newey for HAC standard errors