Independence Assumptions Guide

Every standard statistical test assumes independent observations. Independence means that knowing the value of one observation provides no information about the value of another. In real experiments, this assumption is routinely violated by design — clustered observations, hierarchical data structures, and longitudinal measurements are all forms of non-independence. In the current product, independence-related concerns are handled across multiple related checks rather than by a single formal independence test.

STEP 1 —The Pitfall

Independence violations take many forms: patients from the same clinic are more similar than patients from different clinics (clustering); animals from the same litter share genetic and environmental factors (nesting); measurements from the same subject over time are autocorrelated (longitudinal structure). When non-independence is ignored, standard errors are too small, confidence intervals are too narrow, and p-values are artificially inflated.

The magnitude of the effect depends on the intraclass correlation coefficient (ICC): how similar observations within a cluster are relative to observations across clusters. An ICC of 0.1 is considered moderate; an ICC of 0.3 effectively requires the sample size to double to maintain the same power as an independent design.

STEP 2 —Journal Requirement

Clustered data must be analyzed with hierarchical models, generalized estimating equations (GEE), or cluster-robust standard errors. This is explicitly required by CONSORT for cluster-randomized trials, by STROBE for multi-site observational studies, and by most methods-oriented journals for any data with a detectable clustering structure.

STEP 3 — What Licklider Currently Provides

How independence is handled in the current product

Independence is not handled by a single formal test or a single checker. Instead, several related checks and gates surface independence-related risks across different surfaces:

• Pseudoreplication risk — Card 17 flags possible pseudoreplication when observation structure suggests non-independent samples, and asks for user confirmation via sampling_independence_status.
• Paired vs. independent decision — Card 1 asks the user to confirm whether a comparison should be treated as paired or independent via paired_mode.
• Temporal dependence — Card 20 surfaces temporal dependence as a separate concern when timepoint structure is present.
• Repeated-measures guidance — analysis_model_guidance_branch can suggest repeated-measures or mixed-model alternatives when the analysis context warrants it.
• Batch / plate confounding — batchConfounding summarizes structural risk from contract columns and row distribution.

Confirmations and disclosures are distributed across cards and snapshot state. Unresolved independence-related concerns can affect export-facing status for claim-bearing output.

What the product does not do

• The product does not compute ICC, effective sample size, or lag-1 autocorrelation.
• The product does not automatically recommend GEE, cluster-robust standard errors, or specific mixed-model specifications based on clustering structure.
• There is no single independence score or unified independence checker.

Known limitations

Independence wording in docs should stay cautious because the implementation is distributed across several surfaces. Each related check has its own confidence level and resolution state. Readers should review the individual check pages (pseudoreplication, paired vs. unpaired, repeated measures, batch confounding) rather than treating this page as a claim that one comprehensive independence test exists.

For the detailed quality-checks documentation, see Statistical Independence Check in the quality-checks docs.

STEP 4 — Draft Output (Draft / Needs review)

The following is an example of how a researcher might write an independence-related methods section, not output that Licklider generates automatically.

Patients were enrolled from 6 clinical sites (mean cluster size = 20
patients per site). The intraclass correlation coefficient (ICC) for
the primary outcome across sites was 0.31, indicating moderate
clustering. Analysis was performed using generalized estimating equations
(GEE) with an exchangeable correlation structure to account for within-site
correlation. Robust standard errors are reported.