Statistical association

A statistical association is a systematic dependence between variables. It need not represent a causal effect, because it may arise from confounding, selection, or reverse causation.

A correlation coefficient computed from ranks, measuring monotone association. Ties need a stated ranking convention. A strong nonlinear but monotone relationship can have a strong Spearman rank correlation even when a straight-line summary in the original units is inappropriate.

A model-based correlation for ordered categories, commonly estimated by treating the categories as thresholded versions of continuous jointly normal latent responses. Sparse categories and departures from that latent-response model can make estimates unreliable; using it does not remove the need for adequate data.

The elaboration model compares a pooled statistical association with the associations conditional on a third variable. Replication describes a similar pattern within the strata. Specification describes a relationship whose size or direction varies between strata. Attenuation can suggest explanation by an antecedent confounder, or interpretation through an intervening causal mediator. These causal readings require justified temporal and causal assumptions; conditional tables alone do not identify the third variable's role.^[ref]

Assess the patterns through conditional probabilities or comparable effect sizes. Different p-values also reflect different sample sizes and standard errors, so significant and nonsignificant results need not differ significantly.

An observational study measures exposures and outcomes without assigning the exposure by an intervention. Its causal interpretation therefore requires assumptions that address confounding and selection bias.

A case–control study selects subjects according to an outcome: cases have the outcome and controls represent an appropriate comparison population. It compares their prior exposures or genetic variants to study association. Its retrospective sampling must be accounted for when interpreting risks; selection bias and confounding can distort an unadjusted association. In genetics, matched family pseudo-control genotypes can replace unrelated controls for a conditional transmission disequilibrium test.

A longitudinal study observes the same individuals repeatedly. Within-person changes distinguish temporal development from persistent differences between people, although calendar-period changes, selective dropout and measurement error still require attention. A random-intercept linear mixed model can represent persistent individual differences and correlated repeated measurements.

Variation over time within an individual, distinguished from differences between individuals. A predictor of which children score higher need not identify what changes a particular child's trajectory.

A model relating repeated measures of variables across occasions. Conventional cross-lagged paths can mix stable between-person differences with within-person change and do not automatically identify causal effects.

A sample selected to include elevated familial or early developmental risk. It can increase information about pathways but its comorbidity and prevalence estimates require qualification before generalising to the population.

A study following a defined group to relate earlier characteristics or exposures to later outcomes. Prospective measurement improves temporal ordering but does not automatically remove confounding, selective attrition or exposure misclassification.

Loss of participants or outcome observations across follow-up. If remaining under observation depends on exposure and determinants of the outcome, analyzing only retained participants can induce selection bias.

Loss of participants or observations during follow-up. It reduces available information and can bias an estimate if continued participation selects individuals in a way relevant to the target relation.

A cross-sectional study measures different individuals during one observation period. Differences between ages can reflect confounding or birth-cohort differences as well as changes within individuals; a longitudinal study is needed to measure the latter directly.

Reverse causality occurs when an apparent exposure-outcome association is partly or wholly generated by the outcome, or by an early stage of it, affecting the measured exposure.