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Confounding is a causal concept, and as such, cannot be described in terms of correlations or associations. [ 1 ] [ 2 ] [ 3 ] The existence of confounders is an important quantitative explanation why correlation does not imply causation .
There are different ways that blocking can be implemented, resulting in different confounding effects. However, the different methods share the same purpose: to control variability introduced by specific factors that could influence the outcome of an experiment.
Graphical model: Whereas a mediator is a factor in the causal chain (top), a confounder is a spurious factor incorrectly implying causation (bottom). In statistics, a spurious relationship or spurious correlation [1] [2] is a mathematical relationship in which two or more events or variables are associated but not causally related, due to either coincidence or the presence of a certain third ...
The stronger the confounding of treatment and covariates, and hence the stronger the bias in the analysis of the naive treatment effect, the better the covariates predict whether a unit is treated or not. By having units with similar propensity scores in both treatment and control, such confounding is reduced.
In other cases, controlling for a non-confounding variable may cause underestimation of the true causal effect of the explanatory variables on an outcome (e.g. when controlling for a mediator or its descendant). [2] [3] Counterfactual reasoning mitigates the influence of confounders without this drawback. [3]
This confounding is depicted in the Figures 1–3 on the right through the bidirected arc between Tutoring Program and GPA. If students are assigned to dormitories at random, the proximity of the student's dorm to the tutoring program is a natural candidate for being an instrumental variable.
A paired difference test is designed for situations where there is dependence between pairs of measurements (in which case a test designed for comparing two independent samples would not be appropriate). That applies in a within-subjects study design, i.e., in a study where the same set of subjects undergo both of the conditions being compared.
An experiment must also control the possible confounding factors—any factors that would mar the accuracy or repeatability of the experiment or the ability to interpret the results. Confounding is commonly eliminated through scientific controls and/or, in randomized experiments, through random assignment.