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The confounding variable makes the results of the analysis unreliable. It is quite likely that we are just measuring the fact that highway driving results in better fuel economy than city driving. In statistics terms, the make of the truck is the independent variable, the fuel economy (MPG) is the dependent variable and the amount of city ...
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 ...
This chapter introduces the idea of confounding and describes how causal diagrams can be used to identify confounding variables and determine their effect. Pearl explains that randomized controlled trials (RCTs) can be used to nullify the effect of confounders, but shows that, provided one has a causal model of confounding, an RCT does not ...
All of those examples deal with a lurking variable, which is simply a hidden third variable that affects both of the variables observed to be correlated. That third variable is also known as a confounding variable, with the slight difference that confounding variables need not be hidden and may thus be corrected for in an analysis. Note that ...
In the first example provided above, the sex of the patient would be a nuisance variable. For example, consider if the drug was a diet pill and the researchers wanted to test the effect of the diet pills on weight loss. The explanatory variable is the diet pill and the response variable is the amount of weight loss.
Propensity scores are used to reduce confounding by equating groups based on these covariates. Suppose that we have a binary treatment indicator Z, a response variable r, and background observed covariates X. The propensity score is defined as the conditional probability of treatment given background variables:
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.
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]