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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.
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]
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 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 ...
Note: Full factorial designs have no confounding and are said to have resolution "infinity". For most practical purposes, a resolution 5 design is excellent and a resolution 4 design may be adequate. Resolution 3 designs are useful as economical screening designs. Response(s): The output(s) of a process. Sometimes called dependent variable(s).
These artificial pairs are constructed based on additional variables that are thought to serve as confounders. By pairing students whose values on the confounding variables are similar, a greater fraction of the difference in the value of interest (e.g. the standardized test score in the example discussed above), is due to the factor of ...
The same is true for intervening variables (a variable in between the supposed cause (X) and the effect (Y)), and anteceding variables (a variable prior to the supposed cause (X) that is the true cause). When a third variable is involved and has not been controlled for, the relation is said to be a zero order relationship. In most practical ...
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 ...