= Confounder =

A '''confounder''' is a variable that is associated with both a dependent and independent variable.

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== Description ==

Confounders are one possible failure of causal inference. An association has been identified between two variables, ''X'' and ''Y'', but in actuality there is a confounder ''Z'' that causes both.

In this example, controlling for ''Z'' explains all correlation. (Note that in [[R]], the [[Analysis/BernoulliDistribution|Bernoulli distribution]] is handled as a special case of the [[Analysis/BinomialDistribution|Binomial distribution]].)

{{{
> Z <- rbinom(1000, 1, 0.5)
> X <- rbinom(1000, 1, 0.9*(1-Z) + 0.1*Z)
> Y <- rbinom(1000, 1, 0.9*(1-Z) + 0.1*Z)
> cor(X,Y)
[1] 0.6458128
> cor(X[Z==1], Y[Z==1])
[1] -0.0191339
> cor(X[Z==0], Y[Z==0])
[1] 0.01227915
}}}



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CategoryRicottone