Freedman's paradox
In statistical analysis, Freedman's paradox, named after David Freedman, is a problem in model selection whereby predictor variables with no relationship to the dependent variable can pass tests of significance – both individually via a t-test, and jointly via an F-test for the significance of the regression. Freedman demonstrated (through simulation and asymptotic calculation) that this is a common occurrence when the number of variables is similar to the number of data points. Specifically, if the dependent variable and "k" regressors are independent normal variables, and there are "n" observations, then as "k" and "n  jointly go to infinity in the ratio k"/"n"="ρ", More recently, new information-theoretic estimators have been developed in an attempt to reduce this problem, in addition to the accompanying issue of model selection bias, whereby estimators of predictor variables that have a weak relationship with the response variable are biased.