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- Statistical paradoxes

Berkson's paradox

Berkson's paradox, also known as Berkson's bias, collider bias, or Berkson's fallacy, is a result in conditional probability and statistics which is often found to be counterintuitive, and hence a ver

False positive paradox

No description available.

Abelson's paradox

Abelson's paradox is an applied statistics paradox identified by Robert P. Abelson. The paradox pertains to a possible paradoxical relationship between the magnitude of the r2 (i.e., coefficient of de

Stein's example

In decision theory and estimation theory, Stein's example (also known as Stein's phenomenon or Stein's paradox) is the observation that when three or more parameters are estimated simultaneously, ther

Proof of Stein's example

Stein's example is an important result in decision theory which can be stated as The ordinary decision rule for estimating the mean of a multivariate Gaussian distribution is inadmissible under mean s

Accuracy paradox

The accuracy paradox is the paradoxical finding that accuracy is not a good metric for predictive models when classifying in predictive analytics. This is because a simple model may have a high level

Simpson's paradox

Simpson's paradox is a phenomenon in probability and statistics in which a trend appears in several groups of data but disappears or reverses when the groups are combined. This result is often encount

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 si

Friendship paradox

The friendship paradox is the phenomenon first observed by the sociologist Scott L. Feld in 1991 that most people have fewer friends than their friends have, on average. It can be explained as a form

Lord's paradox

In statistics, Lord's paradox raises the issue of when it is appropriate to control for baseline status. In three papers, Frederic M. Lord gave examples when statisticians could reach different conclu

Will Rogers phenomenon

The Will Rogers phenomenon, also called the Okie Paradox, is when moving an observation from one group to another increases the average of both groups. It is named after a joke by the comedian Will Ro

Gambler's fallacy

The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the incorrect belief that, if a particular event occurs more frequently than normal during th

Proebsting's paradox

In probability theory, Proebsting's paradox is an argument that appears to show that the Kelly criterion can lead to ruin. Although it can be resolved mathematically, it raises some interesting issues

Base rate fallacy

The base rate fallacy, also called base rate neglect or base rate bias, is a type of fallacy in which people tend to ignore the base rate (i.e., general prevalence) in favor of the individuating infor

Elevator paradox

The elevator paradox is a paradox first noted by Marvin Stern and George Gamow, physicists who had offices on different floors of a multi-story building. Gamow, who had an office near the bottom of th

Lindley's paradox

Lindley's paradox is a counterintuitive situation in statistics in which the Bayesian and frequentist approaches to a hypothesis testing problem give different results for certain choices of the prior

Low birth-weight paradox

The low birth-weight paradox is an apparently paradoxical observation relating to the birth weights and mortality rate of children born to tobacco smoking mothers. Low birth-weight children born to sm

Ellsberg paradox

In decision theory, the Ellsberg paradox (or Ellsberg's paradox) is a paradox in which people's decisions are inconsistent with subjective expected utility theory. Daniel Ellsberg popularized the para

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