List of Paradoxes - Mathematics - Statistics

Statistics

• Accuracy paradox: predictive models with a given level of accuracy may have greater predictive power than models with higher accuracy.
• Berkson's paradox: a complicating factor arising in statistical tests of proportions.
• Freedman's paradox describes a problem in model selection where predictor variables with no explanatory power can appear artificially important
• Friendship paradox: For almost everyone, their friends have more friends than they do.
• Inspection paradox: Why one will wait longer for a bus than one should.
• Lindley's paradox: Tiny errors in the null hypothesis are magnified when large data sets are analyzed, leading to false but highly statistically significant results.
• Low birth weight paradox: Low birth weight and mothers who smoke contribute to a higher mortality rate. Babies of smokers have lower average birth weight, but low birth weight babies born to smokers have a lower mortality rate than other low birth weight babies. (A special case of Simpson's paradox.)
• Will Rogers phenomenon: The mathematical concept of an average, whether defined as the mean or median, leads to apparently paradoxical results — for example, it is possible that moving an entry from an encyclopedia to a dictionary would increase the average entry length on both books.