4.4 Statistical Paradoxes

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Presentation transcript:

4.4 Statistical Paradoxes

Total SAT Subpopulation Scores by Ethnic Group SAT Scores Below is a table of SAT scores broken down by ethnic group for 1976 and 1990. All of the non-white groups saw their scores increase or hold the same while overall scores declined for the population as a whole. Why? Total SAT Subpopulation Scores by Ethnic Group Year White Black Asian American Indian Mexican Puerto Rican 1976 944 686 932 808 781 765 1990 933 737 938 825 809 764 Berliner, D. (1993) Educational Reform in an Era of Disinformation. Educational Policy Analysis Archives http://www.gseis.ucla.edu/courses/ed230a2/simpson.html

Better in Each Case, But Worse Overall It is possible for something to appear better in each of two or more group comparisons but actually be worse overall. This occurs because of the way in which the overall results are divided into unequally sized groups.

Simpson’s Paradox The general case in which a set of data gives different results for each of several group comparisons than it does when the groups are taken together. Named for Edward Simpson who described it in 1951. The same idea also described by Scottish statistician George Yule around 1900.

Who has the better overall shooting percentage? 2-pt. FG 3-pt. FG DeMarcus Cousins Kentucky Wildcats 0.558 0.167 Andy Rautins Syracuse 0.582 0.403

Same Decision? 2-pt. FG 3-pt. FG Total FG 192/344 0.558 1/6 0.167 ? DeMarcus Cousins Kentucky Wildcats 192/344 0.558 1/6 0.167 ? Andy Rautins Syracuse 32/55 0.582 94/233 0.403

Which treatment for kidney stones is better? Treatment A Treatment B Small Stones 81/87 234/270 Large Stones 192/263 55/80 Total Which treatment would you recommend? Why? C. R. Charig, D. R. Webb, S. R. Payne, O. E. Wickham (29 March 1986). "Comparison of treatment of renal calculi by operative surgery, percutaneous nephrolithotomy, and extracorporeal shock wave lithotripsy". Br Med J (Clin Res Ed) 292 (6524): 879–882. doi:10.1136/bmj.292.6524.879. PMID 3083922. PMC 1339981. http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=3083922.

Drug Tests The following chart represents drug tests of 2000 applicants for a job. Find the percent of false positive tests. Find the percent of false negative tests. Find the percent of positive tests. Find the percent of drug users. Should the test be set-up this way? Drug Users Nonusers Positive test result 297 34 Negative test result 3 1666

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