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4.4 Statistical Paradoxes

4.4 Statistical Paradoxes. 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?.

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4.4 Statistical Paradoxes

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  1. 4.4 Statistical Paradoxes

  2. 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? http://www.gseis.ucla.edu/courses/ed230a2/simpson.html

  3. 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.

  4. 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.

  5. Who has the better overall shooting percentage?

  6. Same Decision?

  7. Which treatment for kidney stones is better? • 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. PMID3083922. PMC1339981. http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=3083922.

  8. 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?

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