# Simpson’s Paradox. Don’t use unfair or silly averages! Moe and Jill want to decide who is the better pilot. Moe says he is because he landed 83% of his.

## Presentation on theme: "Simpson’s Paradox. Don’t use unfair or silly averages! Moe and Jill want to decide who is the better pilot. Moe says he is because he landed 83% of his."— Presentation transcript:

Don’t use unfair or silly averages! Moe and Jill want to decide who is the better pilot. Moe says he is because he landed 83% of his last 120 flights on-time compared to Jill’s 78%. Is he right? DayNightOverall Moe90 out of 100 90% 10 out of 20 50% 100 out of 120 83% Jill19 out of 20 95% 75 out of 100 75% 94 out of 120 78%

This is an example of unfair averages. Jill’s flights are mostly at night, which are more difficult. Her overall average is heavily influenced by her night flights. Moe’s average benefits from his mostly day flights. With the very different patterns of flying conditions, taking an overall average is misleading.

Graduate Student Admission Rates at University of California Berkley It was reported that 45% of male applicants were admitted to graduate school programs and 30% of female applicants were admitted. How is this an example of Simpson’s Paradox?

Bottom of the ninth… It’s the bottom of the ninth in an important game. Your team is down with the bases loaded and two outs. The pitcher is due up, so you’ll be sending in a pinch hitter. There are two batters available. Whom should you send in? PlayerOverallVs. LHPVs. RHP A33 for 103.320 28 for 81.346 5 for 22.227 B45 for 151.298 12 for 32.375 33 for 119.277

The moral of Simpson’s Paradox is to be careful when you average across different levels of a second variable. It’s always better to compare percentages or averages within each level of the other variable.

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