CH. 3 Day 4 AP Statistics EQ: What is Simpson’s Paradox?

What is Simpson’s Paradox? A reversal of a decision based on finding different averages. Be careful when you average across different levels of a second variable. Unfair or silly averaging is used

Suppose there are two pilots, Moe and Jill Suppose there are two pilots, Moe and Jill. Moe argues that he’s the better pilot since he managed to land 83% of his last 120 flights on time compared with Jill’s 78%.

Here are the results for each of their 120 flights broken down by time of day they flew: Night Overall Moe 90/100 10/20 100/120 Jill 19/20 75/100 94/120

Look at the day and night flights separately. Jill Moe

How can it be that Jill is better at both night and day flights, but Moe is better overall?

Ex. For a 1973 study on sex bias in admissions to the graduate school at the University of California, Berkeley, the table shows the information obtained for the five largest majors on that campus. Males Females Major # of Applicants # Admitted Total Major 1 800 520 120 102 Major 2 550 341 32 23 Major 3 400 160 410 148 Major 4 350 126 347 129 Major 5 200 48 387 105

Ex. 1. Out of the total male applicants, what is the probability of males admitted? 2. Out of the total female applicants, what is the probability of females admitted?   3. Who is getting admitted more often?

Ex. Taking into account the lurking variable of major type, the table can be changed. Major Admitted Denied Total Major 1 Major 2 Major 3 Major 4 Major 5

Ex. 4. For each major, find the percentage of males admitted.   5. For each major, find the percentage of females admitted.    6. Is there discrimination going on at the University of California, Berkeley in the graduate school? Why or Why not?

Homework P. 43 # 37, Worksheet