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

2. 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

3. 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%.

4. 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

5. Look at the day and night flights separately.
Jill
Moe

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

7. 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

8. 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?

9. 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

10. 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?

11. Homework
P. 43 # 37, Worksheet