Assignment 02.12a Simpson\'s Paradox and Other Cautions The Berkeley Graduate Ad
ID: 3204197 • Letter: A
Question
Assignment 02.12a Simpson's Paradox and Other Cautions
The Berkeley Graduate Admissions Study
In the Fall of 1973, an observational study on possible gender bias was conducted at the University of California, Berkeley. In that year, there were 12,763 applicants for graduate admission; the following is a two-way table that gives the data according to the variable's outcome (admitted or denied) and gender (male or female).
Admitted
Denied
Male
3738
4704
Female
1494
2827
Of course, it's hard to draw any conclusions about the question of gender bias from this table because different numbers of men and women applied for graduate admission. Clearly, we should work with percentages instead.
Construct a two-way table that gives the percentages of men admitted and denied, and the percentages of women admitted and denied.
Percentage
Admitted
Denied
Male
Female
From your table in Exercise 1, you should have observed that approximately 44% of men were admitted, but only about 35% of women were admitted.
Do you believe that there was gender bias in graduate admissions at UC Berkeley in 1973?
Can you think of possible causes for the discrepancy in admission rates other than gender bias?
One factor that you probably thought of in the last exercise was the qualification of the applicants. Naturally, a discrepancy in admission rates could result if the women, as a group, were less qualified than the men, in terms of college grades or standardized tests. In fact, however, there was no significant difference between the qualifications of the men and the women, as groups.
In light of this information, answer questions b and c again.
Let us now introduce a new variable that may help explain the data. At UC Berkeley, as in most universities, decisions about graduate admission are made at the department level. In 1973, UC Berkeley had 101 different graduate departments, but for simplicity, we will consider only the six largest departments (which collectively account for 4486 of the applicants). The following table is a three-way table that presents the admissions data according to the variables department (A, B, C, D, E, F), gender (male, female), and outcome (admitted, denied). The table is adapted from data in reference [2].
Male
Female
Admitted
Denied
Admitted
Denied
A
512
313
89
19
B
313
207
17
8
C
120
205
202
391
D
138
279
131
244
E
53
138
94
299
F
22
351
24
317
Once again, construct the three-way table that gives the percentages of men admitted and denied, and the percentages of women admitted and denied for each department.
Male
Female
Admitted
Denied
Admitted
Denied
A
B
C
D
E
F
Construct the two way table (both with counts and percentages) for the variables outcome and gender. Sketch the corresponding histogram.
Count
Admitted
Denied
Male
Female
Percentage
Admitted
Denied
Male
Female
Construct the two way table (both with counts and percentages) for the variable's outcome and department. Sketch the corresponding histogram.
Count
Admitted
Denied
A
B
C
D
E
F
Percentage
Admitted
Denied
A
B
C
D
E
F
Construct the two-way table (both with counts and percentages) for the variables gender and department. Sketch the corresponding histogram.
Count
Male
Female
A
B
C
D
E
F
Percentage
Male
Female
A
B
C
D
E
F
Based on your analysis, do you now believe that there was gender bias in graduate admissions at the University of California at Berkeley in 1973?
A group of college students believes that herbal tea has remarkable powers. To test this belief, they make weekly visits to a local nursing home, where they visit with the residents and serve them herbal tea. The nursing home staff reports that after several months many of the residents are more cheerful and healthy. A skeptical sociologist commends the students for their good deeds but scoffs at the idea that herbal tea helped the residents.
Identify the explanatory and response variables in this informal study.
Identify the lurking variables and explain what they may have accounted for in the observed association.
A study shows that there is a positive correlation between the size of a hospital and the median number of days that patients remain in the hospital. Does this mean that you can shorten a hospital stay by choosing a small hospital? Explain your response.
A newspaper claims, “There is a strong positive correlation between the number of firefighters at a fire and the amount of damage the fire does. So sending lots of firefighters just causes more damage.” Explain why this reasoning is wrong.
A study of elementary age school children (aged 5 to 11) finds a strong positive correlation between weight and reading comprehension. Therefore, we should start feeding elementary age school children as much as possible in order to increase their reading comprehension. Explain what is wrong with this thinking and a more appropriate conclusion.
Children who watch many hours of television get lower grades in school on the average than those who watch less TV. Explain clearly why this fact does not show that watching TV causes poor grades. Identify some alternate possibilities for the association.
Admitted
Denied
Male
3738
4704
Female
1494
2827
Explanation / Answer
a) two-way table that gives the percentages of men admitted and denied, and the percentages of women admitted and denied
total male=3738+4704=8442
total female=1494+2827=4321
% of admitted= (admitted/total )*100
male admitted= (3738/8442)*100=44.27=44%
Male denied=100-44=56%
Female admitted=(1494/4321)*100=34.5=35%
Female denied=100-35=65%
From the calculation we can say that their is a possibility of gender bias as the admitted percentage of male is greater than female.
b)
the three-way table that gives the percentages of men admitted and denied, and the percentages of women admitted and denied for each department.
c)
the two way table (both with counts and percentages) for the variables outcome andgender. Sketch the corresponding histogram.
Count
Admitted
Denied
Male
3738
4704
Female
1494
2827
Percentage
Admitted
Denied
Male
44
56
Female
35
Percentage Admitted Denied Male 44 56 Female 35 65