Causation vs. Correlation
•
•
•
•
Example ‐ long hair and grades
Common mistake – need for theory
The Bell Curve and the relationship between IQ and economic success.
How about some other examples?
– Infant health and bottled water
– Smoking and grades
– Age and style of walking among women
Conditions for Causal Relationship
1.
2.
3.
™
Temporal ordering
Correlation
Not related to unobserved variables
Difficulty of establishing (1) and (3)
•
Examples
• Impact of divorce on children’s emotional well‐being
• Impact of marriage on men’s earnings
Measurement and Causality
1. Measuring temporal order – extremely difficult
•
•
•
Recall bias
Reverse causation – e.g., attitudes
Importance of panel surveys
2. Accurately measuring cause and outcome – common to all social research
3. Unobserved heterogeneity – omitted variables
Omitted variable bias
• Conditions for omitted variable bias: – (1) the omitted variable is correlated with the independent variable of interest; – (2) the omitted variable is correlated with the dependent variable. • e.g., Occupational status has been found to have a positive effect on health. Could this be due to omitted variable biases? Spurious correlation
• A and B are related. But C is the cause for both A and B.
A
B
C
Example: wedding expenses and marital stability
Example 2: Are college admissions biased against women?
Sex
# Applicants
% Admitted
Men
2,691
0.45
Women
1,835
0.30
Example 2: Are college admissions biased against women?
Men
Women
Major
# Applicants
% Admitted
# Applicants
% Admitted
A
825
(0.31)
0.62
108
(0.06)
0.82
B
560
(0.21)
0.63
25
(0.01)
0.68
C
325
(0.12)
0.37
593
(0.32)
0.34
D
417
(0.15)
0.33
375
(0.20)
0.35
E
191
(0.07)
0.28
393
(0.21)
0.24
F
373
(0.14)
0.06
341
(0.19)
0.07
Another Example
• Information about 326 defendants who were convicted of homicide in 20 Florida counties in 1976‐
1977
Defendant's
race
Death Penalty
Total
Percent
Yes.
No
White
19
141
160
12
Black
17
149
166
10
Why are blacks less likely to be given death penalty?
We need to Consider Victim’s Race
D e fe n d a n t's V ic tim s’
ra c e
R ace
D e a th P e n a lty
P e rc e n t
Y es
No
W h ite
19
132
1 2 .6
B la c k
0
9
0
W h ite
11
52
1 7 .5
B la c k
6
97
5 .8
W h ite
B la c k
• Two conditions:
– (1) Homicide victims are race‐linked, b‐b, w‐w
– (2) White victims more => death penalty
Sample selection bias
• Sample selection bias occurs when the sample being analyzed is not representative of the entire population. • Example 1: Economic returns to college education.
• Example 2: Support for availability of condoms in public schools
Ecological Fallacy
• Definition:ecological fallacy is the mistake of using information pertaining to an aggregate to draw inferences about the units of analysis that comprise the aggregate. • That is, one jumps from evidence at the aggregate to inferences about individuals in the aggregate. • Example of race and literacy