final exam due in 20 hours

Correlation

Correlational Studies
A correlation tells you that a relationship exists between 2 variables (aside from the 3rd variable problem), but tell you absolutely nothing about cause and effect.

CAUSALITY
When variable A actually causes the change in B.

Sheer Coincidence
Variables A and B really do NOT have anything to do with each other but happen to go up or down simultaneously.

Common Underlying Cause(s)
Variable A is correlated with variable B but there is a third factor C (the common underlying cause) that causes the changes in both A and B.

Correlation vs. Causality
How do you show the difference?
To show causality you need to establish three things
Time order (one variable must precede the other to be the cause
They must be correlated or associated (reasonable r or r2 value)
There must be no other outside variable to explain the 2nd variable’s variation

Figure 1. Correlation Between Crime Rate and Ice Cream Sales in Chicago

Figure 2. Chicago Temperature and Ice Cream Sales by Month

Figure 3. Chicago Temperature and Crime Rate by Month

Figure 1. Correlation Between Crime Rate and Ice Cream Sales in Chicago

R
2
= 0.8115
0.225
0.275
0.325
0.375
0.425
0.475
1350015500175001950021500
Crime Rate (Total)
Ice Cream Sales
(Pints Per Capita)
10
20
30
40
50
60
70
80
123456789101112
Month
Temperature (Deg. F.)
0.2
0.25
0.3
0.35
0.4
0.45
Ice Cream Sales
(Pints Per Capita)
Temperature
Ice Cream
10
20
30
40
50
60
70
80
123456789101112
Month
Temperature (Deg. F.)
12500
14000
15500
17000
18500
20000
21500
Crime Rate (Total)
Temperature
Crime Rate
R
2
= 0.8115
0.225
0.275
0.325
0.375
0.425
0.475
1350015500175001950021500
Crime Rate (Total)
Ice Cream Sales
(Pints Per Capita)