What’s So Funny About Correlation?
Cartoon from xkcd.com
What is Correlation?
• When two things go together:
• cookies & milk
• macaroni & cheese
• peanut butter & jelly
What is Statistical Correlation?
• A mutual relationship between
two variable quantities.
• Correlation coefficients measure
how closely related the two
variables are.
Correlation Coefficient
Strength
1
Perfect Positive
0.7 to 0.9
Strong Positive
0.4 to 0.6
Moderate Positive
0.1 to 0.3
Weak Positive
0
No Correlation
-0.1 to -0.3
Weak Negative
-0.4 to -0.6
Moderate Negative
-0.7 to -0.9
Strong Negative
-1
Perfect Negative
Does the amount of uranium stored at nuclear plants
correlate with the amount of power they generate?
Does the amount of uranium stored at nuclear plants
correlate with the amount of power they generate?
Year
Uranium
Power
1996
66.1
674.7
1984
160.2
327.6
1997
65.9
628.6
1985
153.2
383.7
1998
65.8
673.7
1986
144.1
414
1999
58.3
728.3
1987
137.8
455.3
2000
54.8
753.9
1988
125.5
527
2001
55.6
768.8
1989
115.8
529.4
2002
53.5
780.1
1990
102.7
576.9
2003
45.6
763.7
1991
98
612.6
2004
57.7
788.5
1992
92.1
618.8
2005
64.7
782
1993
81.2
610.3
2006
77.5
787.2
1994
65.4
640.4
2007
81.2
806.4
1995
58.7
673.4
2008
81.9
806.2
Does the amount of uranium stored at nuclear plants
correlate with the amount of power they generate?
Graph from www.tylervigen.com
Does the amount of uranium stored at nuclear plants
correlate with the amount of power they generate?
Uranium Stored vs Power Generated
900
800
700
Power Generated
600
500
400
300
200
100
0
0
20
40
60
80
100
Uranium Stored
120
140
160
180
Does the amount of uranium stored at nuclear plants
correlate with the amount of power they generate?
Uranium Stored vs Power Generated
900
800
700
Power Generated
600
500
400
300
200
100
0
0
20
40
60
80
100
Uranium Stored
120
140
160
180
Does the amount of uranium stored at nuclear plants
correlate with the amount of power they generate?
Does the amount of uranium stored at nuclear plants
correlate with the amount of power they generate?
-0.89905
Why might the amount of uranium stored at nuclear plants
correlate with the amount of power they generate?
What is Causation?
What is Causation?
• The action of causing something;
the relationship between cause
and effect.
• Smoking causes cancer
• Sugar causes cavities
• Gravity causes objects to fall
How does per capita consumption of chicken
correlate with crude oil imports?
How does per capita consumption of chicken
correlate with crude oil imports?
Graph from www.tylervigen.com
How does per capita consumption of chicken
correlate with crude oil imports?
Year
Per capita chicken consumption
(lbs.)
Total crude oil imports
(millions of barrels)
2000
54.2
3311
2001
54
3405
2002
56.8
3336
2003
57.5
3521
2004
59.3
3674
2005
60.5
3670
2006
60.9
3685
2007
59.9
3656
2008
58.7
3571
2009
56
3307
Chicken data from USDA. Oil data from Dept. of Energy.
How does per capita consumption of chicken
correlate with crude oil imports?
0.9
How does per capita consumption of chicken
correlate with crude oil imports?
Chicken Consumption vs. Crude Oil Imports
3750
3700
3650
3600
Oil
3550
3500
3450
3400
3350
3300
3250
53
54
55
56
57
58
Chicken
59
60
61
62
How does per capita consumption of chicken
correlate with crude oil imports?
Chicken Consumption vs. Crude Oil Imports
3750
3700
3650
3600
Oil
3550
3500
3450
3400
3350
3300
3250
53
54
55
56
57
58
Chicken
59
60
61
62
Does eating more chicken cause crude oil
imports to increase?
?
Correlation and Causation
• Correlation is a measure of how well data fit the relationship.
• A correlated relationship between two quantitative variables is not the
same as a causal relationship.
• The determination that one thing causes another requires a controlled
randomized experiment.
• "Correlation is not causation, but it sure is a hint.“
- Edward Tufte, American Statistician
What’s So Funny About Correlation?
Cartoon from xkcd.com