What’s So Funny About Correlation? xkcd.com. What is Correlation? When two things go together:...
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Transcript of What’s So Funny About Correlation? xkcd.com. What is Correlation? When two things go together:...
xkcd.com
What’s So Funny About Correlation?
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.• Stronger relationships mean that
a change in one variable is accompanied by a systematic change in the other.
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
1984 160.2 327.6
1985 153.2 383.7
1986 144.1 414
1987 137.8 455.3
1988 125.5 527
1989 115.8 529.4
1990 102.7 576.9
1991 98 612.6
1992 92.1 618.8
1993 81.2 610.3
1994 65.4 640.4
1995 58.7 673.4
1996 66.1 674.7
1997 65.9 628.6
1998 65.8 673.7
1999 58.3 728.3
2000 54.8 753.9
2001 55.6 768.8
2002 53.5 780.1
2003 45.6 763.7
2004 57.7 788.5
2005 64.7 782
2006 77.5 787.2
2007 81.2 806.4
2008 81.9 806.2
www.tylervigen.com
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?
20 40 60 80 100 120 140 160 1800
100
200
300
400
500
600
700
800
900
Uranium Stored vs Power Generated
Uranium Stored
Pow
er G
ener
ated
Does the amount of uranium stored at nuclear plants correlate with the amount of power they
generate?
20 40 60 80 100 120 140 160 1800
100
200
300
400
500
600
700
800
900
Uranium Stored vs Power Generated
Uranium Stored
Pow
er G
ener
ated
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?
• The action of causing something; the relationship between cause and effect.
• Smoking causes cancer
• Sugar causes cavities
• Gravity causes objects to fall
What is Causation?
• We can make an inference about a causal relationship based on the strength of correlation.
• We have to be careful about assuming an actual causal relationship, though.
How does consumption of chicken correlate with crude oil
imports?
www.tylervigen.com
How does consumption of chicken correlate with crude oil
imports?
Chicken data from USDA. Oil data from Dept. of Energy.
How does 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
How does consumption of chicken correlate with crude oil
imports?0.9
How does consumption of chicken correlate with crude oil
imports?
53 54 55 56 57 58 59 60 61 623100
3200
3300
3400
3500
3600
3700
3800
Chicken Consumption vs. Crude Oil Imports
Chicken
Oil
How does consumption of chicken correlate with crude oil
imports?
53 54 55 56 57 58 59 60 61 623100
3200
3300
3400
3500
3600
3700
3800
Chicken Consumption vs. Crude Oil Imports
Chicken
Oil
Does eating more chicken cause crude oil imports to
increase??
But wait…
…if eating more chicken doesn’t cause crude oil imports to increase, then why are they so closely correlated?
?
The Lurking Variable
Total US Population
Year
Correlation and Causation
• Correlation is a measure of how well data fit a relationship.
• A correlated relationship between two quantitative variables is not the same as a causal relationship.
• Causal inferences about correlated events can be made based on underlying theories and knowledge.
• The determination that one thing causes another requires a scientific experiment.
"Correlation is not causation, but it sure is a hint.“Edward Tufte, American Statistician
Cartoon from xkcd.com
What’s So Funny About Correlation?