what’s so funny about correlation? xkcd.com. what is correlation? when two things go together:...

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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?