Cartoon from 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.

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

Graph from 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?

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?

Graph from www.tylervigen.com

How does per capita consumption of chicken correlate with crude oil imports?

Chicken data from USDA. Oil data from Dept. of Energy.

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

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?

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 per capita 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?

?

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

Cartoon from xkcd.com

What’s So Funny About Correlation?