Correlation vs. Causation. In a Gallup poll, surveyors asked, “Do you believe correlation implies causation?’” 64% of American’s answered “Yes”. 38% replied.

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Presentation transcript:

Correlation vs. Causation

In a Gallup poll, surveyors asked, “Do you believe correlation implies causation?’” 64% of American’s answered “Yes”. 38% replied “No”. The other 8% were undecided.

Ice-cream sales are strongly correlated with crime rates. Therefore, ice-cream causes crime.

The Simpsons (Season 7, "Much Apu About Nothing") Homer:Not a bear in sight. The "Bear Patrol" is working like a charm! Lisa:That's specious reasoning, Dad. Homer:[uncomprehendingly] Thanks, honey. Lisa:By your logic, I could claim that this rock keeps tigers away. Homer:Hmm. How does it work? Lisa:It doesn't work; it's just a stupid rock! Homer:Uh-huh. Lisa:But I don't see any tigers around, do you? Homer:(pause) Lisa, I want to buy your rock.

Without proper interpretation, causation should not be assumed, or even implied.

Consider the following research undertaken by the University of Texas Health Science Center at San Antonio appearing to show a link between consumption of diet soda and weight gain. The study of more than 600 normal-weight people found, eight years later, that they were 65 percent more likely to be overweight if they drank one diet soda a day than if they drank none. And if they drank two or more diet sodas a day, they were even more likely to become overweight or obese.

Third or Missing Variable Problem A relationship other than causal might exist between the two variables. It's possible that there is some other variable or factor that is causing the outcome.

 Ice cream sales and the number of shark attacks on swimmers are correlated.  Skirt lengths and stock prices are highly correlated (as stock prices go up, skirt lengths get shorter).  The number of cavities in elementary school children and vocabulary size are strongly correlated.

There are two relationships which can be mistaken for causation: 1. Common response 2. Confounding

1.Common Response: Both X and Y respond to changes in some unobserved variable, Z. All three of our previous examples are examples of common response.

2.Confounding The effect of X on Y is indistinguishable from the effects of other explanatory variables on Y. When studying medications, the “placebo effect” is an example of confounding.

Unless data have been gathered by experimental means and confounding variables have been eliminated, correlation never implies causation. When controlled experiments are performed. When can we imply causation?

Kids’ TV Habits Tied to Lower IQ Scores IQ scores and TV time r = -.54

Eating Pizza ‘Cuts Cancer Risk’ Pizza consumption and cancer rate r =.-59

Gun Bill Introduced to Ward Off Crime Gun ownership and crime r =.71

Reading Fights Cavities Number of cavities in elementary school children and their vocabulary size r = -.67

Graffiti Linked to Obesity in City Dwellers BMI and amount of graffiti and litter r =.45

Stop Global Warming: Become a Pirate Average global temperature and number of pirates r = -.93