2. Prediction and Causation

3. How do we predict a response? Explanatory Variables can be used to predict a response: 1. Prediction is based on fitting a line to a set of data. 2. Prediction works best when the line fits the data closely. It is more trustworthy if the data is close together. 3. Prediction outside of the range of the available data is risky.

4. Example… Y = 0.88x + 52.14 If x = 55 minutes, does that guarantee me a 100 on the test (actually 100.54)? Why not?

5. Who knows… Correlation is strongly affected by outliers. What do you think Hawai’i is known for that is definitely an outlier compared to the other 49 states?

6. In fact, in one 24 hour period, Hawai’i received more than 40 inches of rain, and the largest amount of rainfall annually they had was over 700 inches!

7. Don’t forget…

8. Causation A “correlation” between two variables does not immediately mean that one variable “causes” the other. The relationship is often influenced by other variables “lurking” in the background.

9. How to see causation?? The best evidence for causation comes from randomized comparative experiments. Why? The relationship may be due to direct causation, common response, or confounding.

10. Direct Causation O There is a strong correlation between smoking cigarettes and death from lung cancer. O Does smoking cigarettes cause lung cancer? O There is a strong correlation between the availability of hand guns in America and the homicide rate. O Is the availability of hand guns the cause of the homicide rate?

11. Does watching TV make you live longer? This is called a “nonsense” correlation. People with TV’s are also in more developed countries, have better health care, etc.

12. Common Response O If “watching too much television” is the explanatory variable and “obesity in children” is the response variable, a possible lurking variable can be “poor food choices”. O Did poor food choices make obesity in children? O Did poor food choices make children watch too much television (junk food in front of TV)?

13. Confounding O You just don’t know if it was the explanatory variable or the lurking variable which caused the response variable. There is an association between variables, but you don’t know if there is a cause and effect relationship.

14. How they look… O The arrows represent a cause-and-effect link. O The dashed lines represent an association. O X = Explanatory, Y = Response, Z = Lurking

15. If an experiment is not possible… 1. The association is strong. 2. The association is consistent. 3. Higher doses are associated with stronger responses. 4. The alleged cause precedes the effect in time. 5. The alleged cause is plausible. You need to make sure you can prove the following to establish causation when you cannot perform an experiment:

16. Now for you and your groups… O Create 5 confounding diagrams related to different topics. Make sure you use different variables (especially different lurking variables, each time).