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Stats

Chapter 7: Correlation doesn’t mean causation

+Do Now:

The following graph shows ages of men and woman who are married to each other. Based on the graph, would calculating the correlation coefficient be appropriate? Why? Why not?

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+Pirates are causing global warming?

+EVIL MAN PIRATE.

+Cheese is killing people?

+Margarine killing the love?

+Political Action Committees are killers?

+Skiing facilities! NO!!!!

+Hmmmm….

Do NOT confuse association, correlation and causation.

+Association

Deliberately vague term to describe the relationship between two variables. This can be used for CATEGORICAL data

Ex: Did you know there’s a strong correlation between playing an instrument and drinking coffee…. NO. It’s an association!

+Correlation

Precise term describing the strength and direction of the linear relationship between quantitative variables.

+Causation

Scatterplots and correlation coefficients NEVER prove causation.

This is why it is so hard to prove something causes something else– for example, just because lung cancer and smoking is correlated doesn’t mean that one causes the other and when considering one causing the other you need to consider both. Does smoking cause cancer? OR Does cancer cause smoking?

You need to do further tests to actually figure this out.

+Example 1

A news reporter claims “There appears to be a strong correlation between whether you own a pet and the condition of a person’s yard.”

Thoughts on this?

+Example 2:

A researcher studies children in elementary school and finds a strong positive linear association between height and reading scores. Does this mean that taller readers are generally better

readers? What might explain the strong correlation?

+What is wrong? Example 3

The correlation coefficient between Olympic gold medal times for the 800 m hurdles and year is -0.66 seconds per year.

+Answer

Correlation Coefficient has NO UNITS.

+What’s wrong? Example 4

The correlation coefficient between Olympic Gold Medal times for the 100m dash and year is -1.37

+Answer

Correlation Coefficient of -1.37 is impossible! Correlation coefficient will always be between -1 and 1!

+What’s Wrong? Example 5

Since the correlation coefficient between Olympic gold medal times for the 800m hurdles and 100m dash is -0.41, the correlation coefficient between times for the 100m dash and the 800m dash hurdles will be 0.41

+Answer

Correlation does not change if we reverse x and y variables.

+What’s Wrong?- Example 6

If we were to measure Olympic gold medal times for the 800m hurdles in minutes instead of seconds, the correlation coefficient would be -.66/60 = -0.011

+Answer

Correlation does not change when we change units!

+Practice Problems

Try some on your own!

As always call me over if you are confused!

+Exit Ticket

Explain the error:

Your friend claims that the correlation coefficient between what continent you live on and how many hours you sleep is 0.14.