+ 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.
+ 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.