Causation and Correlation

You are probably familiar with the phrase, cause and effect. An action causes a subsequent reaction. For example:

  1. Placing a pan of water on a hot stove element causes the water to boil.
  2. A student does very well on a test because he or she studied the night before.
  3. Oil from an oil spill coats the feathers of a sea bird and it dies.

Humans are very good at spotting cause and effect relationships. In the past, our success in hunting, gathering and farming depended on this skill. It is easy however to fool ourselves. Sometimes we create a linkage that doesn't exist. Sometimes we see a reaction and decide it was caused by some action, when they are not related at all!


Shoe Size IQ
3 50
6 70
7 87
8 95
9 96

For example, the results of a study shows that shoe size is related to intelligence. The bigger your shoe size - the greater your intelligence quotient (IQ). You would suspect that there is a problem here - the study can't be right. Look at the data table to the right that shows the test results for 5 test subjects. Clearly, the larger the shoe size, the greater was the IQ score!


Shoe Size IQ Age
3 50 4 years
6 70 8 years
7 87 12 years
8 95 34 years
9 96 28 years

What is going on?! Let's add some more data from the study. Look at this new table on the left.

Now we see that the testing hasn't done on just adults, but included children. It wasn't really shoe size that mattered, but the test subject's age. In this example, shoe size is related to age, so it was easy to misstate the results of the testing.


There is a correlation between shoe size and IQ. Correlation means that there is a relationship between shoe size and the IQ results, but the shoe size did not cause the differences in IQ score. The cause for the IQ differences was the age of the test subjects.

We must be careful when examining data looking for causes. A well designed experiment or set of observations tries to eliminate confusion between causation and correlation.

Assignment:

On the back of this sheet, explain in complete sentences if these are cause and effect relationships or correlation.

  1. Thunder is caused by lightning.
  2. Lightning is caused by thunder.
  3. Riding to school causes my bicycle tires to go flat.
  4. Exercise causes a person to lose weight.
  5. Beethoven became deaf because he was always playing the piano.