Correlation Vs. Causation

Correlation vs. Causation

We have been discussing correlation. We have looked at situations where there exists a strong positive relationship between our variables x and y. However, just because we see a strong relationship between two variables, this does not imply that a change in one variable causes a change in the other variable. Correlation does not imply causation ! Consider the following:

1) In the 1990s, researchers found a strong positive relationship between the number of television sets per person x and the life expectancy y of the citizens in different countries. That is, countries with many TV sets had higher life expectancies. Does this imply causation? By increasing the number of TVs in a country, can we increase the life expectancy of their citizens? Are there any hidden variables that may explain this strong positive correlation?

2) Here's another example where an apparent correlation is actually the result of a hidden third variable. Mr. Jones gave a math test to all the students in his school (grades 1 – 12). He made the startling discovery that the taller students did better than the shorter ones. His conclusion was that as your height increases, so does your math ability. Is this an example of causation? As your height increases, does this cause your test scores to increase?

3) There is a strong positive correlation between ice cream sales and shark attacks. That is, as ice cream sales increase, the number of shark attacks increase. Is it reasonable to conclude the following? Ice cream consumption causes shark attacks.

All of the previous examples show a strong positive correlation between the variables. However, in each example it is not the case that one variable causes a change in the other variable. For example, increasing the number of ice cream sales does not increase the number of shark attacks. There are outside factors, also known as lurking variables, which cause the correlation between these variables.

Causation means that a change in one variable causes a change in the other. In other words, there is a cause-and-effect relationship that exists between the two variables. The only true way to prove a cause-and-effect relationship between two variables is to perform well designed experiments in which the effects of outside variables are controlled. Only then can you know whether changes in one variable are causing changes in the other and that another outside variable is not playing a role.

However, it is not always plausible to conduct these types of experiments. Let’s look at examples of situations that have a strong correlation in which we can reasonably conclude that causation exists.

4) Aura is taking her friends to the movies for her birthday. There is a strong positive relationship between the number of movie tickets she buys and the amount of money she spends. Is it reasonable to assume causation in this situation? That is, as Aura increases the number of movies tickets she purchases, does this cause her to spend more money?

5) Peter heads out jogging at a constant rate of 6 mph. There is a strong positive correlation between the amount of time he jogs at this pace and the number of calories he burns. Is this an example of causation? That is, does jogging for a longer amount of time cause Peter to burn more calories?

6) Danny is a truck driver for a construction company. The staff at the warehouse loads up his truck with flats of cement bricks while the truck is parked on a scale. They consider the weight of the truck as additional flats of bricks are added to the truck. There is a strong positive relationship between the number of flats loaded onto the truck and the weight of the truck. Does this imply causation? That is, as the number of flats loaded onto the truck increases, does this cause the weight of the truck to also increase?