Correlation vs. Causation

class of students You've learned that data with a strong negative or positive correlation does not necessarily have a a casual relation. Recall the example of having nerves and low test scores. You graphed the data and found that there is a strong negative correlation between the data. But does that mean there is a causal relation as well?

While it is true that nerves can affect your test scores; there are other factors that affect test scores as well. Perhaps the other reasons are:

not feeling well
not have studied enough
distractions in the room

In other words, there is no way to tell if nerves were the main cause of a drop in grades.

The following are a few more examples of how data can have a strong correlation but no causation.

Bubonic plague
In the 1300’s the Black Death came to England. Many people believed that being close to people caused the disease. The thought this because the death rate in crowded cities was higher than it was in the country where there were fewer people. The graph for this theory might have looked like this.

plague graph

Even though there were more deaths in the crowded cities, the cause of the black death was actually a bacteria carried by the fleas that lived on rats. There was a correlation between population and deaths. That is the higher the population in a city, the more deaths there were, but that is just because the bigger the city, the higher the population of rats that lived close to the people. Correlation does not mean cause.

The students of a high school with a winning basketball team believed that the team scored more points when the fans wore their school colors. Here are the data and scatterplot.

Number of Fans Wearing School Colors	Score
5	20
30	25
50	45
75	55
20	60

school spirit graph

The correlation for this relationship is 0.94. The closer the correlation is to 1.0, the better the correlation.

The actual cause for the relationship is that as the basketball team got better, they scored higher. When the team started to win more games, school spirit increased and more people came to the games wearing their school colors.

A researcher studied the relationship between how agreeable students were and how many behavior problems they had in school. The research gave the students a survey that measured agreeableness. The table below shows their survey scores. Higher numbers mean a more agreeable person (someone who gets along with others).

Agreeable	4.5	3.2	3.4	3.3	3	4	4.7	2.4	2.9	4.6
Behavior Problems	5	22	10	12	23	21	2	35	12	4

behavior graph

This correlation indicates that the more agreeable a student is, the fewer behavior problems they demonstrate. The correlation is – 0.79.

Let's take one more look at correlation and causation.