Correlation and Causality

Section 5E

Correlation exists between two variables when higher values of one variable consistently go with higher values of the other, or when higher values of one variable consistently go with lower values of the other.

In laymen's terms, two things have a correlation if the likelihood of one happening is strongly related to the likelihood of the other happening or not happening. For example, we've heard the statement "The family that prays together stays together." That says that the event "family prayer" is correlated to the event "family unity." Statistical studies have borne out that statement.

Height and weight are correlated. Taller people tend to be heavier.

Keep in mind that correlation does not dictate an absolute relation. We all know families that have had strong faith yet had divorces. We all know tall people who are light. We all know short people who are heavy. What correlation speaks to is a tendency. Some correlations are strong (if a number gets larger then 2 times the number ALWAYS gets larger). Others are not as strong (height/weight).

One other aspect of correlation is whether there is a positive correlation (one quantity goes up when the other quantity goes up) or negative correlation (one quantity goes down when the other quantity goes up). An example of negative correlation is smoking and life expectancy. The more a person smokes the lower his life expectancy.

Another issue involved in correlation comes up when two things are indeed correlated. That is the issue of trying to decide whether or not one of the things CAUSES the other. When two events are correlated, there are basically three possible explanations.

1. The correlation is a coincidence.

2. One event causes the other.

3. The two events are both caused by some third event.

For example, suppose I notice that the two events of "many people wearing warmer clothing" and "people getting colds" tend to happen together a lot. Is that a coincidence? Does wearing warmer clothing CAUSE people to get colds? Does getting colds CAUSE people to wear warmer clothing? Is there some third event that causes the other two? My guess would be that "weather getting colder" causes both of the above mentioned events.

Suppose we note that marriages and suicides both go up in June. (I don't know if this is true or not. I'm just using it as a hypothetical example.) Which is it? Coincidence? Increased marriages cause increased suicides? Increased suicides cause increased marriages? Some third event causes both? My guess would be that it would be purely coincidence.

Superstitions come about as a result of people misunderstanding the idea of causality/coincidence/correlation. A man has a black cat cross his path. Later that day something bad happens. Did the black cat CAUSE the bad thing to happen? Of course not. The very idea is absurd. The only way it could have caused it to happen is if the man becomes so convinced something bad will happen that his nervousness causes something to happen.

On page 348 the book gives a good list of things to consider in order to try to decide whether one event causes another. It then gives a couple of good examples to consider.