Correlation and causation

When the measures of two phenomena (or factors or variables) change in relation to one another, they are said to be correlated. Sometimes, when one phenomenon changes, the other phenomenon changes because of the first one. That is, there is causation between the first and the second. But that is not always the case, though people often infer that it is. We must be careful not to confuse correlation and causation.

Correlation AND Causation

The graph below shows the relationship between the number of miles a person drives each week and the amount of money she spends on gas each week. As you can see, as the number of miles driven increases so does the amount spent on gas. There is a correlation between these two variables. But is there a causal relationship?

Graph of grammatical errors

In this case, the answer is yes because a person needs the gas to make the car run, so the more the car is driven, the more gas that has to be bought.

There could also be a negative correlation, in which case one variable increases while the other decreases. The graph below shows that as the number of minutes spent proofreading a paper increases, the fewer grammatical errors that remain.

Graph 2

As in the first situation above, there is not only a correlation but a causal effect: by spending more time proofreading a paper, the more likely one is to catch grammatical mistakes.

Correlation but Not Causation

Let’s take a look at another pair of phenomena that are often related: heart rate and amount of sweat produced. While these are often positively correlated, does a change in one of these variables cause the other? This answer is no, there is some other variable that causes both heart rate and amount of sweat produced to increase or decrease. When a person exercises, for example, the heart beats faster and the body sweats to keep the person cool. When the person stops exercising, both begin to decrease. Medical conditions can also be the cause of the correlative change in heart rate and sweating.

Weight Loss

What about diet supplements and weight loss? We see many supplements advertised as the key to weight control. There may be a correlation between taking supplements and weight loss, but is it the supplements that cause the weight loss? Most research says no, that the supplements do not really do anything. So what is the cause for the correlation? It is that along with taking supplements, people are more likely to eat less and exercise more – and these are the two main factors in weight loss. Eating less (and better) puts fewer calories into the body and exercise burns off more calories. So while taking diet supplements may reduce appetite in some cases or have other effects on the body, their real effect is as the trigger to eating better and exercising; they are not the direct cause of the weight loss.

Education

In education, especially colleges and private schools, administrators measure student satisfaction. There is often a positive correlation between ratings of satisfaction and grades. Does a high level of satisfaction cause grades to be better? Or do high grades lead to ratings of high satisfaction with the school? Or perhaps neither one causes the other, and there is a third factor, such as small classes or personal concern on the part of faculty that lead to both.

The lesson to learn is that when you find logical variables that are correlated, do not assume that there is a causative relationship, also. (We can find many, many correlations in which the two variables have nothing to do with each other. These correlations are generally meaningless and are not worth further investigation.) It may be important to investigate factors that could lead to the correlation. Once you suspect what factor(s) may be influencing the correlation, further research is necessary to determine if you are correct and the degree to which the other factor(s) affect the correlated ones. Determining causation is usually the harder part of research once a relevant correlation is found.

Learn More

If you are interested in learning more about correlation and causation, consider pursuing a degree in data science.