Have you heard the expression “correlation doesn’t equal”? It’s basically true, but it glosses over some subtle but important ideas. And we need to understand these ideas if we want to use data accurately in analyzing Christianity.

What is a correlation? Very simply, a correlation is an observed association between two things. You know that you’re looking at a correlation when you observe two things, and when one thing is at a high level, the other thing is also at a high level. (This is a positive correlation. A negative correlation has a high level with one thing and a low level of the other). A simple example. There is a correlation between rain and people carrying umbrellas. When we see it raining, we also see more people carry umbrellas. When we see people carrying umbrellas, we are more likely to see rain. Note this is a correlation even though not everyone carries an umbrella when it rains. (Technically correlations refer to probabilistic rather than deterministic associations).

Interpreting correlations. Correlations are really easy to observe. We do it every day. The tough part is interpreting them correctly. What are the true causes underlying a correlation? Sometimes they are obvious. In the case of rain and umbrellas, we know that people carry umbrellas in response to rain—as opposed to it raining because people carry umbrellas. So, in this sense, rain “causes” umbrella usage. Most of the time, however, causality is much harder to pin down.

Smoking and church attendance. Consider going to church and smoking. These two activities are (negatively) correlated because the more likely someone is to do one of them, the less likely they are to do the other. As shown in the figure, people who attend church the most often are the least likely to smoke. (Note: These data come from the 1972-1998 General Social Survey. Base rates of smoking have since dropped). If you’re into numbers, the correlation coefficient between smoking and church attendance is -.25.

 

This fits with my experiences. It’s been awhile since I’ve seen a pastor give a sermon with a cigarette dangling from the side of the mouth or Sunday school teachers huddled outside the church’s back door on a smoking break.

Multiple interpretations. While it’s easy to show that church attendance and smoking are correlated, it’s not at all clear why they are correlated. Which cause or causes produce this correlation? It’s like being a detective at a murder scene. There is a body, but who did it? The detective may have multiple suspects but not know for which one is the murderer. And maybe there are more than one murderers. Here are some of the causal suspects for the correlation between church attendance and smoking.

1. Church attendance reduces smoking. It could be that there’s something about going to church that makes people be less likely to smoke. If they don’t smoke, they don’t start. If they do smoke, they quit. Maybe church teachings emphasize good health. Or maybe there’s an informal norm at churches—thou shall not smoke—and violating this norm is greeted with disapproval.

2. Smoking reduces church attendance. Or, it could be that there is something about smoking that makes people less likely to go to church. Maybe smokers are afraid of feeling judged. Or, maybe smokers don’t want to spend the morning without a cigarette. Or, maybe, if a smoker is already attending a church, they quit because they feel uncomfortable with no one smoking.

3. They share a root cause. Finally, it could be that church attendance and smoking share the same root cause, and this creates what is called a “spurious” correlation. There might be something that changes church attendance and smoking in opposite directions. This would make them correlated even if they don’t cause each other. For example, maybe the personal trait of low self-control makes people less likely to attend church and more likely to smoke.

The problem.  Here’s the problem. In the study of Christianity, as with most topics, careless researchers and commentators jump in, see a correlation, and assume that they know exactly what caused it. They over-interpret the data—making unwarranted and premature conclusions. It’s like a detective, at the murder scene, arbitrarily pointing to one of the suspects and saying “you did it.” They may be right, or they may be wrong, but they don’t really know.

Finding causality. What does it take to test causality? Ideally randomized experiments. For example, we could randomly assign levels of church attendance or smoking, and then observe the impact of this change. When experiments are not possible, and sometimes they are not, then researchers simulate experiments using complex, multivariate models.

In this blog, I will try to be careful in distinguishing between correlation and causation. I will call also out other people who are not being careful. Careless interpretation of correlations creates misinformation and sows confusion. Studying correlations requires that we accept ambiguity, and this is difficult for us human types. If we are to use data to analyze Christianity in society, we must start by carefully distinguishing between correlation and causation.