Reverse causation and sleeping in the nude

"Correlation does not imply causation."

You probably have heard this point being made especially with respect to medical studies. If Factor A correlates with Disease B (i.e. they tend to appear together) does not mean that A caused B. Indeed the possibility exists that B caused A and that A is a symptom of B rather than a cause. Or there may be no causal relationship at all.

A good rule of thumb is to consider causality in both directions. If A correlates with B, then one possibility is that A => B i.e. A caused B. However one should consider the reverse causation that maybe B => A i.e. B caused A. A third possibility is that C => B and C => A i.e. there is a third factor C that caused both A and B. A fourth possibility is that C => B and D => A and the correlation between A and B is either by chance or indirect.

Sometimes causality only makes sense in one direction. For example, there is a high correlation between lung cancer and smoking. One possibility (that turned out to be correct) is that smoking causes lung cancer. The reverse causation that lung cancer causes smoking doesn't make sense because people smoke for years before contracting lung cancer. Careful studies were necessary to eliminate the possibility of a third factor that caused lung cancer and correlated with smoking (e.g. poverty).

However in other cases causation could conceivable work in either direction. This came to mind when I read the following passage in the Daily Mail:

"Of 1,004 Britons, 57 per cent of those who sleep in the nude said they were happy in their relationships, compared with 48 per cent of those in pajamas, 43 per cent of nightie wearers and 38 per cent of those in onesies."

The author of the article concluded that "the best way to keep a marriage happy is to sleep in the nude."

Well to be safe let's test reverse causation. Instead of sleeping in the nude causing a happy marriage, perhaps a happy marriage causes sleeping in the nude. That seems plausible.

A priori it is not clear which direction the causation is or whether there is a third factor that causes a happy marriage and that may correlate with sleeping in the nude.

A final interesting possibility is that there may be some sort of positive feedback loop (i.e. virtuous cycle), i.e. A => B and B => A. In other words, sleeping in the nude may cause a happy marriage and a happy marriage may cause sleeping in the nude. This type of self-reinforcement would make the correlation even stronger.

Thus, the writer is incorrect to conclude a causal relationship from a correlation, and indeed even if a causal relationship does exist, it is not clear in which direction. Regardless sleeping in the nude with your spouse is probably not a bad idea.

Figure 1. Does sleeping in the nude lead to a happier marriage or does a happier marriage lead to sleeping in the nude? Perhaps both?