Someone, criticizing efficacy-of-relgions studies, wrote:
Correlation does not imply causation.
And then someone else, seeming to defend them, wrote:
I thought correlation doesn't PROVE causation.
And than Paul Brandon wrote:
A weaker inference.
The problem here is in the explication in the word "imply." For logicians, implication is a *logical* implication. For instance, in a valid argument, premises *imply* the conclusion. That is, it is *logically impossible* for the premises to be true and the conclusion false. In this context, implication is the (logical) equivalent of proof. (Actually, it is even more complicated than this because logicians distinguish between "material" implication, "formal" implication, "modal" implication, "entailment," and a host of others.)
In more more casual usage, people take "imply" to mean something weaker such as "suggest." Unless one spells out exactly what kind of relationship is thought to exist, however, this kind of usage can only lead to confusion in technical or scientific contexts.
The fact of the matter is that correlation tells one virtually nothing about causation at all. It is certainly not sufficient (things can be correlated without having a causal connection), and it probably isn't even necesary (Imagine, e.g., that A causes B, but only in context C, which is rare. Since C is rare, the correlation between A and B will be very low across a variety of contexts, most of which are much more common than C).
In the situation of efficacy-of-religion, the problem is that *even if* religious belief is correlated with better medical outcomes (a phenomenon that I think is far from having been conclusively extablished), religious belief may itself be correlated with lots of other things that are the true causes of the better medical outcomes. Imagine, for instance, that religious-based hospitals give (perhaps even unknowingly) better care to those they know to have religious belief. Because the pct. of hosptials that are religious-based is not insubstantial, this would have an impact on the correlation between religious belief and better medical outcomes. Before people accuse of having *alleged* that religious-based hospitals give better care to religious patients, allow me to give another *hypothetical* exampe. Imagine that religious people have better social support networks -- more card, flowers, visitors, etc. -- which not only help keep patients' moods elevated (for which there is some, even if not conclusive, evidence of positive effect on medical outcome), but also it would be more likely that someone would be present in the hospital room should there be a need for immediate medical intervention. As a result, in those relatively few cases in which immediate medical intervention in the hospital is required, religious folks would be more likely to have a better medical outcome. This would have some impact on the correlation between religious belief and outcome. Keep in mind, in a study with hundreds or even thousands of patients, one doesn't need a very big correlation coefficient in order for it to come out "signficant."
Regards, -- Christopher D. Green Department of Psychology York University Toronto, Ontario, Canada M3J 1P3
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