According to a news article which just got posted on Richard Dawkins' website, a study shows that "people with higher IQs are less likely to believe in God." Apparently the creme de la creme among scientists are not only geniuses but have chucked the belief in talking snakes and cops in the sky: "A survey of Royal Society fellows found that only 3.3 per cent believed in God - at a time when 68.5 per cent of the general UK population described themselves as believers."
Well, let's assume that's true--that highly intelligent blokes are more likely to be nonbelievers. As is known to all here I don't subscribe to any postulated supernatural entity whether you call them gods, goddesses, deities, angels, higher powers and principalities, your heavenly juju or holy mojo or Elvis for that matter. On the other hand, I have no idea what my IQ is. Since I'm a true-blue, dyed-in-the-wool, in-your-face atheist, does it follow then that I am more likely to have above average IQ? Can I conclude that I'm most likely an Einstein? Let's find out.
First, for the sake of clarity let's give the news article's claim some concreteness. So let's say that it's been determined that those with IQ >100 have an 80% chance of being atheistic. Now let's try and encode that in the nomenclature of probability theory since we are dealing with likelihoods.
AA = above average intelligence
NB = non-belief
P() = probability of
The above proposition then can be expressed as:
If a person has AA then P(NB) = 80% [let's call this P1]
We now move on to the question we're trying to answer. Does it follow that if I'm a nonbeliever there is an 80% of oh so humble moi having above average intelligence? In other words, is the following statement true:
If a person is an atheist then P(AA) = 80% [P2]
Well, you probably guessed it's not.
P1 can be written succinctly as P(NB|AA), which is read as the "probability of nonbelief given the person has above average intelligence." The vertical bar means "given."
P2 on other hand can be written as P(AA|NB), the probability of having AA given NB.
P1 and P2 are known as conditional probabilities and the values for these two are not necessarily the same. More often than not they're different. If we want to find the value for P(AA|NB) we'd need to have the figures for P(AA) and P(AA and NB), the latter being the probability that a person has above average intelligence and is an atheist--the intersection between the set of people with AA and the set of atheists. Mathematically, P(AA|NB) = P(AA & NB) / P(NB).
So the answer to our inquiry is: No, we cannot conclude at all that I can now be a member of Mensa or any clique and club of snobbish, condescending eggheads and geniuses.?
I couldn't think of a good title for this piece and so have that clumsy one up there. It alludes to the conversion error whereby given "if A then B" is true we presume it follows that "if B therefore A."