If only religious apologists understood statistics…

Apr 06, 2012 Comments Off by

The last time I uploaded many articles in quick succession, I had just returned from on the all-inclusive holiday with my parents in Spain during which I authored said articles. My return to writing for this site after a long recess also involves authorship during such a holiday. This is what is often called a coincidence. When people insist, “there’s no such thing as a coincidence”, they seek to imply some deeper significance behind an apparent example of a coincidence. There is a distinction statisticians draw between two types of “error”, falsely seeing a coincidence and falsely seeing something more than coincidence. These are called “type I” and “type II” errors in some order (I forget which). As biologists have observed, animals (including humans) are biased in favour of seeing “something more”, in case there is something. Everything from Skinner’s pigeons to humans’ arguments for the supernatural attest to this. That’s right: I’m making a point about religion. Given where you’re reading this, you should have seen that coming; that is not a coincidence.

How many more anecdotal examples must we endure in “debate”? If data doesn’t undermine the null hypothesis in a proper statistical analysis, no alternative hypothesis is reasonable to believe. Of course, statistics can get abused every which way but loose; it is well-known, for example, that a statistically significant data set can be split into two subsets each of which isn’t statistically significant. (A point often missed is that “significant” doesn’t mean “big”, but “not a coincidence unless an unusually big one, which isn’t likely”.) Climate-change deniers love this theorem. The last thirty years of temperatures are indubitably a period of very intense warming – “significant” in both the statistical and common meanings of the term. But cut it into two 15-year periods, and significance survives in neither one, which is why the number 15 was chosen in the first place. It is also possible to falsify significance by choosing a small subset of data in which no significance is present. Another climatological example is that of deniers of anthropogenic climate change attributing temperature changes to solar cycles by focusing on brief periods in which it looks like temperatures and solar forcing correlate well. In fact, the Sun has been dimming for decades. So both ways to mislead by cherry-picking data to be found among ACC deniers, and the second trick is what all supernatural anecdotes rely on (unless they use something even more blatantly silly like making up stuff or not being cynical enough of stories that clearly are likely made up). Everything from prayer to astrology to alternative medicine is rendered invalid by this trick, no matter what their advocates say.

Charles Darwin’s cousin Francis Galton largely founded modern mathematical statistics; at any rate, he developed many important concepts, including “covariance”, and his experimental work gave some statistical tests early applications. He also pioneered at least one topic’s statistical analysis, namely that of whether or not prayer does anything. As every medic knows, “treatment X works” means “treatment X works better than a placebo in a double blind trial”, and of course “better” means “better to a statistically significant extent”. Galton decided to test prayer’s use in treating illness, and found it didn’t work. Many, many pieces of research have repeated this test since then, and literally every single one has come to the same conclusion. Believe it or not, there are religious groups who are fully aware of this track record who continue to fund such research, because they know sooner or later a false positive has to happen, just as if you toss a coin often enough it will land heads up 10 times in a row. Naturally, all such groups hereby abdicate from all their integrity, including the Templeton Foundation. So, not much integrity was lost then.

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About the author

For most of my time as an undergraduate there was an atheist society in my university, which was founded late in my first year there. I was a committee member from then until my degree ended, by which time the society was atheist, secularist and humanist (you needn't be all three!). This gives me many experiences to relate. I have long critiqued pro-religious arguments, including in hundreds of posts - many of them thorough rebuttals to articles - on richarddawkins.net under my name. My degree was in physics, and I know a lot of the science - physics and otherwise - relevant to the debate on religion.
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