“Miracles” and the Law of Large Numbers

Michael Shermer uses statistics to show why “miracles” happen hundreds of times a day in America (hint: events with a low probability of occurring in a small sample have a high probability of occurring in a large sample)—and why miracle talk is especially unfair to the faithful:

Let’s say 1 million people have cancer in America (it’s much higher than this), and only one-tenth of 1 percent experience a spontaneous recovery (it’s actually higher than this). 1,000,000 x .001 = 1,000 people. Out of that cohort of 1,000 people, what are the chances that half a dozen of them have compelling narrative stories worthy of broadcast television? Pretty good! Here is a show you will never see on any television series: “Next, we examine the remarkable fact that 99.99 percent of people who were diagnosed with incurable cancer and were prayed for died anyway. Stay tuned, for you won’t want to miss these stark statistical realities.”
Of course you will never see such a show because of the confirmation bias, in which we look for and find confirmatory evidence for what we already believe and ignore or rationalize the disconfirmatory evidence. This is naturally what any religion or television production team is going to do when telling a story about miracles: They will pick and choose the most compelling cases that seemingly defy science and reason, and present those to the public, while blindly (and cruelly) ignoring all those devoutly religious people whose loved ones prayed in earnest for them and who died nonetheless.

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  1. weaselbreath says:

    So while it may be useful to remind everyone that much we find impressive comes about because of selective sampling, it’s unclear why this is news today. Many, including Shermer, have made this point for years. Anecdotal evidence fails to represent statistical odds even as it informs us of local conditions and, simply by giving us an unique experience, biases our point of view. Now that we have several means of nearly instant communication on a global scale, the anecdotal is amplified greatly. That alone fuels belief, particularly belief that isn’t faith based but requires, if only unconsciously and despite denials to the contrary, evidence of some sort. Seems this shows that an alert and discriminative awareness (to be distinguished from a prejudiced one) is going to be even more necessary now than it has been previously. Is that why this topic has come around once again?

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