Belief & Coincidence

People Don't Understand Statistics So Have Mistaken Beliefs About Coincidences

One of the reasons people believe in psychic phenomena is not because of experiments which purport to show something statistically significant — these results only serve to bolster beliefs which already exist. People’s beliefs are instead based upon their own personal experiences. The more such experiences a person has, the stronger their belief will be.

What sorts of experiences are involved? There is a wide variety, too many to cover each one separately here. Many involve dreams — a person dreams about some event, usually an accident or tragedy, and then it mysterious takes place shortly thereafter. Some involve waking premonitions — a person thinks about an old friend and then that friend suddenly calls on the phone. Somewhere, somehow, a person just “knows” that an event is going to occur, and then it does indeed occur.

According to people’s reports, their experience could not have occurred by accident or by coincidence. Therefore, lacking any clear scientific explanation, they conclude that the events were the result of some cosmic, spiritual, or supernatural forces beyond our current understanding.

On the face of it, this conclusion may seem reasonable, but it is not. Even if there were no current scientific explanation, this does not mean that the alleged causes really are true. Ignoring that for the moment, however, the argument also fails because of the key premise: that such an event cannot possibly be the result of coincidence. Not only is this premise not supported, it is in fact false.

People’s failure to realize this is due to their ignorance of statistics, in particular the statistics of large numbers. Studies have even shown that believers in the paranormal are worse than the average person when it comes to estimating the statistical chances of certain events occurring. The same people have also been shown in experiments to be more likely to perceive themselves as having some sort of “mental” control over events happening around them.

When someone cannot reliably evaluate the chances of an event happening, they are much more likely to attribute it to something other than chance — and lacking any specific, scientific interpretation, their need to find some explanation will lead them to adopt a paranormal belief. David Marks explains such misunderstanding thus:

    “It is a simple deduction from probability theory that an event that is very improbable in the short run of observations becomes, nevertheless, highly probable somewhere in a long run of observations. For example, if we flipped five coins at once, the probability of getting five heads is 1/32, or about .03. But if we repeated the flipping of five coins ten times, the probability of getting five heads somewhere in the ten tests is about .27. If we ran 100 tests, the probability of five heads rises to .96, which is highly probable indeed. [a probability of 1.0 is a certainty] But if we stopped anywhere in these 100 tests and asked what the probability would be of getting five heads on the very next trial, we are back to the starting probability of .03 because we have switched from a long-run question to a short-run question.”

To better see why, first consider the large numbers of people involved — billions of people across the planet. How many people, right now, are thinking about old friends? Most of them will not have that friend call or visit in the next day or so, but a couple of them will. We only hear about a few who fall into this latter category and it seems amazing to us. It certainly seems amazing to them, but their experience is not statistically unexpected and their subjective perception of events does not match reality.

Selective memory also plays an important role in how people perceive these coincidences. David Marks calls such coincidences “oddmatches,” and although it is true that oddmatches happen and give some people reason to believe that these events have some supernatural or paranormal cause, it is also true that it occurs much more often that such matches fail. People just don’t remember them. The more normal and expected an event is, the less likely it is to be remembered. The more odd and unexpected it is, the more likely it is to be remembered. According to Marks:

    “...this type of match has a distinct quality of oddity, because we cannot explain it by any common knowledge. An oddity captures our attention and causes us to search further for an explanation. The more striking the oddity, the longer we think about it and remember it.”

We remember cases where we thought of an old friend who called shortly thereafter, but not the many more instances of thinking of old friends without receiving calls. We remember cases where we dreamed of a tragedy before one occurred, but not all the tragic dreams that weren’t accompanied by tragic events. We remember the things that validate our beliefs in our power, not the things that would contradict us.

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