Dr. J. Allen Hynek
Center for UFO Studies

Probabilities, of course, can never prove a thing.  When, however, in the course of UFO investigations one encounters many cases each having a fairly high probability that "a genuinely new empirical observation "  was involved, the probability that a new phenomenon was not observed becomes very small, and it gets smaller still as the number of cases increases. The chances, then, that something really new is involved are very great, and any gambler given such odds would not hesitate for a moment to place a large bet.

This point bears emphasis. Any one UFO case, if taken by itself without regard to the accumulated worldwide data (assuming that these have already been passed through the "UFO filter"), can almost always be dismissed by assuming that in that particular case a very unusual set of circumstances occurred, of low probability (but strange things and coincidences of extremely low probability do sometimes occur). But when cases of this sort accumulate in noticeable numbers, it no longer is scientifically correct to apply the reasoning one applies to a single isolated case Thus, the chance that a thoroughly investigated UFO case with excellent witnesses can be ascribed to a misperception is certainly very small, but it is finite. However, to apply the same argument to a sizable collection of similar cases is not logical since the compounded probability of their all having been due to misperceptions is comparable to the probability that if in one throw of a coin it stands on edge, it will stand on edge every time it is thrown.