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Nunilier of correct hits by chance out of 25

Figure 6:

Bell curve for a test of 25 questions with 5 possible answers. If chance is operating, probability predicts that most people (79 percent) will get between 3 and 7 correct, whereas the probability of getting 8 or more correct is 10.9 percent (thus, in a group of 25, several scores in this range will always occur purely by chance), of getting 15 correct is about 1 in 90,000, of getting 20 correct is about 1 in 5 billion, and of getting all 25 correct is about 1 in 300 quadrillion.

Nunilier of correct hits by chance out of 25

Figure 6:

Bell curve for a test of 25 questions with 5 possible answers. If chance is operating, probability predicts that most people (79 percent) will get between 3 and 7 correct, whereas the probability of getting 8 or more correct is 10.9 percent (thus, in a group of 25, several scores in this range will always occur purely by chance), of getting 15 correct is about 1 in 90,000, of getting 20 correct is about 1 in 5 billion, and of getting all 25 correct is about 1 in 300 quadrillion.

for misinterpretation of the high scores. In this scenario, a tiny fraction would be 3 standard deviations above the mean, or get 11 hits, a still smaller percentage would reach 4 standard deviations, or 13 hits, and so on, all as predicted by chance and the randomness of large numbers. Believers in psychic power tend to focus on the results of the most deviant subjects (in the statistical sense) and tout them as the proof of the power. But statistics tells us that given a large enough group, there should be someone who will score fairly high. There may be lies and damned lies, but statistics can reveal the truth when pseudoscience is being flogged to an unsuspecting group.

After the ESP experiment, one woman followed me out of the room and said, "You're one of those skeptics, aren't you?"

"I am indeed," I responded.

"Well, then," she retorted, "how do you explain coincidences like when I go to the phone to call my friend and she calls me? Isn't that an example of psychic communication?"

"No, it is not," I told her. "It is an example of statistical coincidences. Let me ask you this: How many times did you go to the phone to call your friend and she did not call? Or how many times did your friend call you but you did not call her first?"

She said she would have to think about it and get back to me. Later, she found me and said she had figured it out: "I only remember the times that these events happen, and I forget all those others you suggested."

"Bingo!" I exclaimed, thinking I had a convert. "You got it. 'It is just selective perception."

But I was too optimistic. "No," she concluded, "this just proves that psychic power works sometimes but not others."

As James Randi says, believers in the paranormal are like "unsinkable rubber ducks."