Extra Sensory Perception Statistics:


In today’s post, I am going to combine two of my favorite topics – mindreading and statistics.

I should confess upfront that I do not read minds, at least not literally. I do have a passion for magic and mentalism. I would like to introduce the readers to Joseph Banks Rhine. He is the creator of ESP (Extra Sensory Perception) cards. These are a set of 5 cards with 5 shapes (circle, cross, waves, square and a star). These cards were used for testing ESP. The readers might remember the Bill Murray scene in the movie Ghostbusters. The ESP cards are a common tool for a mentalist.

In 1937, Zenith Radio Corporation carried out multiple experiments under the guidance of Rhine. A selected group of psychics chose a “random” sequence and transmitted it out during the radio show. The listeners were asked to “receive” the transmitted sequence, write it down and send it back to the radio station. The sequence had 5 values and each value was binary in nature. This could be heads and tails, light and dark, black and white, or a group of symbols. The two values were represented as 0 and 1. Thus, a possible sequence could be 00101.

The hypothesis was that human beings are sensitive to psychic transmissions. It is reported that over a million data points were collected as part of these experiments. From a statistics viewpoint, this is a statistician’s dream come true!

The results of the study implied strongly about the existence of ESP. The number of correct guesses was significantly high, if the calculations were based on assumption of randomness.

A million data points is a statistically valid sample size. The studies were blind in nature. The “psychics” in the radio station did not cheat. The responding listeners did not have a way to know the sequence before-hand. So did they prove that ESP is real?

Enter Louis Goodfellow:

Goodfellow (an apt name) was a psychologist involved in the study. He realized something was fundamentally wrong with the study. The data that was transmitted was not truly random. The data was “randomly” chosen by the psychics. Unfortunately, being random is not something that we, human beings, are good at. We will try really hard to create a random sequence, and in the process create a completely non-random sequence. Certain sequences are chosen more than the others, across the board. With over a million data points, there should have been close to 3% occurrence of 11111 or 00000. The data showed this was actually less than 1%. Additionally, with such a large sample size, we would expect uniform data, meaning all sequences should show up with nearly equal proportions. This was not the case either.

In other words, the study revealed that the psychics were indeed human beings. Goodfellow repeated the study without involving the psychics. The study group was required to create a “random” sequence. The resulting data was very much similar to the Zenith radio data. Goodfellow also repeated studies with truly random sequences, and the study group failed to “receive” the sequences. (A psychological interpretation of the results of the Zenith radio experiments in telepathy)

The basic assumptions of independence and randomness were not followed for the original study. Thus, we still do not have evidence that ESP is real.

Always keep on learning…