Hypothesis test 1: an experiment on telepathy

Home > Subject areas > Studying statistics > Testing hypotheses > Hypothesis test 1: an experiment on telepathy

Telepathy is communication which does not rely on any of the known senses: by some unknown method one person becomes aware of what another person is thinking, despite the absence of any opportunity to communicate. For this experiment, a pack of cards was shuffled and split so one of the cards was visible to volunteer X, who then concentrated hard on it. In another room, volunteer Y tried to see if she could determine what card volunteer Y was thinking about. They then wrote it down on a piece of paper. Volunteer Y got the card right! Conditions were checked, but there was definitely no way volunteer Y could have known which card was chosen except by means of telepathy. There were only two viable explanations: either volunteer Y was guessing and was lucky, or they were communicating telepathically with volunteer X.

The general idea of hypothesis testing is that you set up a null hypothesis – typically a hypothesis that nothing interesting is happening – and then check if the data you’ve got is consistent with this hypothesis.

In this case the null hypothesis is that volunteer Y is guessing. We now need to work out the probability of getting our observed data – volunteer Y guessing the card correctly – if the null hypothesis is true. In other words, we want the probability of volunteer Y getting the card right if she is guessing.

If volunteer Y was guessing she only had a 2% chance of getting it right (Click here to see why) Do you think this suggests that telepathy is the more likely explanation? If you think that telepathy is not the more likely explanation, this is probably because you think telepathy is very unlikely or even impossible. Volunteer Y may be unlikely to get it right by guessing, but if telepathy is impossible, this is the only viable explanation.

We could get stronger evidence by asking volunteer Y to repeat the experiment. Let’s imagine they guessed another card, under exactly the same circumstances, and got this one right too. Their score is now two out of two. What is the probability of this happening if the null hypothesis (guessing) is true?

This probability comes to just under 0.04%, or about one in 2,700. (Click here to see why.) This is much less likely to happen by chance, which makes telepathy a more plausible explanation. Do you think this stronger evidence suggests that volunteer Y really is telepathic? Again, there is no right answer here. If you think telepathy is completely impossible, then you will cling to the chance explanation, however unlikely it is to result in two correct guesses.

These probabilities are called p values or significance levels. They tell us how likely the data is to have arisen from the null hypothesis. The lower the p value, the less plausible the null hypothesis is, and so the more likely is the alternative hypothesis – telepathy.

This is an artificial example, but i n the 1920s and 30s, the psychologist, J B Rhine, found a number of people who appeared to be telepathic. In one series of experiments, Hubert Pearce Junior, did a card guessing experiment 8,075 times, and got the card right on 3,049 occasions. There were five cards in the pack, so guesswork would have produced about 1615 hits. Rhine argues that Pearce's performance is so much better than guesswork that telepathy must be involved; others have taken the hypothesis that Pearce was cheating more seriously. Working out the p value for Rhine’s experiment is more difficult. You either need to use more advanced probability or computer simulation (see Making Sense of Statistics, p. 104 and Chapter 5).

This content has been written by Michael Wood author of Making Sense of Statistics