Question

A researcher looking for evidence of extrasensory perception (ESP) tests 500 subjects. Four of these subjects do significantly better (P < 0.01) than random guessing.
a) Is it proper to conclude that these four people have ESP? Explain your answer.
b) What should the researcher now do to test whether any of these four subjects have ESP?

Answer 1

@perl

Answer 2

@inkyvoyd

Answer 3

so for a, we reject the null that they don't have ESP because the P value is less than .01? so it is proper to say these four people could have ESP

Answer 4

lets make this more concrete, lets suppose the ESP test is to guess the correct
flips when someone flips a coin in a room . and there are say 5 flips of a coin

Answer 5

okay

Answer 6

Lets say the ESP test consists of reading someones mind as they flip a coin eight times and correctly stating the sequence of flips heads or tails.
If we suppose that the true order of flips is :
HHTTHTHT

it makes sense that someone could get it right due to guessing. We can make a histogram of all the guesses.
There is .01 probability of 5 people or less getting it right, so 4 people is not impossible.

Answer 7

okay

Answer 8

I changed the number of flips from 5 to eight.
Now let X = # of people out of 500 who guess the coin sequence correctly.
This is a binomial random variable, which has probability n * p , here p is the probability of getting all coins right (1/2)^8 = .0039
and n = 500.

Answer 9

but when you multiply 500*.0039 = 1.95, you expect around 2 people to get it right. thats the point im trying to make

Answer 10

because the sample size is so large

Answer 11

oh okay yeah that makes sense

Answer 12

if the sample size was small, say 30 people, then it would be unusual for any of them to get it right (to accurately predict a sequence of 8 coin tosses).

30 * .0039 = .117 , which is less than 1 person.

Answer 13

okay

Answer 14

I think the `(P<.01)` in the problem stands for probability (not p value).
So the ESP test involves something which has a low probability of getting right, less than .01, like flipping a coin 7 or eight times and guessing the correct sequence

Answer 15

so what would we say for a?

Answer 16

because of the size of the sample it is not unusual to get 5 or less people to pass the ESP test.

Answer 17

okay what would we do for b?

Answer 18

so after identifying the ones who got correct out of 500 people, you should do a new ESP test on them. if the probability P of passing the test is less than .01, then it is unlikely that any of these 4 people will pass it. here np = 4 * .01 = .04 , which is less than 1 person

Answer 19

okay thank you! do you have time to help on a couple more?

Answer 20

ok, please make a new post

Answer 21

okay will do