Telepathy Investigation IntroductionThe aim of this investigation is to statistically analyse the results of telepathy tests run on a selection of people to determine whether none/one/some/all of them poses telepathic powers. These results could be used as a representative sample of other similar people.The selection of people will be children, all 16 or 17 years old, from a further mathematics class. These children are similar in age and assumed to be similarly intelligent. A group of people similar in these characteristics has been chosen, so this group could be used as a representative sample of other similar people.The sample size will be 10 people large, as this should be large enough to show if any of them have telepathic powers compared to the rest. This size should also be large enough to show if further investigation into this group of society about their telepathic powers should be considered, should some of them exhibit telepathic powers. This size should also be large enough to determine whether the "transmitter" (see below), possesses telepathic powers.A person will take card from a pack of cards and will look at it, while not letting anyone but him/her to view the card. Another person will then state what suit they think the
card is, heart, diamond, club or spade. Whether they got the suit right or wrong will be recorded.This investigation will try and determine whether any people in the group can receive telepathic messages, and so the person viewing the card - the "sender", will be the same person throughout the investigation. This means that the telepathic "sending" ability of the person viewing the card is also tested. When looking at the results from the group as a whole, the telepathic powers of the sender can be analysed, while looking at individual results of people trying to received messages will give ...
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card is, heart, diamond, club or spade. Whether they got the suit right or wrong will be recorded.This investigation will try and determine whether any people in the group can receive telepathic messages, and so the person viewing the card - the "sender", will be the same person throughout the investigation. This means that the telepathic "sending" ability of the person viewing the card is also tested. When looking at the results from the group as a whole, the telepathic powers of the sender can be analysed, while looking at individual results of people trying to received messages will give an idea as to their own telepathic powers.Each person will try and receive the suit of 20 cards, as this size appears to be a large enough set of tests to determine whether the subject has any telepathic abilities. The card will be picked from a shuffled pack of cards, in case any tampering has been involved.The results of the test will be compared to a binomial model that assumes that the suit that the receiver picks is picked at random (that the receiver or transmitter has no telepathic powers). This distribution model requires the events to be independent of each other. Certain precautions must be taken to ensure this. The subject must not be told whether or not they got a suit right or wrong, as this may affect their next answer. Also, the subject must not be able to see the transmitter, as this may also affect their answer, as the transmitter's expression may give an idea to whether they stated the correct suit.The mean and standard deviation will be calculatedfrom the real data, and from the binomial model, sothey can be compared. They can then be compared to seeif there are any significant differences that couldmean telepathic powers are present.ResultsPerson No of correct Answers1 62 83 84 25 36 87 68 69 910 9Number of correct answers 2 3 4 5 6 7 8 9Frequency 1 1 0 0 3 0 3 2Calculations Using DataLet x be number of correct answersMeanStandard DeviationBinomial ModelThe binomial probability model can be calculated fromthe following formula, where given n trials of anevent, the probability of r occurrences of an outcomethat has a probability p occurring at each trial.To calculate the probability distribution for the setof telepathy tests, assuming that the chance of eachsubject stating the correct card is ¼, and there are20 tests run on each subject, the formula istherefore:Using this formula, the probability distribution forcorrectly stating the suit of card is as follows,where X is the number of suits correctly chosen.x p(x)0 3.1712 x 10-31 2.1141 x 10-22 6.6695 x 10-23 1.1339 x 10-14 1.8969 x 10-15 2.0233 x 10-16 1.6861 x 10-17 1.1241 x 10-18 6.0887 x 10-29 2.7061 x 10-210 9.9223 x 10-311 3.0068 x 10-312 7.5169 x 10-413 1.5419 x 10-414 2.5699 x 10-515 3.1712 x 10-616 3.5693 x 10-717 2.7994 x 10-818 1.5552 x 10-919 5.4570 x 10-1120 9.0949 x 10-13MeanThe mean of this probability distribution can becalculated thus:Standard DeviationAnalysisThe mean of the real data is 30% higher than the meanof the probability distribution. There could beseveral reasons for this. It could mean that thetransmitter has some telepathic powers. It could meanthat many of the people in the group to receivemessages are telepathic. It could be a combination ofboth.However the standard deviation for the test data isapproximately 18% higher than for the probabilitymodel. This means that there is a higher spread, thatthere are more results further from the mean thanthere would be if the subjects were simply guessingthe suit. This does suggest that some of the subjectsthat could have possessed telepathic powers were notgetting the correct suit right on purpose. To put itsimply, they were "fighting" the messages they weresent. It could also mean that the transmitter couldhave been sending them incorrect messages. I think that data doesn't show that anyone in the testhad any extremely significant telepathic powers. Thehighest number of correct cards in the test was 9.This happened twice. This is quite an improbableevent; the probability of such an event happeningonce, is 0.027061. However, as there are so manythings that could happen - from getting 0 right togetting all 20 right, they are all improbable, justsome are more probable than others.Here I have found I have contradicted myself. The meanand standard deviation show that some of the peoplehave telepathic powers, but looking at the data theydon't. I think this is because this test was severelylimited. The results of the test could have beenrandom, and the mean and standard deviation simple"happen" to be higher. I think that the test was farto short and the test group too small to be certain ofany telepathic powers. A future test should test eachperson more and ask him or her to identify more suitsof cards. The sender would have to be tested morealso, and try and transmit more cards to more people.To make sure that this group of people doesn't havetelepathic powers within it, they should all besubject to longer tests, as this will confirm whetherthey have telepathic powers or not.A large limitation of this test was deciding whetherthe results show if it is the sender, or the receiversthat were telepathic. This could be done by making thereceivers try and receive messages from a selection ofpeople, and analysing the results to find which peoplewere the best transmitters.