- This will continue until all 50 cards have been used.
- The tester will then thank the subject for participating in the experiment before retrieving the table and filling in the ‘Actual Answers’ column. The score will then be counted and recorded in a separate table.
To prevent anyone cheating and ensuring the events were independent of each other the following was ensured:
- The Tester did not sit with their back to a window, as the light would make it easier for the subject to see through the card to the shape drawn on the other side.
- No one was sitting behind the Tester and signalling to the test subject.
- The test subject did not mark their own test, as they may have tried to alter the results so that they appeared more or less telepathic than they actually are.
- By not telling the test subject whether their answers were right or wrong, as this may affect which symbol they drew next.
- The test subjects should remain free of distractions because they should be able to concentrate on detecting the shape on the card. The experiment should be conducted away from any noise or distractions.
- For the investigation it has been assumed, and assured that the subject does not write down the same symbol for the entire experiment, as this would ensure a result of 10 out of 50. This would make the distribution a Binomial model.
- The testers face shall remain neutral throughout the investigation so that the test subject cannot guess what the symbol is by reading the testers facial expression.
Constants
- The same tester was used throughout the investigation, because if two people were to be ‘senders’ they may have different telepathic abilities, and so make it easier or harder for anyone with telepathic abilities to choose the right shapes.
- Same age range, as the investigation is to see whether students between 16 and 19 show evidence of telepathic abilities.
- Same cards
- Same condition, for example a noise and distraction free environment.
Variables
- Sequence of cards will vary, as they are shuffled to prevent cheating.
Controlled Variables
- Male or Female
- Age, because the selected students could be either 16, 17, 18 or 19.
50 cards were chosen, as this size is large enough to determine whether any of the test subjects are telepathic. Each subject tested for telepathy had a 10 in 50 chance of guessing the correct answers. This can be seen by the Binomial to Normal Distribution shown below:
X ~ B (n,p)
Using n*p, where n = number of cards (50)
p = probability that it will occur/guess correctly (0.2)
X ~ B (50, 0.2)
So n*p = 50 * 0.2
= 10
The mean and standard deviation will be calculated from the data, for both males and females so that they can be compared to see if there are any significant differences that could mean telepathic powers are present. So an estimate can be made for the parent population’s average.
The Central Limit Theorem states that when sampling from a population:
- The distribution of the sample means is approximately Normal if the simple size is large enough. This is why a sample of 60 students was collected – 30 males and 30 females.
- The mean of the distribution of the sample means is equal to the population mean.
- The variance of the distribution of the sample means is the variance of the parent population divided by the sample size.
Confidence Intervals
One way of showing how confident you are in your estimate of a population mean is by stating the size of a sample and the standard error for the mean. The degree of confidence you have in the estimate is more accurate by using an ‘interval estimate’. Thus, as the degree of confidence increases, the confidence interval also increases because to be more confident, a larger interval is needed to fit more values in.
For a Normal distribution, confidence intervals are based on a 90%, 95% or 99% confidence. To calculate this, the standard error that gives these percentages must be found.
Results and Analysis
Key
x = scores
n = sample size
Σ = total of
x ơ n = standard deviation of numbers put in
x ơ n-1 = standard deviation predictor if this is the sample
x = mean
CI = Confidence Interval
Formulas:
μ = x ± CI * x ơ n-1
n
x = Σx
n
x ơ n = Σx2 – x2
n
x ơ n-1 = ơ n2 * n
n-1
Male Results:
x = 9.53
x ơ n = 3.14
x ơ n-1 3.18
95 % Confidence Interval for the true mean:
As there is a 95% confidence interval 1.96 shall be used in the following equation.
9.53 ± 1.96 * 3.18
√30
9.53 + 1.14 = 10.67
9.53 – 1.14 = 8.39
[ 8.39, 10.67 ]
Female results:
x = 9.17
x ơ n = 2.03
x ơ n-1 = 2.07
95 % Confidence Interval for the true mean:
9.17 ± 1.96 * 2.07
√30
9.17 + 0.74 = 9.91
9.17 – 0.74 = 8.43
[ 8.43, 9.91 ]
This diagram shows that there is a 95 % chance that the true mean of the population is within the intervals. So for males, the true mean is between [ 8.39, 10.67 ], whilst for females it is between [ 8.43, 9.91 ].
As can be seen, the male interval has a larger distribution than that of the females. Although this means that the mean could be higher than the females, it could also be lower
To separate the two intervals, which currently overlap, the following is calculated:
Male x – Female x
= 9.53 – 9.17
= 0.18
0.18 = 1.96 * 2.625
√n
0.18 * √n = 1.96 x 2.625
0.18 * √n = 5.145
√n = 5.145
0.18
√n = 28.58
n = 28.582
n = 817.01
Female population
9.17 ± 1.96 * 2.07
√817.01
9.17 + 0.14 = 9.31
9.17 – 0.14 = 9.03
[ 9.03, 9.31 ]
Male population
9.53 ± 1.96 * 3.18
√817.01
9.53 + 0.22 = 9.75
9.53 – 0.22 = 9.31
[ 9.31, 9.75]
This diagram shows that Males appear to have a greater chance of scoring higher than females, although the intervals show that the mean that was acquired from the data is lower than expected in both sexes. Each subject tested for telepathy had a 10 in 50 chance of guessing the correct answers.
I then decided to compare Non-believers and Believers, to see whether beliefs affected the results.
Non-Believers
x = 9.42
x ơ n = 3.00
x ơ n-1 = 3.05
n = 31
95 % Confidence Interval:
9.42 ± 1.96 * 3.05
√31
9.42 + 1.07 = 10.49
9.42 – 1.07 = 8.35
[ 8.35, 10.49 ]
Believers
x = 9.28
x ơ n = 2.20
x ơ n-1 = 2.23
n = 29
95 % Confidence Interval:
9.42 ± 1.96 * 2.23
√29
9.42 + 0.81 = 10.09
9.42 – 0.81 = 8.47
[ 8.47, 10.09 ]
There are more male Non-believers than Believers, which is a direct contrast to females, which shows that there are more female Believers than Non-believers.
This diagram is similar to that of the male against female intervals. This may have occurred for the following reason:
- It was noted that after collecting the results, they showed that there were a higher proportion, nearly 2:1 that the Believers would be female, whilst there was a similar proportion, nearly 2:1 that Non-believers were male. Thus 21 out of total 31 Non-believers were male, whilst 20 out of the total 29 Believers were female. So, although the intervals are different, the same pattern, in that the Non- believers, (the majority of whom are male) have a wider distribution than the Believers, (the majority of whom are female). This can be compared to the male against female confidence intervals, which appear similarly distributed. Thus, the Non-believers show the same behaviour as the males, due to being largely made up of male subjects, whilst the Believers show the same behaviour as the females due to being largely made up of female subjects. To further investigate this, the same number of male and female Believers and Non-believers could be compared, although this would distort the data so that it may seem that there are more Believers or Non-believers than there actually are in the whole population and so would not be representative of the whole population of students attending New College.
To separate the two intervals, which currently overlap, the following is calculated:
Non Believers x – Believers x
= 9.42 – 9.28
= 0.14
0.07
0.07 = 1.96 * 2.64
√n
0.07 * √n = 1.96 x 2.64
0.07 * √n = 5.17
√n = 5.17
0.07
√n = 73.86
n = 73.862
n = 5454.88
Non-believers population
9.42 ± 1.96 * 3.05
√5454.88
9.42 + 0.08 = 9.50
9.42 – 0.08 = 9.34
[ 9.34, 9.50 ]
Believers population
9.28 ± 1.96 * 2.23
√5454.88
9.28 + 0.06 = 9.34
9.28 – 0.06 = 9.22
[ 9.22, 9.34 ]
The diagram shows that the Believer and Non-believers no longer overlap except at one point, 9.34. This gives a clearer view of where the separate means lie, in that they can no longer be in the same interval. The diagram gives a clearer picture of which group is most likely to score highest, in this case, the Non-believers. However, both the Believers and the Non-believers score a mean well below 10, which is the score that would be expected by chance. Although the average was lower than expected, there were individual high scores, for example, two Non-believers scored 17 out of 50. However, this was counteracted with many numbers below 10, the lowest being 5 which was the result of both some Believers and Non-believers.
Evaluation
Improvements:
- The test was relatively long, due to there being 50 cards. Thus people’s attention may have wander and thus they may not try to guess, or even care what answers they give. Also, if the subject is not given enough time, they will be rushed into guessing an answer.
- Instead of the subject having to draw the symbols each time, they could be given a form with boxes to tick. This is both quicker and simpler.
- Instead of choosing subjects by opportunity sampling, if I had longer to collect the results and had access to the resources, I would make a list of every student between the 16 and 19 age range, and then randomly pick 60 people.
My results show that whilst males perform on average better than their female counterparts, both sexes perform under the expected average. Males have an average of 9.53 and females have an average of 9.17. This leads me to believe that something other than guessing is going on, although the averages are relatively close to 10.
Similarly, whilst Non-believers performed worse on average than the Believers, both groups performed below the expected average. Non-believers have an average of 9.42 and Believers have an average of 9.28.
These results are lower than expected. This could be a result of the following:
- The ‘sender’ is not telepathic, hence the symbol not being conveyed to the test subject.
- The ‘sender’ is unconsciously sending conflicting images to the test subject.
- If any of the subjects are telepathic, they may be purposefully trying not to get the correct images, so as to be ‘normal’.
-
A phenomenon known as ‘Psi missing’ illustrates that at times, certain individuals may persist in giving the wrong answers in psi tests, such as telepathy. The accumulation of systematically wrong answers can be so obvious that it suggests something quite different than a mere lack of psi abilities: it is as if people use psi to consistently avoid the target, unconsciously "sabotaging" their own result.
A further investigation would be to gather the results which were, for example above or below the expected mean of 10 by about 4, so all those with results below 6 and above 14. I would then retest the individuals to see whether they can repeat their previous results. If someone with a score of 17 were able to repeat their previous performance, it would lead to the conclusion that they may have some telepathic ability.
The results may only reflect a minority group, and therefore any conclusions drawn may not reflect the whole New College student population.
Resources
Statistics 1, by Cambridge University Press.
Published in 2001. ISBN: 0 521 78802 1
Information about telepathy:
