More Problems
Are you Psychic (or just psychotic)?
Do you have hidden psychic powers? Is there a career
waiting for you on the Psychic Hotline? We will use
statistical hypothesis testing to find out. (Disclaimerwe
actually are more interested in learning how statistical
hypothesis testing works, but I hope you find the exercise
both enjoyable and instructive.)
You will pair up, one of each pair taking the role of the
sender and the other of the receiver. You will then sit
backtoback, and the sender will write a circle or an X on
a sheet of paper. He/She will then concentrate on that
image, and the receiver will write what he/she thinks it is.
The receiver then passes the result to the sender who
tallies a score showing number right and number wrong. You
will do this procedure 25 times.
However, before we get to this step, we have to decide
what we are looking for. If there is nothing psychic
happening, we expect that by random chance about 50% of the
answers will be correct.
We need to begin with an assumption, and it will be the
assumption that we want to disprove. Should we begin by
assuming you are not psychic? Or should we begin with the
assumption that you are in fact psychic? Explain.
(Should we consider all wrong answers as evidence of some
sort of psychic ability? Or do we only want to conclude a
person is psychic when most answers are correct? This is
asking whether we want a onetailed test or a twotailed
test.)
We will then gather data and ask whether these results
are consistent with the hypothesis. For example, if you get
14 right of 25 tries, you might argue that since you did
better than expected, this result indicates you have a
little bit of psychic ability. However, most people would
say that you just got lucky, since guessing 13 or 14 will
happen a lot by random chance if you are not psychic. On the
other hand, if you guess 25 of 25 correct, that also could
happen by random chance even if you are not psychic, but it
is very, very unlikely. Instead of explaining this result as
luck, we might conclude that these results are highly
suggestive that you are psychic.
Before you begin to gather data, you must specify what
evidence will make you reject the hypothesis that you are
not psychic and accept instead the alternative that you
are.
How unlikely will the results have to be before you will
think psychosis (oops, I guess that should be psychic
ability) is plausible? 1 in 20? 1 in 100? 1 in 1000? 1 in
1000000?
Explain your decision rule and why you made it.
Gather your data.
If you are not psychic, you should get 50% right by
random chance. We are drawing from a zeroone box. For the
box the mean is .5 and the standard deviation is .5. If we
compute what we expect for the sum, the expected value of 25
draws is 12.5 and the standard error of the sum is 2.5. (If
you do not know where these numbers came from, please stop
and ask.) With this we can do a ztest:
 ((Observed number right)12.5)/2.5 =
What do you decide? Is it chance, or are you psychic?
Explain.
An early version of Are You Psychic
Introduction to Hypothesis Testing
Are you Psychic (or just
psychotic)?
Do you have hidden psychic powers? Is there a career
waiting for you on the Psychic Hotline? We will use
statistical hypothesis testing to find out. (Disclaimerwe
actually are more interested in learning how statistical
hypothesis testing works, but I hope you find the exercise
both enjoyable and instructive.)
You will pair up, one of each pair taking the role of the
sender and the other of the receiver. You will then sit
backtoback, and the sender will write a circle or an X on
a sheet of paper. He/She will then concentrate on that
image, and the receiver will write what he/she thinks it is.
The receiver then passes the result to the sender who
tallies a score showing number right and number wrong. You
will do this procedure 20 times.
However, before we get to this step, we have to decide
what we are looking for. If there is nothing psychic
happening, we expect that by random chance about 50% of the
answers will be correct. In fact, using the binomial tables,
we can compute exact probabilities of what random guessing
will yield:
 Probability of 10 right = .1762
 Probability of 9 thru 11 right = .4965
 Probability of 8 thru 12 right = .7368
 Probability of 7 thru 13 right = .8847
 Probability of 6 thru 14 right = .9586
 Probability of 5 thru 15 right = .9882
 Probability of 4 thru 16 right = .9974
 Probability of 3 thru 17 right = .9995
 Probability of 2 thru 18 right = .9999

 We can present this information in this way:
 Probability of being 1 or more away by random chance
= .8238
 Probability of being 2 or more away by random chance
= .5035
 Probability of being 3 or more away by random chance
= .2732
 Probability of being 4 or more away by random chance
= .1253
 Probability of being 5 or more away by random chance
= .0414
 Probability of being 6 or more away by random chance
= .0118
 Probability of being 7 or more away by random chance
= .0026
 Probability of being 8 or more away by random chance
= .0005
 Probability of being 9 or more away by random chance
< .0001

 Probability of getting 09 or 1120 by random chance
= .8238
 Probability of getting 08 or 1220 by random chance
= .5035
 Probability of getting 07 or 1320 by random chance
= .2732
 Probability of getting 06 or 1420 by random chance
= .1253
 Probability of getting 05 or 1520 by random chance
= .0414
 Probability of getting 04 or 1620 by random chance
= .0118
 Probability of getting 03 or 1720 by random chance
= .0026
 Probability of getting 02 or 1820 by random chance
= .0005
 Probability of getting 01 or 1920 by random chance
< .0001
We need to begin with an assumption, and it will be the
assumption that we want to disprove. Should we begin by
assuming you are not psychic? Or should we begin with the
assumption that you are in fact psychic? Explain.
(Should we consider all wrong answers as evidence of some
sort of psychic ability? Or do we only want to conclude a
person is psychic when most answers are correct? How would
you chance the tables if you only want to consider correct
answers?)
We will then gather data and ask whether these results
are consistent with the hypothesis. For example, if you get
11 right of 20 tries, you might argue that since you did
better than expected, this result indicates you have a
little bit of psychic ability. However, most people would
say that you just got lucky, since guessing 11 will happen a
lot by random chance if you are not psychic. On the other
hand, if you guess 20 of 20 correct, that also could happen
by random chance even if you are not psychic, but it is
very, very unlikely. Instead of explaining this result as
luck, we might conclude that these results are highly
suggestive that you are psychic.
Before you begin to gather data, you must specify what
evidence will make you reject the hypothesis that you are
not psychic and accept instead the alternative that you
are.
Explain your decision rule and why you made it.
Gather your data.
What do you decide?
