Re: Math Midget seeks help with odds

In article <1165827554.340991.147530@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"Proginoskes" <CCHeckman@xxxxxxxxx> wrote:

chrystalia wrote:
Greetings:

I am not a math professional, but I am hoping someone will help me. My
partner and I are running what could be termed "binary prediction
tests", in that we are testing subjects on their ability to predict the
outcome of coin tosses (heads or tails) and the colors of unseen
playing cards (red or black). The tests are, obviously, designed to
determine the presence or absence of so-called psychic abilities
(precognition, mainly). We have data sets that obviously show non
random affects. The question is, how unlikely are the divergences? For
example, we have one subject who has tossed a total of 222 tails
(longest streak 23 consecutive tails) and 135 heads in a single series
of tosses, and consistently tosses a head/tail ratio of 2:1.

We have another subject who made 213 correct guesses and 151
incorrect guesses of playing card colors for a total of 364 guesses. We
would like to be able to analyse binary trials of this type. Are there
simple formulas we can use to do so?

Yes. What you are doing is a Bernoulli process. Formula (21) of
http://mathworld.wolfram.com/BernoulliDistribution.html shows how to
calculate the probability of getting exactly n "hits" out of N trials.
By adding formulas like this, you can determine what the probability of
getting between a and b "hits" out of N trials is.

--- Christopher Heckman

But you must take care, since if you have a lot of people performing an
experiment, the probability of at least one of them producing rare
results can be quite large.
.

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