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From: rpjday@watrose.UUCP (rpjday)
Newsgroups: sci.math
Subject: a mathematical problem in psi (read it anyway, ok?)
Message-ID: <8250@watrose.UUCP>
Date: Mon, 10-Nov-86 07:17:23 EST
Article-I.D.: watrose.8250
Posted: Mon Nov 10 07:17:23 1986
Date-Received: Mon, 10-Nov-86 22:15:33 EST
Distribution: sci
Organization: U of Waterloo, Ontario
Lines: 29


  Now that the furor about my original posting requesting analog models
of computation has died down, how about another problem -- the use of
statistics in psychic experiments (this is a MATHEMATICAL article, so just
keep reading).
  I'm sure that we are all familiar with the 25-card deck that is commonly
used to test psychic ability.  There are 5 shapes used, with 5 of each shape
in the deck (wavy lines, cross ... whatever).  Since the subject knows the
shapes and their frequency distributions, we would expect that, just by
guessing, any subject should get 5 out of 25 correct.  Nothing deep here.
But this takes into account that the subject does not get any feedback.
We could imagine that there are two kinds of feedback he may receive:
	
	1) He may be told whether he is correct or not.
	2) He may actually be shown the card.

  Based on either of the above types of feedback, what is the expected number
of "hits" now?  I'm more interested in this value for case 2).  The strategy
in case 2) seems clear (at least to me).  The subject keeps track of which
cards have come up, and always guesses the shape for which there are the most
cards left in the deck.  This, however, does not supply the expected
number of hits.  Anyone have an answer and the accompanying justification?

  On a different note, psyshic experimenters also like to bandy about the
phrase "psi missing", when the subject does particularly poorly (eg. 1 or 2
hits out of 25).  Given the feedback in case 2), how can a subject get the
LOWEST possible score and what is the expected value of this score?

DISCLAIMER:  Yeah, sure, it's mine, so what?