Hit-Miss Data
This calculator can be used to analyse data from
parapsychological experiments in which data are recorded as hits or misses.
Examples of such experiments are:
Testing Procedure
First, select the testing procedure (Open Deck or Closed Deck).
The Open Deck procedure applies when all targets are
equally likely to occur on ANY trial. For example, in ESP card-guessing
experiments, the cards are shuffled, one is selected for guessing and then this
card is returned to the pack before shuffling again and selecting the next
card. In Open Deck procedures, although every card has an exactly equal chance
of being selected on every trial, the resulting frequencies of each card will
not necessarily be the same. Thus when selecting 25 ESP cards in this way, you
will not necessarily get 5 each of the 5 different symbols.
The Closed Deck procedure applies when the set of targets
used is predetermined. For example, in ESP card-guessing experiments, the cards
are shuffled, one is selected for guessing and then put to one side before selecting the next card from the
remaining deck (which may or may not be reshuffled at this point). Using this procedure, the chance of selecting a particular card
on any trial depends on which cards have already been eliminated. However (as
long as the total number of trials is a multiple of the number of different
symbols) the resulting frequencies for each card will be identical and hence the
overall probabilities of selecting the different symbols are equal. Thus when
selecting 25 ESP cards in this way, you will always get 5 each of the 5
different symbols.
In general, Open Deck procedures are recommended in
parapsychological research.
Probability of Hit
Next, choose the probability of a hit. This will depend on the
number of different outcomes that are possible. For example, in a standard ESP
card-guessing experiment there are 5 different cards, so the probability of a
hit is 1 in 5 . In a PK experiment in which people are trying to throw sixes
using a die, the probability of a hit is 1 in 6.
Note that this calculator should only be used when the
different outcomes are equally likely to occur.
Trials and Hits
Next enter the total number of trials (hits and misses
combined) and the total number of hits in the appropriate boxes. Then
click "Calculate".
Statistical Analysis
If there are sufficient data, statistical analysis will be
performed.
The statistical procedure used is the
z-test. This compares the number of hits obtained with the number of hits expected by chance. The latter is known as the
Mean Chance Expectation
(MCE) and is equal to (number of trials) x (probability of hit).
The z test calculates the probability (p) of obtaining results
which differ from the MCE to the extent observed. If this probability is low
(generally 0.05 or less), the results are said to be statistically significant
and are therefore possible evidence of psi, or paranormal ability.
The z score (sometimes called the critical ratio)
indicates the direction of the results when compared with the MCE. If z is
positive, this indicates more hits than expected by chance (possible evidence of
psi-hitting). If z is negative, then fewer hits than expected occurred (possible
evidence of psi-missing).
If there is a strong prior expectation of either psi-hitting or
psi-missing, the statistical analysis may be carried out on the basis of a
one-tailed test. A one-tailed test does not examine the possibility that the
non-expected outcome may result. Although the probabilities obtained will be
halved, a one-tailed test is not generally recommended and, in most cases,
statistical analysis should be two-tailed (which tests for both
psi-hitting and psi-missing).
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