Statistical Calculator

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:

• When guesses in ESP experiments are recorded as correct or incorrect.

  
  

• When events in Psychokinesis (PK) experiments are recorded as matching or not matching the intended outcome.

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".

If there are sufficient data, statistical analysis will be immediately 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).