## Abstract

An attempt is made to recognize a system behind the psi effects that are evaluated in terms of hit rates. For this purpose we formulate five rules which seem to apply at least to studies of good quality with the most common chance hit rates * *= ½ or ¼. A problem in the statistical evaluation of the results arises from the fact that the hit rate cannot be smaller than 0 or larger than 1. This implies that the -scores of an experiment, i.e. the ratio of deviation to standard deviation, and their mean values < > are limited as well. Since the true effect size should in principle be unbounded, its standard definition by < > may be expected to fail near the boundaries. Especially for one-trial experiments where the effect size is concentrated in a single choice between hit or miss, a definition is needed which is unlimited but at small enough values merges with < >. For such an extension, two models will be proposed, one of them with three variants. On this basis it is calculated how the measured < > could be related to the true effect size. A sixth rule elaborates on the scattering of the effect size and is called preliminary as it rests solely on PK experiments with random number generators. It is used to estimate the average hit rate and average < >-score when the limits affect the integral of the hit rate. It turns out that the average hit rate measured in one-trial experiments can be influenced by the limits of even when it is not near one of the limits. A comparison of theory and experiment favors one of the models or a variant of the other, but no definitive conclusions can be drawn because of the large uncertainties of the data and possible inadvertent errors in counting the number of experiments.

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