An Acceptance-Rejection Theory Of Statistical Psychokinesis

Journal of Parapsychology, The, June, 2000 by Michael Ibison

MICHAEL IBISON [1]

ABSTRACT: This paper presents a theory of statistical psychokinesis that explains observed statistical anomalies with a minimal assumption about the influence of an agent upon a random process. The theory attributes the agent with an ability to accept or reject the immanent outcome of a random frail: if the immanent outcome is deemed unfavorable, the agent is attributed with the ability to "choose again" from the same distribution. From this very simple in-going assumption, it is deduced that the PK effect at the run level is maximized when the variance of the underlying random process is maximal. The theory thereby gains support from the modern view of psychokinesis as an essentially statistical phenomenon. This "acceptance-rejection" theory of Pit gives rise to a mathematical specification of the trial level influence that is identical to that of a classical model due to Schmidt. At the trial-level specification, and the run-level prediction, acceptance-rejection theory conflicts with decision augmentation theory and a mean-shift model. Suggestions are made for an experimental test between these three competing models.

BACKGROUND

PK as a Statistical Anomaly

The modern view of PK is that it is an essentially statistical phenomenon, that determinism precludes, and randomicity favors, PK. Consequently, one is led to speculate that the origin of PK will be found to lie in quantum mechanics (QM), possibly as a component of the mysterious process of wave function collapse (Walker, 1975; Schmidt, 1982). Though even without a detailed physical model of the modality of PK at the quantum level, one can confidently specify some characteristics demanded of a classical statistical level description. Specifically: if the manifestation of PK requires noise, then an anomalous PK-induced effect at the run level should probably be a monotonic function of the variance of the underlying random process.

Earlier Work

Schmidt (1975) has given a classical statistical level model with this property. Though the model presented here is framed rather more psychologically than statistically or physically, it is nonetheless identical at the statistical level to Schmidt's model: both models exhibit the same (arguably) desirable relationship between a PK-induced run-level effect and the underlying variance. To date, there has been no focused experimental test of this particular statistical relationship. Comparative tests have been performed involving two systems in which, in some component, the data has a different variance (Schmidt, 1974; Ibison, 1998). In these experiments, however, in order to blind the operator to the origin, the variance of the displayed data is the same for both systems. Cognizant of these efforts, and in order to minimize the ambiguity of its predictions, acceptance-rejection theory (ART) is conservatively presented here as applicable only when the variance of a binary random process is also the variance of the observed data. Consequently, the lack of uniformity (of the variance) throughout the system disqualifies these experiments as tests of the theory.

Schmidt's 1976 Experiment

Schmidt (1976) performed an experiment particularly relevant to the theory in this paper. He compared the PK-susceptibility of two machines that were designed to give different probabilities to the high outcome of a binary trial. In these, binary trials were generated with high (= "hit") outcome probability p = 1/8 (low probability p = 7/8) from a "difficult" machine, and with high (= "hit") probability p= 7/8 (low probability q = 1/8) from an "easy" machine. Which of these two machines was responsible for the trial value presented to the PK agent was decided by a prerecorded look-up-table (LUT), whose entries were the output of another random process with p = q = 1/2. The agent was blinded to the value of this decision variable. (The LUT is present to test a feature of Schmidt's model that is peripheral to the issue of concern here.)

Since the variance of the easy and difficult machines was the same, ART predicts that the operator performance reported by the z-score should have been the same for both machines. However, as shown below, this is also true for the two other contending models; all the models discussed in this paper predict the same performance on machines with the same variance. Therefore, the data from this experiment cannot be used to decide between these models, but could nonetheless have refuted all of them at once if indeed PK performance on the two machines was found to significantly differ.

Using subscripts e and d to denote easy and difficult machines respectively, Schmidt's 1976 data gives [z.sub.e] = -1.26 from [N.sub.e] = 20,892 trials, and [z.sub.d] = 1.74 from [N.sub.d] = 20,068 trials. The differential

[z.sub.diff] = \[square root][N.sub.e][z.sub.e] - [square root][N.sub.d][z.sub.d]\/[square toot][N.sub.e] [N.sub.d]

then tests the hypothesis that the two PK performances are the same. The above gives [z.sub.diff]= 2.12 which gives a two-tailed probability [p.sub.diff] = 0.034. Therefore, Schmidt's results appear to be marginally significant evidence that none of the three models in this paper are correct: the probability that a PK agent successfully biases a binary outcome does not depend solely on the variance pq, but also appears to depend on the absolute p-value of the random process. However, Schmidt's pilot data for the same experiment goes in the other direction: he reports [z.sub.e] = 0.27 from [N.sub.e] = 5,364 trials, and [Z.sub.d] = -1.28 from [N.sub.d] = 5,176 trials. Folding these into an overall (pilot plus main phase) differential z gives 1.42 (to be subjected to a two-tailed test), which is not significant.