Abstract

This paper builds and expands on three previous meta-analyses conducted in the same area (Radin & Nelson, 1989; Radin, 1997; Radin & Nelson, 2002). It surveys the historical background of random number generator (RNG) experiments and outlines the main findings of the prior meta-analyses. It examines (a) the existence of a potential correlation between human intention and the output of a RNG; (b) the relationship between study size and effect size; and (c) potential moderator variables.

The analyses were restricted to studies investigating the correlation between direct human intention and the concurrent output of a RNG, and in which the chance expectation of a hit could be calculated. The 357 experimental studies and 142 control studies both yielded the same effect size of pi = .50003, although the effect size from the control studies went down to pi =.49999 once one large control run reporting a significant effect had been removed. There was a significant, non-linear correlation between effect size and study size (p = .0001), indicating that any experimental effect comes primarily from smaller studies. A sensitivity analysis showed that only 67 studies, each with an average of 2366 bits, would be required to bring the database down to non-significance. Thus just a few studies could potentially change the conclusions from this meta-analysis. The experimental database was extremely heterogeneous (x² = 1442.90, p = 1.44^-130)

Initial analyses on moderator variables yielded at best weak evidence for better performance with (i) selected participants; and (ii) RNGs based on a radioactive source. Homogenous studies using auditory feedback performed significantly better than those using visual feedback (N = 183, z(diff) = 5.52, p = 1.6^-8). The meta-analysis clearly suggested that studies with graphic feedback should be avoided; from the outset these studies were clearly homogenous and at chance. There was some support for Data Augmentation Theory (DAT), with homogenous studies in which a human started the RNG performing better than those in which the RNG was started automatically (N = 175, z(diff) = 5.50, p = 2.2^-7). Nevertheless, for both the auditory feedback studies and the studies in which a human started the RNG, there were significant correlations with the safeguard variable of post-hoc selection of the data (auditory feedback N = 35, rho = -0.40; human selection, N = 142, rho = -0.15). Thus, the difference in performance in these subsets may not be as robust as one might first think. Moreover, most auditory feedback studies used radioactive RNGs, bit-by-bit feedback and usually presented the bits at a slower rate to the participants. Because all these variables are interlinked it is difficult to say which, if any, is primarily responsible for any effect. More detailed and sophisticated analyses are planned in future work.