Princeton Engineering Anomalies Research, Princeton University, Princeton, NJ 08544

Effect sizes achieved by human operators in random event generator anomalies experiments show correlations with the ordinal positions of the experimental series in both the collective and individual databases. Specifically, there are statistically significant tendencies for operators to produce better scores over their first series, then to fall off in performance in their second and third series, and then to recover to some intermediate levels during their fourth, fifth, and subsequent series. Such correlations appear in both local and remote experiments, and are also indicated over a sequence of different experimental protocols, but no similar effects are found in baseline or calibration data. These serial position patterns thus appear to be primarily psychological in origin, and may subsume the rudimentary "decline," "primacy," "recency," and "terminal" effects propounded in the parapsychological and psychological literature. The results also emphasize the importance of very large individual databases in determining the asymptotic effect sizes in any given experiment of this type.