Retrieving "fraudulent" Soal-Goldney target series from the source originally reported: Confirmation by Benford’s Law and empirical expectation

Abstract

  Given abiding questions in the establishment of fraud in the Soal and Goldney (1943) study of "precognitive telepathy," retrieval was attempted of a sample of its target series from their reported source, viz., final digits of 7-figure logarithms. Distinct from earlier efforts, but consistent with Soal's statements, the length of retrievals was not assumed, and it was hypothesized that retrievals should most frequently occur within the first 20 pages of the published source. Testing 30 published series largely marked as fraudulent, their retrieval was indicated in comparison to chance-control sources, and the early-entry hypothesis also was supported. These findings were maintained when exhaustively and exclusively searching for the longest possible retrievals, and the earliest of entries per retrieval. Additionally, Benford's Law for the distribution of leading digits offered theoretical expectations that were matched by each chance-control source, but surmounted by Soal's reported source, precisely in the range indicated by his method. Alternative logarithmic sources could not reproduce these effects. While reserving implications for the population of target series, it could appear that Soal derived the target series as reported, while withholding details that might query his reliability. Clarification and elaboration of extant fraud scenarios are offered by this interpretation.