Vigilance research has been focused on differences, yet ratios might have intrinsic, numerical significance. Reanalysis of data from Watkins' 1963 psychophysical experiment and 49 vigilance reports showed that individual and group ratios, including errors or misses:detections, were related to roots (particularly of base 1/12 and multiples), powers, e-base ratios (EBR), and fractions. Examples are given from well-known experiments of remarkably exact relationships between conditions, time periods, etc. It is suggested that these phenomena are the product of biological rhythms. Theoretical implications are briefly discussed and the advantages of ratio analysis noted, as when this method proved that criterion β changes, given as nonsignificant, formed part of an ordered set. In a real-world application, the frequency of lane-drifts in O'Hanlon and Kelley's 1977 report is shown to follow a mathematical pattern.
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