Vigilance as a Table of Numbers

Abstract

Data from vigilance experiments have structure. Its bases include 1/12 and multiples thereof, single-digit fractions, and 1/e. Continuing previous research, a table of e-based ratios (e-BR) was developed. Data from 9 published experiments with regular and irregular signals (RS-IS) and from 9 with extraverted and introverted subjects (E-I) were re-analyzed. Significant numerical correlations were obtained, some concerning effects originally reported as nonsignificant. Detection (D) means all categories (“levels” of both factors) were linearly related, with p(D)≈X̅(5/8 + y/9) and p <.01. Cross-factor averaged mean products of ratio D for each time period also showed convergence (p <.01). The over-all mean and stability ratio of detections (SR[D], i.e., D for final time period/D for initial time period, gave the scaling effect $\sqrt[8]{1/24} : \sqrt[24]{1/24}$ . Response-time means and standard deviations for different groups in Mackie, Wylie, and Smith's 1994 sonar experiments were related by the derivatives of [1 − 1/e] included in the new table (p = .002). Although by no means specific to vigilance (or psychophysics), the numeric factor still seems relevant to research.