PerceptttalandMotorSkills, 1990, 70, 143-154. O Perceptual and Motor Skills 1990
VIGILANCE RATIOS IMPLICATE BIOLOGICAL RHYTHMS
'
NORMAN RICHARDSON Adelazde. South Australia Summary.-V~g~lnnce research has been focused on differences, yet ratios might have intrinsic, ntrmrr~calsignificance. 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 Eractions. 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 advancages of ratio analysis noted, as when this method proved that criterion 0 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.
Since the discovery that the typical decrement in vigilance2 has more to d o with changes in response criterion than in ability to discriminate signals, the focus has tended to shift from percentage detections to criterion (P) and sensitivity (d'). Yet, paradoxically, the information potential of the original measure has been exploited only in part, as differences, between subjects, conditions, and time periods are, generally, considered, but not ratios. Detections or misses:signals (D, M) and the ratio between them (M:D, D:M)-(a), as well as the ratios between subjects, between conditions, and between time periods-(b), might have intrinsic, numerical significance. It is appropriate to ask, How are ratios distributed? If nonuniformly, do they present a pattern? Does randomness or orderliness tend to prevail among the quantities obtained from an experiment? With regard to (b), visual inspection shows that group curves often form clusters or "levels." These are reflected in periodic or near-periodic average missed signal lag times (AMSL, see Richardson, 1985). This shows that performance is not an undifferentiated continuum but leaves open the question, whether yields are significant in themselves, irrespective of signal rate. An example favorable to this possibility may be found in Colquhoun and Baddeley's 1967 experiment on training effects in auditory vigilance, where near-regular fractions (RF) obtain between D:M ratios for the signal-rate groups but d o not reach significance (see also Results [4, p. 1471 regarding this example). 'Requests for reprints should be addressed to Norman Richardson, c/o G P O Adelaide, South @str&a 5000. A neurologist's term for "a state of maximum physiological [italics added] efficiencyM (Davies & Parasuraman, 1982, p. 2).
144
N. RICHARDSON
The study of such patterns, if reliable and widespread, that is, of the "structure" of experimental data, and of ratio distributions in general (a), might give new perspective to the problems of decrement and suboptimal performance. For example, some investigators (Giambra & Quilter, 1987; Teichner, 1974) have supported the idea of a general decremental function, linked to the initial probability of detection (IPD); on the other hand, Koelega, Brinkman, Hendriks, and Verbaten (1989, p. 60) found that "vigilance level and vigilance decrement dissociate." Suboptimal monitoring performance in real-world conditions might also be better understood. This study, therefore, was designed to investigate the "numbers" of vigilance. METHOD 1. Examination of several vigilance reports did not confirm the hypothesis that an order based on whole numbers underlay the data. 2. The results of Watkins' 1964 (1763) forced-choice psychophysical experiment on the influence of auditory noise stimulation upon the detection of visual signals were reanalyzed. The discovery of correlates for individual error:detection ratios (E:D) directed attention beyond whole (rational) numbers and led to (3). 3. A sample was collected, comprising most of the available references with detection data from Davies and Parasuraman's 1982 chapter on "Criterion Shifts" (Chap. 4, pp. 60-79), to which were added others from the general literature. The total of 49 included 32 visual, 15 auditory, and two dual reports, mainly from the 1960s and 1970s. Signal variables were the major category, others were, training and knowledge-of-results (KR), subjects, environment, etc. I n 21 cases, theory of signal detection (TSD) measures had been employed. 4. Data were collated from each report as follows: (a) detection, miss, and miss:detection ratios (D, M, M:D) over-all, on both signal- and percent-basis, where applicable, (b) ratios of these ratios for first (t,) and last (t,) time periods, namely, stability ratios (SR), (c) ratios by alternative response criteria from the following cases (seven): Binford and Loeb (19661, Broadbent and Gregory (1965), Colquhoun (1967), Loeb and Binford (1764), Milosevic (1975), Milosevic (1974, data incomplete), and Sostek (1978), and (d) SR for criterion /3 from 14 cases. 5 . Attempts were made to relate the distributions from (4) to theoretical s , e-base ratios (EBR; see numbers (TN), including fractions, r ~ o t s / ~ o w e rand Results 14, p. 1471). 6. The ratios from each report were, in each case, inspected, compared, and manipulated, in a search for patterns. 7. A more detailed analysis of (4c) and (4d) was carried out. 8. False alarm (FA) data were considered. 7. Significance testing was, mainly, by the Binomial test. As "accep-
145
VIGILANCE RATIOS AND BIOLOGICAL RHYTHMS
tance limits" could be based either on absolute quantities or proportions of interroot- etc., intervals, both bases were adopted and results averaged. Note: "roots of (e.g.) base 1/12" means the exponential series, W, and so on.
m,m,
1. Reanalysis of data from Watkins (1963, 1964) Individual error:detection ratios (E:D) for training (Tg.) and experimental ( E l . ) sessions combined (see Table 1) were manipulated by dividing E:D or means of pairs into one another. I t was found that ratios could be closely reproduced in this way. For example, the largest ratio, divided into the mean of the smallest two, yields the next smallest exactly. The question arose, could a single number, taken to powers or roots, generate these ratios? As shown in Table 1, the base is 12, and the roots required are those from W to m,changing each time by a factor of 2 ( p < .01). TABLE 1 CORELATES OF ERROR: DETECTION RATIOS(E:D) FOXSUB~ECTS OF WATKINS' 1964 (1963) PSYCHOPHYSICAL EXPERIMENT* Subject
E:D
Correlate
MB
Nominal
,442 ,454 Js ,541 qnr2 BY ,677 JnD ES .736 gT2 HG ,828 Nofe.-E:D ratios computed from tabular data in Watkins' 1963 report. *p
VIGILANCE RATIOS IMPLICATE BIOLOGICAL RHYTHMS
'
NORMAN RICHARDSON Adelazde. South Australia Summary.-V~g~lnnce research has been focused on differences, yet ratios might have intrinsic, ntrmrr~calsignificance. 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 Eractions. 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 advancages of ratio analysis noted, as when this method proved that criterion 0 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.
Since the discovery that the typical decrement in vigilance2 has more to d o with changes in response criterion than in ability to discriminate signals, the focus has tended to shift from percentage detections to criterion (P) and sensitivity (d'). Yet, paradoxically, the information potential of the original measure has been exploited only in part, as differences, between subjects, conditions, and time periods are, generally, considered, but not ratios. Detections or misses:signals (D, M) and the ratio between them (M:D, D:M)-(a), as well as the ratios between subjects, between conditions, and between time periods-(b), might have intrinsic, numerical significance. It is appropriate to ask, How are ratios distributed? If nonuniformly, do they present a pattern? Does randomness or orderliness tend to prevail among the quantities obtained from an experiment? With regard to (b), visual inspection shows that group curves often form clusters or "levels." These are reflected in periodic or near-periodic average missed signal lag times (AMSL, see Richardson, 1985). This shows that performance is not an undifferentiated continuum but leaves open the question, whether yields are significant in themselves, irrespective of signal rate. An example favorable to this possibility may be found in Colquhoun and Baddeley's 1967 experiment on training effects in auditory vigilance, where near-regular fractions (RF) obtain between D:M ratios for the signal-rate groups but d o not reach significance (see also Results [4, p. 1471 regarding this example). 'Requests for reprints should be addressed to Norman Richardson, c/o G P O Adelaide, South @str&a 5000. A neurologist's term for "a state of maximum physiological [italics added] efficiencyM (Davies & Parasuraman, 1982, p. 2).
144
N. RICHARDSON
The study of such patterns, if reliable and widespread, that is, of the "structure" of experimental data, and of ratio distributions in general (a), might give new perspective to the problems of decrement and suboptimal performance. For example, some investigators (Giambra & Quilter, 1987; Teichner, 1974) have supported the idea of a general decremental function, linked to the initial probability of detection (IPD); on the other hand, Koelega, Brinkman, Hendriks, and Verbaten (1989, p. 60) found that "vigilance level and vigilance decrement dissociate." Suboptimal monitoring performance in real-world conditions might also be better understood. This study, therefore, was designed to investigate the "numbers" of vigilance. METHOD 1. Examination of several vigilance reports did not confirm the hypothesis that an order based on whole numbers underlay the data. 2. The results of Watkins' 1964 (1763) forced-choice psychophysical experiment on the influence of auditory noise stimulation upon the detection of visual signals were reanalyzed. The discovery of correlates for individual error:detection ratios (E:D) directed attention beyond whole (rational) numbers and led to (3). 3. A sample was collected, comprising most of the available references with detection data from Davies and Parasuraman's 1982 chapter on "Criterion Shifts" (Chap. 4, pp. 60-79), to which were added others from the general literature. The total of 49 included 32 visual, 15 auditory, and two dual reports, mainly from the 1960s and 1970s. Signal variables were the major category, others were, training and knowledge-of-results (KR), subjects, environment, etc. I n 21 cases, theory of signal detection (TSD) measures had been employed. 4. Data were collated from each report as follows: (a) detection, miss, and miss:detection ratios (D, M, M:D) over-all, on both signal- and percent-basis, where applicable, (b) ratios of these ratios for first (t,) and last (t,) time periods, namely, stability ratios (SR), (c) ratios by alternative response criteria from the following cases (seven): Binford and Loeb (19661, Broadbent and Gregory (1965), Colquhoun (1967), Loeb and Binford (1764), Milosevic (1975), Milosevic (1974, data incomplete), and Sostek (1978), and (d) SR for criterion /3 from 14 cases. 5 . Attempts were made to relate the distributions from (4) to theoretical s , e-base ratios (EBR; see numbers (TN), including fractions, r ~ o t s / ~ o w e rand Results 14, p. 1471). 6. The ratios from each report were, in each case, inspected, compared, and manipulated, in a search for patterns. 7. A more detailed analysis of (4c) and (4d) was carried out. 8. False alarm (FA) data were considered. 7. Significance testing was, mainly, by the Binomial test. As "accep-
145
VIGILANCE RATIOS AND BIOLOGICAL RHYTHMS
tance limits" could be based either on absolute quantities or proportions of interroot- etc., intervals, both bases were adopted and results averaged. Note: "roots of (e.g.) base 1/12" means the exponential series, W, and so on.
m,m,
1. Reanalysis of data from Watkins (1963, 1964) Individual error:detection ratios (E:D) for training (Tg.) and experimental ( E l . ) sessions combined (see Table 1) were manipulated by dividing E:D or means of pairs into one another. I t was found that ratios could be closely reproduced in this way. For example, the largest ratio, divided into the mean of the smallest two, yields the next smallest exactly. The question arose, could a single number, taken to powers or roots, generate these ratios? As shown in Table 1, the base is 12, and the roots required are those from W to m,changing each time by a factor of 2 ( p < .01). TABLE 1 CORELATES OF ERROR: DETECTION RATIOS(E:D) FOXSUB~ECTS OF WATKINS' 1964 (1963) PSYCHOPHYSICAL EXPERIMENT* Subject
E:D
Correlate
MB
Nominal
,442 ,454 Js ,541 qnr2 BY ,677 JnD ES .736 gT2 HG ,828 Nofe.-E:D ratios computed from tabular data in Watkins' 1963 report. *p
