A Two-Term Exponential Functional Description of the Time Course of Sustained Attention

Abstract

A consensus of critical reviews of single-process theories of vigilance or sustained attention has supported the view that the vigilance decrement must be the result of two or more coacting or interacting processes or systems. One theoretical position, as well as the ubiquity of exponential functions in characterizing the time course of biological processes, led to the hypothesis that the time course of sustained attention could be best modeled by the function

A[e^-T1-time 11(1 + e^T2*time)].

An experimental test (n = 613) using 23 points showed that this function accounted for 96.7% of the variance of detection accuracy and was 1.2 times better than a previously proposed single-term model. All parameter estimates were highly statistically significant. Fits to data from three other studies also supported the two-term exponential model. The model fitted target response time less well, accounting for 75.6% of the variance.

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References

Craig, A. , and Colquhoun, W. P. (1975). Vigilance: A review. In C. G. Drury and J. G. Fox (Eds.), Human reliability in quality control (pp. 71–88). London: Taylor & Francis.

Davies, D. R. , and Parasuraman, R. (1982). The psychology of vigilance. London: Academic Press.

Eysenck, M. (1982). Attention and arousal: Cognition and performance. Berlin: Springer-Verlag.

Fisk, A. D. , and Schneider, W. (1981). Control and automatic processing during tasks requiring sustained attention: A new approach to vigilance. Human Factors, 23, 737–750.

Giambra, L. M., and Quilter, R. E. (in press). Sustained attention in adulthood: A unique large sample longitudinal and multicohort analysis using the Mackworth Clock-Test. Psychology and Aging.

Grodins, F. S. (1963). Control theory and biological systems. New York: Columbia University Press.

Hays, W. L. (1963). Statistics for psychologists. New York: Holt, Rinehart & Winston.

Jerison, H. J. (1963). On the decrement function in human vigilance. In D. N. Buckner and J. J. McGrath (Eds.), Vigilance: A symposium (pp. 199–212). New York: McGraw-Hill.

Levine, J. M. , Romashko, T. , and Fleishman, E. A. (1973). Evaluation of an abilities classification system for integrating and generalizing human performance research findings: An application to vigilance tasks. Journal of Applied Psychology, 58, 149–157.

10.

Loeb, M. , and Alluisi, E. A. (1977). An update of findings regarding vigilance and reconsideration of underlying mechanisms. In R. R. Mackie (Ed.), Vigilance: Theory, operational performance, and physiological correlates (pp. 719–749). New York: Plenum.

11.

Loeb, M. , and Alluisi, E. A. (1984). Theories of vigilance. In J. S. Warm (Ed.), Sustained attention in human performance (pp. 179–205). Chichester, England: Wiley.

12.

Loftus, G. R. (1985). Evaluating forgetting curves. Journal of Experimental Psychology: Learning, Memory, and Cognition, 11, 397–406.

13.

Mackworth, J. F. (1964). Performance decrement in vigilance, threshold, and high-speed perceptual motor tasks. Canadian Journal of Psychology, 18, 209–223.

14.

Mackworth, J. F. , and Taylor, M. M. (1963). The d' measure of signal detectability in vigilance-like situations. Canadian Journal of Psychology, 17, 302–325.

15.

Ostle, B. (1963). Statistics in research (2nd ed.) Ames: Iowa University Press.

16.

Parasuraman, R. (1984). The psychobiology of sustained attention. In J. S. Warm (Ed.), Sustained attention in human performance (pp. 61–101). Chichester, England: Wiley.

17.

Pribram, K. H. , and McGuinness, D. (1975). Arousal, activation, and effort in the control of attention. Psychological Review, 82, 116–149.

18.

Ray, A. A. (1982). SAS user's guide: Statistics (1982 ed.). Cary, NC: SAS Institute.

19.

Scerbo, M. W. , Warm, J. S. , Doettling, V. S. , Parasuraman, R. , and Fisk, A. D. (1987). Event asynchrony and task demands in sustained attention. In L. S. Mark , J. S. Warm , and R. L. Huston (Eds.), Ergonomics and human factors: Recent research (pp. 33–39). New York: Springer-Verlag.

20.

Scerbo, M. W. , Warm, J. S. , and Fisk, A. D. (1987). Event asynchrony and signal regularity in sustained attention. Current Psychological Research and Reviews, 5, 335–343.

21.

Taylor, M. M. (1963). Tracking the neutralization of seen rotary movement. Perceptual and Motor Skills, 16, 513–519.

22.

Teichner, W. (1974). The detection of a simple visual signal as a function of time of watch. Human Factors, 16, 339–353.

23.

Warm, J. S. , and Berch, D. B. (1985). Sustained attention in the mentally retarded: The vigilance paradigm. International Review of Research in Mental Retardation, 13, 1–41.