Abstract
Discriminability measures such asd’ and logd become infinite when performance is extremely accurate and no errors are recorded. Different arbitrary corrections can be applied to produce finite values, but how well do these values estimate true performance? To answer this question, we directly calculated the effects of a range of different corrections on the sampling distributions of\(\hat d'\) and log\(\hat d\). Many arbitrary corrections produced better estimates of discriminability than did the intuitively plausible technique of rerunning problem conditions. We concluded that when it is not possible to run more trials and when other techniques are not appropriate, the best correction overall is to add a correction constant between 0.25 and 0.5 to all response counts, regardless of their value.
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Alsop, B., Rowley, R., &Fon, C. (1995). Human symbolic matchingto-sample performance: Effects of reinforcer and sample-stimulus probabilities.Journal of the Experimental Analysis of Behavior,63, 53–70.
Brown, G. S. (2003).Memory and reinforcement. Unpublished doctoral thesis, University of Otago, Dunedin, NZ.
Davison, M. C., &Tustin, R. D. (1978). The relation between the generalized matching law and signal-detection theory.Journal of the Experimental Analysis of Behavior,29, 331–336.
Goodman, L. A. (1970). The multivariate analysis of qualitative data: Interactions among multiple classifications.Journal of the American Statistical Association,65, 226–256.
Green, D. M., &Swets, J. A. (1966).Signal detection theory and psychophysics. New York: Wiley.
Hautus, M. J. (1995). Corrections for extreme proportions and their biasing effects on estimated values ofd’.Behavior Research Methods, Instruments, & Computers,27, 46–51.
Hautus, M. J. (1997). Calculating estimates of sensitivity from group data: Pooled versus averaged estimators.Behavior Research Methods, Instruments, & Computers,29, 556–562.
Hautus, M. J., &Lee, A. J. (1998). The dispersions of estimates of sensitivity obtained from four psychophysical procedures: Implications for experimental design.Perception & Psychophysics,60, 638–649.
Jones, B. M., &White, K. G. (1992). Sample-stimulus discriminability and sensitivity to reinforcement in delayed matching to sample.Journal of the Experimental Analysis of Behavior,58, 159–172.
Kadlec, H. (1999). Statistical properties ofd’ and β estimates of signal detection theory.Psychological Methods,4, 22–43.
Loftus, G. R. (1978). On interpretation of interactions.Memory & Cognition,6, 312–319.
Luce, R. D. (1963). Detection and recognition. In R. D. Luce, R. R. Bush, & E. Galanter (Eds.),Handbook of mathematical psychology (Vol. 1, pp. 103–189). New York: Wiley.
Macmillan, N. A., &Creelman, C. D. (1991).Detection theory: A user’s guide. Cambridge: Cambridge University Press.
Macmillan, N. A., &Kaplan, H. L. (1985). Detection theory analysis of group data: Estimating sensitivity from average hit and false alarm rates.Psychological Bulletin,98, 185–199.
McCarthy, D., &Davison, M. [C.] (1981). Towards a behavioral theory of bias in signal detection.Perception & Psychophysics,29, 371–382.
McNicol, D. (1972).A primer of signal detection theory. London: Allen & Unwin.
Miller, J. (1996). The sampling distribution ofd’.Perception & Psychophysics,58, 65–72.
Murdock, B. B., Jr., &Ogilvie, J. C. (1968). Binomial variability in short-term memory.Psychological Bulletin,70, 256–260.
Watson, J. E., &Blampied, N. M. (1988). Quantification of the effects of chlorpromazine on performance under delayed matching to sample in pigeons.Journal of the Experimental Analysis of Behavior,51, 317–328.
White, K. G. (1985). Characteristics of forgetting functions in delayed matching to sample.Journal of the Experimental Analysis of Behavior,44, 15–34.
White, K. G. (2001). Forgetting functions.Animal Learning & Behavior,29, 193–207.
White, K. G., &Wixted, J. T. (1999). Psychophysics of remembering.Journal of the Experimental Analysis of Behavior,71, 91–113.
Wixted, J. T. (1990). Analyzing the empirical course of forgetting.Journal of Experimental Psychology: Learning, Memory, & Cognition,16, 927–935.
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The present research was presented to the Society for Quantitative Analyses of Behavior, New Orleans, May 2001, and was supported by a Claude McCarthy Fellowship to G.S.B. This research was also supported in part by a University of Otago Postgraduate Scholarship to G.S.B. We thank Jonathan Vaughan, Tony Nevin, and an anonymous reviewer for their helpful comments.
Note—This article was accepted by the previous editor, Jonathan Vaughan.
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Brown, G.S., White, K.G. The optimal correction for estimating extreme discriminability. Behavior Research Methods 37, 436–449 (2005). https://doi.org/10.3758/BF03192712
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DOI: https://doi.org/10.3758/BF03192712