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The reason I ask is that I often hear of alternate measures of response bias besides β, but have never heard of an alternate measure of detection sensitivity to d'.

If there is no other measure of detection sensitivity, is that a matter of mathematical necessity?

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Yes, there are several alternatives to d'.

First of all, why do we need alternatives to d'?

  1. d' assumes the distribution of internal representation of signal and noise are Gaussian. This assumption is common, but may not be true, and a measure that does not make this assumption is more robust.

  2. There are technical problems computing d' when the Hit Rate or the False Alarm Rate are 0 or 1 (d' becomes inf or -inf).

Proposed alternatives to d' include:

  1. Area under the ROC (Green & Swets, 1966)
  2. A' (Pollak & Norman, 1964), A'' (Smith, 1995) which is a correction of A', and A (Zhang & Mueller, 2005) which is a correction of A''.
  3. S' (Balakrishnan, 1998)

Balakrishnan, J. D. (1998). Some more sensitive measures of sensitivity and response bias. Psychological Methods, 3(1), 68.

Zhang, J., & Mueller, S. T. (2005). A note on ROC analysis and non-parametric estimate of sensitivity. Psychometrika, 70(1), 203-212.

Smith, W. D. (1995). Clarification of sensitivity measure A'. Journal of Mathematical Psychology, 39(1), 82-89.

Pollack, I., & Norman, D. A. (1964). A non-parametric analysis of recognition experiments. Psychonomic Science.

Green, D. M., & Swets, J. A. (1966). Signal detection theory and psychophysics (Vol. 1). New York: Wiley.

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