A computer program to generate signal-detection theory values for sensitivity and response bias

Abstract

The theory of signal detection was originally proposed by Tanner and Swets (1954) and has come to serve as an alternative to classical psychophysical methodologies. Signal detection's greatest advantage over classical psychophysical methodologies is the separate determination of parameters reflecting sensory and nonsensory factors. The sensitivity of the decision-making process is a function of the variable d'; which is equal to the distance between the noise and signal-plus-noise distribution and which is monotonically related to the signal strength. Nonsensory factors are reflected in the response criterion. The most commonly used measure of response criterion is {3, which is defined as the ratio of the signal-plus-noise distribution at the criterion to the ordinate of the noise distribution. Gardner, Dalsing, Reyes, and Brake (1984) recently published a table of {3 values corresponding to various hit and false-alarm rates. Traditionally, researchers in psychophysics have been primarily interested in measures of sensory sensitivity. The matter of how a subject sets or maintains a criterion at the appropriate value and adjusts that value to take account of relevant intercurrent events has been largely ignored (Treisman & Williams, 1984). One disadvantage of {3 as a measure of response criterion is that it forms an asymmetric distribution such that values cannot be easily averaged over subjects, trial blocks, and so forth. By taking the natural logarithm of {3, one derives a measure of response criterion that can be averaged. In addition, In ({3) is invariant over sensitivity under maximization ofexpected value. The conversion to In ({3) is helpful when the researcher wishes to average {3 or to do other parametric analyses of {3 values. We describe a program (see Appendix), written for the Apple computer, that generates measures of d', {3 and In ((3) from a given pair of hit and false-alarm rates. The ZGEN program is written in Applesoft and uses an approximation for the inverse normal integral function, which is defined as the value of X such that for a given Q: