In the previous example, I portrayed decision time as a potential individual-difference variable influencing recognition performance. Similarly, individuals can differ in the amount of evidence they demand before making a positive recognition response. If a test word is only somewhat familiar, how is that uncertainty translated into a response? Clearly, different people bring different evidential standards to the table, and aspects of our experimental situation also influence how subjects make their decisions. Subjects might want, for example, to maximize the proportion of correct responses to old items—thinking that such a measure more validly reflects memory ability—and thus set a low recognition criterion: If a test item looks even vaguely familiar, they choose to endorse it. This somewhat arbitrary choice can influence our results: In the top part of Figure 24.3 are hypothetical group means, again corresponding to performance as a function of some manipulation of learning. Here the comparison of conditions is complicated by large differences in the overall "agree-ability" of our subjects: Subjects in the left condition say "yes" more often than does the other group—to both old and new items. This fact reveals that our manipulation affected the decision strategies associated with recognition, but it is unclear whether it also influences memorability. To answer this question, we need to implement an experimental strategy similar to the one discussed earlier and gain experimental control over response criterion placement.
The lower part of Figure 24.3 shows performance across a wide range of response biases, plotted on axes corresponding to hit rate and false-alarm rate, yielding a receiver-operating characteristic (ROC). Such data can be elicited by, for example, having subjects complete multiple recognition tests under different payoff conditions. More commonly, subjects are asked to indicate a degree of subjective confidence along with the recognition decision; performance is then plotted as a cumulative function of the hit rate and false-alarm rate at a given confidence level and below. This technique allows for the construction of a ROC from two related but fundamentally different measures: the yes/no recognition response and subjective confidence.
In such a display, differences between subjects or between conditions that reflect differences in criterion setting for the decision component of the recognition judgment are virtually eliminated, and regularities in the form of the ROC are evident. In our example, we can see that the dots, corresponding to the data in the top half of the figure, lie on an isodiscriminability curve. In other words, no differences in memorability are apparent. Yet we could only reach this conclusion by uniting multiple measures and constructing an ROC that fits the data points. Different tasks yield different functional forms, and qualities of the ROC can be directly tied to psychological parameters, given a well-specified theory of the recognition decision.
For example, the Theory of Signal Detection (TSD), which has evolved into a theory of recognition (Banks, 1970; Egan, 1975; Lockhart & Murdock, 1970) by virtue of analogy with problems of discrimination in psychophysics (Green & Swets, 1966) and engineering (Peterson, Birdsall, & Fox, 1954) suggests that all stimuli—studied and unstudied—elicit some degree of mnemonic evidence, and the task for the subject is to set a decision criterion at some point on the spectrum of potential evidence values.
Certain versions of this theory posit that the probability distributions for evidence are Gaussian in form. This theory has implications for the form of the ROC. Specifically, underlying Gaussian probability distributions imply that a plot of the ROC on binormal axes should yield a straight line. More formally,
s ds in which 8S represents the variability of the evidence distribution for studied items, and represents its mean. This function is superimposed on the two conditions in Figure 24.3 (on probability axes).
Distributions of equal variance thus imply that that line should have unit slope. Figure 24.4 shows actual ROC and zROC functions from a representative experiment on recognition memory. The similarities among the Z-transformed functions are striking: they do indeed appear to be linear and have a slope of -0.8 (Ratcliff, Sheu, & Gronlund, 1992). These functions thus reveal that the underlying probability distributions may well be normal, but they are apparently not of equal variance. This particular result suggests that the variance of the
Was this article helpful?