An assessment of response bias for the <Emphasis Type="Italic">same-different </Emphasis> task: Implications for the single-interval task

Biasing variables play an important role in the process of perceptual judgment.These variables relate to such factors as motivation, expectation, and anticipated payoffs and are not part of the sensory stimulus. Nevertheless, they have an inescapable effect on the judge’s response. For example, a wine taster must reduce any propensity toward giving a particular wine an award because of personal preference or friendship with the vintner. In the same way, bidders at auctions need to decipher the fast stream of auditory input they receive from the auctioneer. In doing this, they must ensure that they do not get swept away in the moment and lose track of the criterion they set as a maximum purchase price. Both of these tasks are typically performed against a background of competing stimuli and are subject to bias when a sensory judgment is uncertain. In understanding and quantifying judgments made in such practical situations, as well as those made in an experimental setting, independentmeasures are required that can reflect the separate contributions of sensory capability and biasing factors to the final decision outcome (Simpson & Fitter, 1973). Several detection-theoretic bias indices have been proposed, and it may be beneficial to develop a taxonomy of these measures. Macmillan and Creelman (1991, Chapter 2) provide a good starting point, which we will formalize further now. Four basic types of bias index can be defined on the basis of the relationship between the index and the structure of the decision space: decision variable criterion, likelihood ratio, criterion location, and relative criterion location indices. Figure 1 illustrates the relationship for each type of bias index. Decision variable criterion indices (e.g., xc) are simply the value of the decision axis at the location of the criterion. Likelihood ratio criterion indices (e.g., b ) are based on the ratio of the heights of the two density functions at the location of the criterion. Criterion location indices (e.g., c) are equal to the distance in the units of the decision axis between the criterion and some reference point, often that corresponding to b = 1. The location on the decision axis of the reference point changes with sensitivity. Finally, relative criterion location indices (e.g., c¢ ) typically scale criterion location bias indices by the sensitivityof the observer. This taxonomy is illustrated for the single-interval case in the left-hand part of Table 1. The validity of several of the bias indices in Table 1 has been investigated from both theoretical and empirical perspectives. From a theoretical standpoint, there are two conditionsthat are often required of candidate indices. First, a shift in bias toward a positive response should be reflected in a concomitant increase in both the hit rate and the false alarm rate. Conversely, a shift in bias toward a negative response shouldyield a decrease in both of these rates. This monotonicityconditionis required because bias is directly related to the propensity for making a particular kind of response. The bias indices b and c¢ have been shown to fail the monotonicity condition (Macmillan & Creelman, 1990). Second, if bias and sensitivity represent independent processes, the bias index should maintain independence from the index of sensitivity; otherwise, it could be argued that the two indices are influenced by a common factor—that is, that they are, at least in part, measuring the same thing. However, although indices of sensitivity This research was funded by a grant from the University of Auckland Research Committee. We thank John Irwin for the valuable comments he made on a draft of this manuscript. Correspondence concerning this article should be addressed to M. J. Hautus, Department of Psychology, University of Auckland, Private Bag 92019, Auckland, New Zealand (e-mail: m.hautus@auckland.ac.nz). An assessment of response bias for the same–different task: Implications for the single-interval task