A computational technique for improving estimates of discriminability and bias across multiple dimensions of choice

Abstract

Choice in conditional discriminations such as delayed matching-to-sample (Blough, 1959;White, Ruske, & Colombo, 1996) and the yes-no signal detection task (Macmillan & Creelman, 1991) is traditionally conceptualized as being one-dimensional. For example, the experimentally defined dimension for choice might be red versus green, or yes versus no. Brown and White (2009) argued that choice in such paradigms may be conceptualized as multidimensional. Depending on the procedure, other dimensions, such as choice side (left vs. right) or match to a priming stimulus (congruent vs. incongruent), could influence responding, in addition to an overall bias to choose red versus green or yes versus no. Brown and White (2009) showed that, if they do, standard measures of discriminability and bias will underestimate true performance and will not be statistically independent. They proposed alternative equations for such situations. Simulations and reanalyses of previous data confirmed that Brown and White's (2009) equations produced more accurate estimates of discriminability than did traditional measures, and to an extent that could alter the conclusions of an experiment. As we will show below, however, the disadvantage of their equations is that they have a lower measurement ceiling and range than do standard measures. This results from a finer partitioning of response data and, consequently, smaller cell frequencies. As a result, Brown and White's (2009) measures can be more susceptible to inaccuracies that arise from a small number of trials and extreme discriminability or bias (Brown & White, 2005;Hautus, 1995). In the present article, we introduce a computational estimation technique that overcomes this disadvantage. Standard Choice Measurements in Conditional Discrimination ProceduresChoice in conditional discrimination tasks such as matching-to-sample is typically characterized along one dimension, B 1 versus B 2 (e.g., choice of red vs. green) following the presentation of a sample stimulus, S 1 or S 2 (red or green). Discriminability measures the tendency to choose the "correct" responses: 1 B 1 given S 1 , and B 2 given S 2 . Discriminability is commonly measured by calculating the ratio of correct to incorrect responses in each trial type and then taking the log of their geometric mean. Examples include choice theory's ln (Luce, 1963;McNicol, 1972 (1)A similar measure is signal detection theory's d (Green & Swets, 1966