Multidimensional Detection Theory
and Multi-Interval Discrimination
The one-interval experiment has now been analyzed in some detail. For two-stimulus experiments, we have learned how to estimate sensitivity and bias from yes-no data and how to plot ROCs from rating data. The analysis generalizes easily to experiments with more than two stimuli. Our models also provide us with a picture of the decision space and the manner in which decisions are made. What is common to all the situations we have so far considered is the assumption that observers base their decisions on a single variable or axis and determine their responses by dividing this continuum into segments using one or more criteria.
In Part II, we consider some of the many situations in which this assumption fails. Most obviously, more than one variable is needed to describe many perceptual and cognitive representations: Changes in tone intensity and light intensity, to take a simple example, have distinct neural and psychological outcomes. To model this additional complexity, we take the obvious step of increasing the dimensionality of the representation. For the most part, we use two-dimensional geometric analyses.
We progress from the simplest cases toward (but not to) the most complex on two parallel tracks. Chapter 6 considers the detection and discrimination of two stimuli whose representation is two-dimensional (such as simultaneous tone-light pairs). Because there are only two stimuli, it turns out that the optimal strategy of relying on a single dimension—the sum of perceived brightness and loudness—is sufficient to analyze such experiments, but that two dimensions are required to allow for reasonable but nonoptimal decision rules. In chapter 8, we examine classification designs,