One of the ways that cognitive psychologists study decision-making is by studying simplified versions of real-world tasks called choice reaction time (CRT) tasks (see Luce, 1986). A basic CRT task can be defined in terms of three components: 1) a relevant stimulus set, which is the set of stimulus properties that you have to discriminate in order to determine what you should do, 2) a response set, which is the set of actions that you may have to perform, and 3) the mapping instructions, which associate each element in the stimulus set with an element in the response set. The relevant stimulus set and the response set are often not just a haphazard collection of elements, but are described by dimensions (called the relevant stimulus dimension and response dimension, respectively), with the elements within the set defined in terms of values of that dimension.
For example, the following would be a typical CRT task: the relevant stimulus dimension is pitch, with a 750 Hz tone and a 250 Hz tone as the elements in the relevant stimulus set; the response dimension is spatial direction, with a pressing of a left or right key as the response set; and the mapping instructions are “press the left key when you hear a high pitch and press the right key when you hear a low pitch.” By manipulating the various stimulus conditions and measuring how they affect the speed and accuracy of responses, psychologists can learn about the underlying process of decision-making.
Choice Reaction Time tasks can also be used to study selective attention, or the ability to filter out irrelevant information. In order to do this, there also has to be a collection of stimulus properties that appear in the task, but that are completely unrelated to what you should do. These are elements of the irrelevant stimulus set, and, like the elements in the relevant stimulus and response sets, they are usually defined in terms of values along an irrelevant stimulus dimension. In the above task, for example, the high- and low-pitched tones could also be presented either loud or soft, where the volume of the tone is completely random, unrelated to pitch or to anything that you should do. A CRT task with an irrelevant stimulus set is called a classification task (Garner, 1978b) or a filtering task (Posner, 1964).
Sometimes there is no relationship between any of the dimensions that define a Choice Reaction Time task. For example, suppose you are presented with a letter in the center of the screen: the letter can be either “H” or “S”, and can be either blue or green, combining to make total of four possible stimuli that can appear. You are told to press a left key whenever you see the letter “H” and a right key whenever you see the letter “S”. In this task, the response dimension is position (left, right), the relevant stimulus dimension is letter (H, S), and the irrelevant stimulus dimension is color (blue, green). All of these dimensions are completely unrelated. As a result, there will be no compatibility effects in this task.
The dimensional overlap model was devised to provide a basic framework for talking about compatibility effects, and rests on the idea of “dimensional overlap” between stimulus and response dimensions. By outlining different ways in which stimulus and response dimensions may overlap, the model is able to define a taxonomy of different types of compatibility tasks, and goes on to provide a theory about how these types of overlap influence cognitive processing.