FOR PROCESS ANALYSIS
This chapter seeks to convey appreciation of how mathematical models can help study perception, thought, and action. Two classes of models are considered, both of which utilize statistics: Addition models, which can be handled with Anova–regression techniques of previous chapters; and signal detection models, which employ a simple application of the normal distribution.
Conceptual issues are the main concern so technical details are mostly bypassed. Much of the discussion thus applies to all mathematical models.
A collateral purpose is to point up a neglected potential of Anova–regression for process analysis. Despite their ubiquity in statistical analysis, Anova–regression models have not often been used in psychological theory. Some writers have asserted that Anova is useless for analyzing information processing. In fact, Anova has proved a powerful tool for revealing cognitive process and structure across many domains (e.g., Figures 20.1–20.3).
Psychological addition/subtraction processes have been established in a number of empirical domains. In fact, there is good evidence for a general purpose adding-type rule of cognition. Because of its simplicity, the addition rule lays bare most problems of model analysis, especially the twin problems of psychological measurement and testing goodness of fit.
To fix ideas, consider children's judgments of time. A toy train runs down a track at a certain speed and enters a tunnel, hiding it from view. The child presses a buzzer when the train enters the tunnel and releases it to indicate when it should have reached a marked distance along the tunnel. The buzzer duration is the response measure.