Abstract
We investigate the relation between speed and accuracy within problem solving in its simplest non-trivial form. We consider tests with only two items and code the item responses in two binary variables: one indicating the response accuracy, and one indicating the response speed. Despite being a very basic setup, it enables us to study item pairs stemming from a broad range of domains such as basic arithmetic, first language learning, intelligence-related problems, and chess, with large numbers of observations for every pair of problems under consideration. We carry out a survey over a large number of such item pairs and compare three types of psychometric accuracy-response time models present in the literature: two ‘one-process’ models, the first of which models accuracy and response time as conditionally independent and the second of which models accuracy and response time as conditionally dependent, and a ‘two-process’ model which models accuracy contingent on response time. We find that the data clearly violates the restrictions imposed by both one-process models and requires additional complexity which is parsimoniously provided by the two-process model. We supplement our survey with an analysis of the erroneous responses for an example item pair and demonstrate that there are very significant differences between the types of errors in fast and slow responses.
Highlights
Modeling the relationship between response time and accuracy in problem solving is a daunting task
In the second subsection we will discuss the results of a survey for which we estimated the CIM, the CDM and two truncations of the two-level branching model on a large amount of item pairs stemming from 4 basic arithmetic domains: multiplication, addition, subtraction and division
In the third subsection we discuss the results of a different survey over item pairs from domains outside basic arithmetic: first language learning, the game of Set and chess
Summary
Modeling the relationship between response time and accuracy in problem solving is a daunting task. A range of models can be found that relate both response time and accuracy to person as well as item characteristics All these models are based on the standard psychometric assumption of local independence: the responses (xi, yi) and (xj, yj) of a single person on two distinct items i and j are conditionally independent given a set of latent parameters O. A third way to model the correlation between xi and yi is by assuming that (xi|yi = 1) is governed by a different parameter than (xi|yi = 0) This gives rise to a two-level branching model that explicitly distinguishes between fast and slow responses. The 3P&2I truncation is obtained from the two-level branching model by constraining the item parameters that govern the accuracies for fast and slow responses to be equal. We demonstrate that the conclusions reached for this example item pair generalize by discussing the results of a survey in which we analyzed numerous different item pairs from different domains
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