A test for conditional independence between response time and accuracy

Abstract

An important distinction between different models for response time and accuracy is whether conditional independence (CI) between response time and accuracy is assumed. In the present study, a test for CI given an exponential family model for accuracy (for example, the Rasch model or the one-parameter logistic model) is proposed and evaluated in a simulation study. The procedure is based on the non-parametric Kolmogorov-Smirnov tests. As an illustrative example, the CI test was applied to data from an arithmetics test for secondary education.

Keywords: Kolmogorov-Smirnov tests; conditional independence; item response theory; response times; sufficiency.