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Updated: Jun 26, 2026

Enabling High Grayscale Resolution Displays and Accurate Response Time Measurements on Conventional Computers
06:50

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Published on: February 29, 2012

A Box-Cox normal model for response times.

R H Klein Entink1, W J van der Linden, J-P Fox

  • 1Department of Research Methodology, Measurement and Data Analysis, University of Twente, Enschede, The Netherlands. r.h.kleinentink@gw.utwente.nl

The British Journal of Mathematical and Statistical Psychology
|February 4, 2009
PubMed
Summary
This summary is machine-generated.

The Box-Cox transformation offers a more flexible approach to modeling response times on tests than the standard log-transform. This method improves the accuracy of statistical models, especially when normality assumptions are violated, enhancing educational measurement.

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Area of Science:

  • Educational Measurement
  • Statistical Modeling
  • Psychometrics

Background:

  • Log-transform is common for response time modeling but can violate normality assumptions.
  • Medical College Admission Test data revealed limitations of the lognormal model.

Purpose of the Study:

  • Investigate Box-Cox transformations for response time modeling.
  • Develop a framework for simultaneous analysis of responses and response times.
  • Compare model fit across different transformation parameters.

Main Methods:

  • Simulation studies to evaluate Box-Cox normal model performance.
  • Real data analysis using the Box-Cox normal model.
  • Development of a transformation-invariant deviance information criterion (DIC).

Main Results:

  • Box-Cox transformation provides a better description of response time distribution shapes.
  • The proposed DIC allows for comparing models with varying transformation parameters.
  • The Box-Cox normal model demonstrates enhanced performance over the lognormal model.

Conclusions:

  • Box-Cox transformations are a valuable extension for response time modeling in educational contexts.
  • The developed methods improve the analysis of response time data, particularly when normality is not met.
  • This approach offers a more robust framework for understanding test-taker behavior.