# How to measure group differences incorporating reaction time / accuracy trade-off?

In a psychological experiment I am measuring subjects' reaction time as well as their error rate. Now I would like to compare two groups (males & females). There might be a bias in the sense that subjects who respond within a small reaction time might also commit more errors.

• What would be an appropriate way to combine reaction time and error rate to create a measure that takes into consideration this trade-off between "reacting fast" and "reacting correctly".
• E.g., could I just divide reaction time by error rate? Should I center or scale reaction time and error rate before I do this?
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The basic approach that you are describing sounds like inverse efficiency scores (e.g., see Townsend and Ashby, 1978,1983), which are measured as

$$\frac{r}{1-e} = \frac{r}{c}$$ where $r$ is reaction time, $e$ is proportion error, and $c$ is proportion correct. John Christie provides a critique of inverse efficiency scores here or see the discussion in Bruyer and Brysbaert (2011).

This existing question on "How to analyze reaction times and accuracy together?" hopefully answers your question. The answers there generally advocate more sophisticated approaches for combining reaction time and accuracy such as the Linear Ballistic Accumulator Model and Ratcliff's diffusion model.

### References

• Bruyer, R. & Brysbaert, M. (2011). Combining Speed and Accuracy in Cognitive Psychology: Is the Inverse Efficiency Score (IES) a Better Dependent Variable than the Mean Reaction Time (RT) and the Percentage Of Errors (PE)?. Psychologica Belgica, 51, 5-13. PDF
• Townsend, J.T., & Ashby, F.G. (1978). Methods of modeling capacity in simple processing systems. In J. Castellan & F. Restle (Eds.), Cognitive theory. Vol. 3. (pp. 200-239). Hillsdale, N.J.: Erlbaum.
• Townsend, J.T., & Ashby, F.G. (1983). Stochastic modeling of elementary psychological processes. Cambridge: Cambridge University Press.
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Thanks for the very helpful references! Is there any implemention of the linear ballistic accumulator model or the ratcliff's diffusion model in R? –  jokel Oct 18 '12 at 16:44