<p>The basic approach that you are describing sounds like inverse efficiency scores (e.g., see Townsend and Ashby, 1978,1983), which are measured as</p>

<p>$$\frac{r}{1-e} = \frac{r}{c}$$
where  $r$ is reaction time, $e$ is proportion error, and $c$ is proportion correct. John Christie provides a <a href="https://cogsci.stackexchange.com/a/668/52">critique of inverse efficiency scores here</a> or see the discussion in Bruyer and Brysbaert (2011).</p>

<p>This existing question on <a href="https://cogsci.stackexchange.com/questions/660/how-to-analyze-reaction-times-and-accuracy-together">"How to analyze reaction times and accuracy together?"</a> 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.</p>

<h3>References</h3>

<ul>
<li>Bruyer, R. &amp; 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. <a href="http://crr.ugent.be/papers/Bruyer%20&amp;%20Brysbaert%202011.pdf" rel="nofollow noreferrer">PDF</a></li>
<li>Townsend, J.T., &amp; Ashby,  F.G. (1978). Methods of modeling capacity in simple
processing systems. In J. Castellan &amp; F. Restle (Eds.), Cognitive theory. Vol. 3.
(pp. 200-239). Hillsdale, N.J.: Erlbaum.</li>
<li>Townsend, J.T., &amp; Ashby, F.G. (1983). Stochastic modeling of elementary psychological processes. Cambridge: Cambridge University Press.</li>
</ul>

CC BY-SA 3.0
2012-10-18T16:44:02.650Z
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
CC BY-SA 3.0
2012-10-08T11:20:46.793Z
2012-10-08T11:20:46.793Z
2017-04-13T12:56:16.417Z
Jeromy Anglim
<p>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 &amp; females). There might be a bias in the sense that subjects who respond within a small reaction time might also commit more errors. </p>

<ul>
<li>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". </li>
<li>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?</li>
</ul>

<measurement><methodology><experimental-psychology><reaction-time>
How to measure group differences incorporating reaction time / accuracy trade-off?
jokel
# How to measure group differences incorporating reaction time / accuracy trade-off?

(Asked by: username_0 on 2012-10-08)

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?

**Tags:** measurement, methodology, experimental-psychology, reaction-time


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## 1 answers

### Answer by username_1 on 2012-10-08. Score: 11

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](https://cogsci.stackexchange.com/a/668/52) or see the discussion in Bruyer and Brysbaert (2011).

This existing question on ["How to analyze reaction times and accuracy together?"](https://cogsci.stackexchange.com/questions/660/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](http://crr.ugent.be/papers/Bruyer%20&%20Brysbaert%202011.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.

> **Comments:**
> **username_0**: Thanks for the very helpful references! Is there any implemention of the linear ballistic accumulator model or the ratcliff's diffusion model in R?  

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