# 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?

$$\frac{r}{1-e} = \frac{r}{c}$$ 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).