  To investigate the structure of individual differences in performance on
behavioral tasks, Haaf and Rouder (2017) developed a class of hierarchical
Bayesian mixed models with varying levels of constraint on the individual
effects. The models are then compared via Bayes factors, telling us which model
best predicts the observed data. One common criticism of their method is that
the observed data are assumed to be drawn from a normal distribution. However,
for most cognitive tasks, the primary measure of performance is a response
time, the distribution of which is well known to not be normal. In this paper,
I investigate the assumption of normality for two datasets in numerical
cognition. Specifically, I show that using a shifted lognormal model for the
response times does not change the overall pattern of inference. Further, since
the model-estimated effects are now on a logarithmic scale, the interpretation
of the modeling becomes more difficult, particularly because the estimated
effect is now multiplicative rather than additive. As a result, I recommend
that even though response times are not normally distributed in general, the
simplification afforded by the Haaf and Rouder (2017) approach provides a
pragmatic approach to modeling individual differences in behavioral tasks.

Applications;Methodology