The following simulation presents a situation
where a dichotomous predictor X, that has a very
strong effect on a response variable Y, results in the
response variable not taking a normal distribution,
despite the errors being normally distributed. The
simulation was completed in R 2.15.2; the relevant code
is attached in an appendix for readers interested in replicating our results. For this simulation, we define
the true population model as the following: