³  A smaller simulation was conducted with data simulated from a model with a meaningful covariance between \(u_{0i}\) and \(u_{1i}\). This smaller simulation showed an increase in both statistical power and specificity, and a decrease in type-I and type-II error rates. This increase made detection of random slope variation nearly perfect for all DIC and permutation methods as any covariance between \(u_{0i}\) and \(u_{1i}\) would imply meaningful variation of \(u_{1i}\) as covariance is conditional on variance. As such, this simulation is not reported.