Single case designs (SCDs) generally consist of a small number of short time series in two or more phases. The analysis of SCDs statistically fits in the framework of a multilevel model, or hierarchical model. The usual analysis does not take into account the uncertainty in the estimation of the random effects. This not only has an effect on the estimates of the fixed effects, but also on their standard error. This research investigates this phenomenon on a selected SCD, and compares the results with the analyses of other people on the panel. The authors presume the results, which are not presented, will show the advantages of fully Bayesian estimates.