Common repeated measures random effects models contain two random components, a random person effect and time-varying errors. An observation can be an outlier due to either an extreme person effect or an extreme time varying error. Outlier statistics are presented that can distinguish between these types of outliers. For each person there is one statistic per observation, plus one statistic per random effect. Methodology is developed to reduce the explosion of statistics to two summary outlier statistics per person; one for the random effects and one for the time varying errors. If either of these screening statistics are large, then individual statistics for each observation or random effect can be inspected. Multivariate, targeted outlier statistics and goodness-of-fit tests are also developed. Distribution theory is given, along with some geometric intuition. Key Words: Bayesian Data Analysis, Goodness-of-Fit, Hierarchical Models, Observed Errors, Repeated Measures. 1 Introduction...