Distribution theory is developed for diagnostics used to investigate variance component estimates and model assumptions in mixed models. Estimation of variance components in a given model is equivalent to estimation of certain linear functions thereof. Each such linear function is realized as an average of natural sample covariances, which may be independent or correlated. The distribution of the set of these sample covariances is developed in both cases, thereby giving a formal basis for a diagnostic procedure which has been used to identify sources of negative variance component estimates and to reveal model deficiencies. Comprehensive tables for the percentiles.01,.05,.10,.90,.95 and.99 of the distribution for a range of correlations and sample sizes are provided. The distribution applies to any random or mixed model, and is illustrated here in actual repeated measures experiments and validated by simulations.