Two recent simulation studies were conducted to aid in the diagnosis and interpretation of equating differences found between random and matched (nonrandom) samples for four commonly used equating procedures: (1) Tucker; (2) Levine equally reliable; (3) Chained equipercentile observed-score; and (4) three-parameter, item response theory true-score equating. For these simulations logistic, test forms were equated to themselves, a situation that does not pattern reality. In the current simulation, test variation was added as an additional variable for study. The results of the current simulation confirmed the results of the previous two simulations and support the prediction based on theoretical grounds that observed-score equating methods, such as Tucker and Chained equipercentile, are more affected by sample variation than are a true-score method (IRT) or an observed score method based on true-score assumptions (Levine equally reliable). The results further suggest that matching equating samples on the basis of a fallible measure of ability, such as anchor test score, is not advisable for any equating method studied except possibly the Tucker method. Three figures and one table present simulation results, and an appendix contains two additional tables. (Contains nine references.) (Author)