An instructional program based on a learning hierarchy and involving the addition of fractions was presented to fourth grade students in a pretest - posttest design. The results of the tests were analyzed using both Walbesser's and White's techniques for validation. There was sufficient disagreement in the results to prevent a conclusion of equivalency of the two methods. Attempts to explain the disagreements did not provide sufficient evidence to disregard these differences. However, a brief comparison of one of Walbesser's ratios and White's statistics did show an interesting similarity, suggesting that a planned comparison might give statistical support to a cutoff score for the consistency ratio. Walbesser's procedure, with this statistical foundation, could provide superior information concerning both the hierarchical nature of the connection, and the quality of the learning program. (Author/RD)