To estimate relational models and test the theoretical hypotheses of binary tree search algorithms, we built binary search trees with random permutations of n (number of nodes) distinct numbers, which ranged from three to seven. Probabilities for building binary search trees corresponding to each possible height and balance factor were estimated. Regression models with variables of number of nodes, height, and average number of comparisons were estimated and the theorem of O(1g(n)) was accepted experimentally by a Lack of Test procedure. Analysis of Variance model was applied to compare the average number of comparisons with three groups by height and balance factor of the trees to test theoretical hypotheses of a binary search tree performance statistically.