When learning is taking place, students test their hypotheses and evaluate them, and modify their current theories on the basis of new information. This phenomenon is known as "hypothesis testing view" or "theory changes." Many students change their rules to another while they are taking a test. This study introduced a new concept called "slip probabilities" that quantifies to what extent a students' scores on an item deviates from the pure scores of his/her original rule. Algebraic relationships between this new slip-random variable and the traditional item score variable are discussed. Then, the indices to measure the stability of rule application and to compute the probability of having the perfect application of the rule are introduced and illustrated with a 64-item signed number test, which was given to 153 eighth graders. Thirty-nine erroneous rules of operations were represented by a set of response patterns on 32 items. A new random variable "u" that represents deviations from a pure rule by having a slip of 1 to 0 or 0 to 1 on an item helps explain the volatile cognitive activities that occur while a test is taken. Six data tables and seven graphs complement the text. (Author/SLD)