On Guessing: An Alternative Adjusted Positive Learning Estimator and Comparing Probability Misspecification With Monte Carlo Simulations

Practitioners in the sciences have used the “flow” of knowledge (post-test score minus pre-test score) to measure learning in the classroom for the past 50 years. Walstad and Wagner, and Smith and Wagner moved this practice forward by disaggregating the flow of knowledge and accounting for student guessing. These estimates are sensitive to misspecification of the probability of guessing correct. This work provides guidance to practitioners and researchers facing this problem. We introduce a transformed measure of true positive learning that under some knowable conditions performs better when students’ ability to guess correctly is misspecified and converges to Hake’s normalized learning gain estimator under certain conditions. We then use simulations to compare the accuracy of two estimation techniques under various violations of the assumptions of those techniques. Using recursive partitioning trees fitted to our simulation results, we provide the practitioner concrete guidance based on a set of yes/no questions.