Adjusting for guessing and applying a statistical test to the disaggregation of value-added learning scores

In 2016, Walstad and Wagner developed a procedure to split pre-test and post-test responses into four learning types: positive, negative, retained, and zero learning. This disaggregation is not only useful in academic studies; but also provides valuable insight to the practitioner: an instructor would take different mitigating actions in response to zero versus negative learning. However, the original disaggregation is sensitive to student guessing. This article extends the original work by accounting for guessing and provides adjusted estimators using the existing disaggregated values. Further, Monte Carlo simulations of the adjusted learning type estimates are provided. Under certain assumptions, an instructor can determine if a difference in positive (or negative) learning is the result of a true change in learning or "white noise."