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- and post-test responses into four learning types: positive, negative, retained, and zero learning. This disaggregation is not only useful in academic studies, it 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 paper extends the original work by accounting for guessing and provides adjusted estimators using the existing disaggregated values. Further, a statistical test is provided for the adjusted learning type estimates. Using this test, an instructor can determine if a difference in positive (or negative) learning is the result of a true change in learning or 'white noise.'