Abstract
We provide statistical measures and additional analyses showing that our original analyses were sound. We use a generalized linear mixed model to account for program-to-program differences with program as a random effect without stratifying with tier and found the GRE-P (Graduate Record Examination physics test) effect is not different from our previous findings, thereby alleviating concern of collider bias. Variance inflation factors for each variable were low, showing that multicollinearity was not a concern. We show that range restriction is not an issue for GRE-P or GRE-V (GRE verbal), and only a minor issue for GRE-Q (GRE quantitative). Last, we use statistical measures of model quality to show that our published models are better than or equivalent to several alternates.