Forecasting SPEAK test score from TOEFL score: a Bayesian model for screening international teaching assistants

Teaching assistantships provide funding to graduate students and support to teaching faculty. At many universities in the United States, students whose first language is not English can only teach if they pass an oral English assessment or complete English courses. Graduate programs face a risk that a prospective international teaching assistant (ITA) may fail the English test, potentially causing financial and logistical consequences. To develop rational decision procedures, which integrate the probability of failure on the test with the consequences and tradeoffs of ITA funding decisions, a probabilistic forecasting model is needed. At the University of Virginia (UVa), ITAs must pass the Speaking Proficiency English Assessment Kit (SPEAK) Test before the semester begins in August. In this study, scores from the Test of English as a Foreign Language Internet-based Test (TOEFL iBT), which are available at the admission time, are used to produce a probability of failing the SPEAK Test at a given threshold. A Bayesian forecasting model is described, estimating the prior probabilities from a sample of SPEAK Test scores of 803 prospective ITAs at UVa between 2006 and 2013, and using the TOEFL iBT scores from 318 students to update the forecast probabilities. Additional discrete predictors, such as the student´s gender and school, are considered, but only the native language is found to reduce uncertainty in the forecast. Overall, this forecasting model demonstrates and explains a useful statistical association between the SPEAK Test scores and the TOEFL iBT scores, used widely in university admissions.