Building insights on true positives vs. false positives: Bayes’ rule

Abstract

COVID-19 pandemic policies requiring disease testing provide a rich context to build insights on true positives versus false positives. Our main contribution to the pedagogy of data analytics and statistics is to propose a method for teaching updating of probabilities using Bayes’ rule reasoning to build understanding that true positives and false positives depend on the prior probability. Our instructional approach has three parts. First, we show how to construct and interpret raw frequency data tables, instead of using probabilities. Second, we use dynamic visual displays to develop insights and help overcome calculation avoidance or errors. Third, we look at graphs of positive predictive values and negative predictive values for different priors. The learning activities we use include lectures, in-class discussions and exercises, breakout group problem solving sessions, and homework. Our research offers teaching methods to help students understand that the veracity of test results depends on the prior probability as well as helps students develop fundamental skills in understanding probabilistic uncertainty alongside higher-level analytical and evaluative skills. Beyond learning to update the probability of having the disease given a positive test result, our material covers naïve estimates of the positive predictive value, the common mistake of ignoring the disease's base rate, debating the relative harm from a false positive versus a false negative, and creating a new disease test.