Society of Actuaries (SOA) PA Practice Exam

How is the False Positive Rate (FPR) calculated?

1. FPR = FP / (FP + TN)

2. FPR = 1 - Sensitivity

3. FPR = (TP + FP) / Total Cases

4. FPR = 1 - Specificity

The correct answer is: FPR = 1 - Specificity

The False Positive Rate (FPR) is calculated as the proportion of actual negatives that are incorrectly identified as positives. This metric is crucial in understanding how well a diagnostic test or a classification algorithm performs, especially in the context of binary outcomes. The relationship between FPR and Specificity—two important concepts in diagnostic testing—is significant. The FPR is defined as the complement of Specificity. Specificity measures the proportion of true negatives that are correctly identified, meaning that if a test identifies a high number of true negatives, it will correspondingly have a low FPR. Mathematically, this relationship can be expressed as follows: since Specificity (the true negative rate) is calculated as TN / (TN + FP), the False Positive Rate is calculated as FP / (FP + TN). Thus, if you know the specificity, you can find the FPR using the formula FPR = 1 - Specificity. This indicates that the higher the specificity, the lower the FPR, highlighting how these two measures are inversely related. Understanding this inverse relationship helps in evaluating the performance of testing methods in various applications, from medical tests to machine learning classifiers. Therefore, the correct calculation of the False Positive Rate involves acknowledging its definition relative to