Society of Actuaries (SOA) PA Practice Exam

How is accuracy defined in terms of a confusion matrix?

1. (TP + TN) / N

2. (FP + FN) / N

3. (TP) / (TP + FN)

4. (TN) / (TN + FP)

The correct answer is: (TP + TN) / N

Accuracy in the context of a confusion matrix is defined as the proportion of true results (both true positives and true negatives) among the total number of cases examined. This is represented mathematically as (TP + TN) / N, where TP stands for true positives, TN for true negatives, and N is the total number of observations. This formula captures the overall correctness of the model's predictions by including both the instances where the model correctly predicts positive cases (TP) and the instances where it correctly predicts negative cases (TN). Therefore, when using accuracy as a performance metric, it provides a holistic view of how well the model is performing across all classifications, making it an important measure for evaluating binary classification models. The other options represent different metrics related to the confusion matrix: - The formula that uses (FP + FN) calculates the proportion of incorrect predictions, which is not a measure of accuracy but rather reflects the errors made by the model. - The formula that displays TP / (TP + FN) is known as Precision, measuring the correctness of positive predictions only. - The formula TN / (TN + FP) indicates Specificity, which assesses the model’s ability to correctly identify negative cases. These distinctions underscore that accuracy combines true positive and true negative