In the previous chapters, we measured classifier accuracy by dividing the proportion of correct predictions by the total number of predictions. This indicates the percentage of cases in which the learner is right or wrong. For example, suppose that for 99,990 out of 100,000 newborn babies a classifier correctly predicted whether they were a carrier of a treatable but potentially fatal genetic defect. This would imply an accuracy of 99.99 percent and an error rate of only 0.01 percent.

At first glance, this appears to be an extremely accurate classifier. However, it would be wise to collect additional information before trusting your child's life to the test. What if the genetic defect is found in only 10 out of every 100,000 babies? A test that predicts no defect regardless of the circumstances will be correct for 99.99 percent of all cases, but incorrect for 100 percent of the cases that matter most. In other words, even though the predictions are...