1. You have developed the Bozo Lie Detector Exam. This Exam tells us whether a person is lying or truthful. To test your exam, you hire a number of people to take your exam. Some of the people are told to be honest and others are told to be dishonest during the exam. Here are the results:

 Truth Honest Dishonest Test Result Truthful 319 4 Lying 12 9

What are the sensitivity, specificity, positive predictive value, and negative predictive values?

The first step is to determine your true positives, false positives, true negatives, and false negatives. To do this, we put a true in the two cells where the test result and truth match and false in the two cells where they do not:

 Truth Honest Dishonest Test Result Truthful 319 True 4 False Lying 12 False 9 True

Next, we place the word "positive" in the two cells where the test result was positive. In this case, we are testing for lying so a test result of lying is a positive result (obviously, positive does not necessarily mean "good" in diagnostic testing). We place the word "negative" in the two cells where the test result was negative.

 Truth Honest Dishonest Test Result Truthful 319 True Negative 4 False Negative Lying 12 False Positive 9 True Positive

Sensitivity is a conditional probability where we are only looking at those cases where people really are lying. Sensitivity is, of those people that actually were lying, the percentage of times the test result was positive for lying. The equation is
Sensitivity

Specificity is a conditional probability where we are only looking at those cases where people really are not lying. Specificity is, of those people that actually were not lying, the percentage of times the test result was negative for lying. The equation is
Specificity

Positive Predictive Value is a conditional probability where we are only looking at those cases where the test results indicated lying. Positive Predictive Value is, of those people that were diagnosed as positive for lying, the percentage of times they really were lying. The equation is
Positive Predictive Value

Finally, Negative Predictive Value is a conditional probability where we are only looking at those cases where the test results indicated lying. Negative Predictive Value is, of those people that were diagnosed as negative for lying, the percentage of times they really were not lying. The equation is
Negative Predictive Value