Imagine that you have recently taken a job working for the Canadian Security Int
ID: 3254671 • Letter: I
Question
Imagine that you have recently taken a job working for the Canadian Security Intelligence Service (CSIS). CSIS, in conjunction with MI-6 and the CIA, has developed a (nearly) foolproof method for detecting foreign spies by combing through their digital histories. If someone is a spy––which is true of .0001% of the global population––the method successfully identifies them as a spy 99.9% of the time. If someone is not a spy, the method successfully identifies this fact in 99.5% of all cases. Excited about the accuracy of the test, your boss says that the government wants to screen every Canadian citizen in order to guard against spies.
a. What are the sensitivity and specificity for the method, and what does each refer
to?
b. Although you are new at your job, you feel compelled to explain to your boss why this is a terrible idea. Please provide statistical evidence that such a program couldn’t possibly be effective (hint: give the probability that I am a spy given that I have a positive test result).
Explanation / Answer
a. Sensitivity for the method = 99.9
[What is a Sensitive Test?
The sensitivity of a test (also called the true positive rate) is defined as the proportion of people with the disease who will have a positive result. In other words, a highly sensitive test is one that correctly identifies patients with a disease. A test that is 100% sensitive will identify all patients who have the disease. It’s extremely rare that any clinical test is 100% sensitive. A test with 90% sensitivity will identify 90% of patients who have the disease, but will miss 10% of patients who have the disease.]
Specificity for the method = 99.5
[Whatis a Specific Test?
The specificity of a test (also called the True Negative Rate) is the proportion of people without the disease who will have a negative result. In other words, the specificity of a test refers to how well a test identifies patients who do not have a disease. A test that has 100% specificity will identify 100% of patients who do not have the disease. A test that is 90% specific will identify 90% of patients who do not have the disease and 10% of patients who do not have the disease.]
b. Of course, this method is terrible, because
i) Survey cost of this method is very high....
ii) Total enumeration of the whole Canadian People is impossible at a time because everyone will be busy with their own work.
iii) Pr(a person is a spy given that he has a positive test result) = 0.0001/100 = 0.000001....
For the lower probability ... Our Prediction may not be always true for this method.
iv) Stratified sampling, or two stage sampling techniques may be used.....