FC Probability of Getting a Positive Test Result for Disease Exam Practice
Question Description
Introduction:
Consider a screening test, meant to detect some disease (e.g. presence of viral RNA, antibodies). For simplicity, assume only two possibilities for “the truth”, the disease is present or the disease is absent. Also assume only two possibilities for a test result: test positive or test negative.
Note: In this scenario, 1000 people are tested at random and 10% have the disease. Unlike real life, we know the ‘truth’ about if they really do have the disease or not, which allows us to make the table. In real life, we only get to see the outcome of the test!
Table:
Disease Present | Disease Absent | Total | |
Test Positive | 90 | 45 | 135 |
Test Negative | 10 | 855 | 865 |
Total | 100 | 900 | 1000 |
Probabilities:
- P(Disease Present)=0.1
- P(Test Positive)=0.135
- P(Test Positive | Disease Present)=0.9
- P(Test Positive | Disease Absent)=0.05
- P(Test Negative | Disease Present)=0.1
- P(Test Negative | Disease Absent)=0.95
- P(Disease Present | Test Positive)=0.67
- P(Disease Present | Test Negative)=0.01
- P(Disease Absent | Test Positive)=0.33
- P(Disease Absent | Test Negative)=0.99
Answer one of the following prompts:
- If someone says that a test was a ‘false positive’, what probability do you think they are referring to? If someone says that a test was a ‘false negative’, what probability do you think they are referring to? Do you think the language of ‘false positive’ and ‘false negative’ are clear?
- If you were worried that you were exposed to the disease and wanted to be tested, which probability or probabilities would you be most concerned with? If you were the Center for Disease Control trying to limit a disease outbreak, which probability or probabilities would you be most concerned with?
- If the test claims a 90% accuracy rate, what probability is that referring to? Would you agree, and/or is there a different probability you would consider the ‘accuracy’ rate?
In your answer, you will need to mention some of the probabilities that were given above. When you reference those probabilities please give the probability notation, the numerical value, and also translate that probability into a sentence that would be understandable by someone who hasn’t taken this class yet.