The Maxwell School

Syracuse University

Syracuse University

Suppose that **5%** of a given population has a disease that is difficult to detect. Call the state where the person has the disease **D** and the state where they don't have it **N**. A test for the disease is available that reports **rD** or **rN** for whether or not the person has the disease. However, it's imperfect: if the person has the disease (**D**), there is a **10%** chance it will report they don't have it, **rN**. In addition, there's also a **10%** chance that it will report that a person who doesn't have the disease (**N**) has it, **rD**.

- What percent of reports of the disease, rD, are false positives? That is, what is the probability of N given rD or Pr(N|rD)?
- What percent of the reports that the person doesn't have the disease, rN, are false negatives? That is, what is the probability of D given rN or Pr(D|rN)?
- How many people in a population of 100,000 will be undertreated? Overtreated?

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URL: https://wilcoxen.maxwell.insightworks.com/pages/5116.html

Peter J Wilcoxen, The Maxwell School, Syracuse University

Revised 05/26/2023

URL: https://wilcoxen.maxwell.insightworks.com/pages/5116.html

Peter J Wilcoxen, The Maxwell School, Syracuse University

Revised 05/26/2023