What Is the Probability That a Positive Test Indicates Actual Disease?

Click For Summary

Homework Help Overview

The discussion revolves around a probability problem involving disease testing, specifically the likelihood that a positive test result indicates the presence of a disease. The context includes a known prevalence of the disease and the false positive rate of the testing method.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the application of Bayes' theorem and the definition of relevant probabilities. There is an exploration of expected outcomes based on testing a sample population.

Discussion Status

The discussion is active, with participants attempting to clarify their understanding of the problem and the implications of the probabilities involved. Some have suggested a numerical approach to visualize the problem, while others are questioning the interpretation of the results.

Contextual Notes

Participants are navigating the definitions of probabilities related to disease prevalence and test accuracy, with specific values provided for the disease occurrence and false positive rate. There is an emphasis on understanding the implications of these values in the context of the problem.

TSN79
Messages
422
Reaction score
0

Homework Statement



Approx. 1/1000 has a disease, and the method of testing has a 5 % false positive rate. If a random person tests positive, what is the probability that he has the disease?

Homework Equations



I'm pretty sure Baye's theorem is the thing to use.

The Attempt at a Solution



I'm having trouble defining my probabilities. I've defined that P(sick) = 0,001 and P(not sick|+) = 0,05. But then I'm stuck...
 
Physics news on Phys.org
You could try the problem this way:

Let's say we test 1,000 people:
How many false positives do we expect to get?
How many real positives do we expect to get?
 
Well, wouldn't that be 50 and 1?
 
So, how likely is a positive test to indicate disease?
 

Similar threads

  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 5 ·
Replies
5
Views
4K
Replies
10
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 10 ·
Replies
10
Views
3K