Accuracy of medical diagnostic tests

Use this diagram to explain that there is no contradiction between the following:

ppositive | disease  =  0.95

pdisease | positive  =  0.514

The two halves of the diagram show the different sets of marginal and conditional probs.

The slider adjusts the marginal proportion of the population with the disease, keeping the characteristics of the actual test constant — e.g. P(positive given disease) stays 0.95.

Drag the slider and observe that the greater P(disease), the greater P(disease given positive) and P(disease given negative).

P(positive given disease) stays 0.95, but P(disease given positive) could potentially be any value.


Medical diagnostic tests for a disease are rarely 100% accurate. There are two types of error:

The probabilities are not for a real disease or diagnostic test.