If a disease has a 15% prevalence in a population and a test has a 95% specifici

If a disease has a 15% prevalence in a population and a test has a 95% specificity, what is the probability of a false positive result? (2021)

If a disease has a 15% prevalence in a population and a test has a 95% specificity, what is the probability of a false positive result? (2021)

Step 1: Understand what specificity means. Specificity is the ability of a test to correctly identify those without the disease. A specificity of 95% means that 95% of the time, the test will correctly show a negative result for people who do not have the disease.
Step 2: Determine the probability of a false positive. A false positive occurs when the test incorrectly indicates that a person has the disease when they do not. This is calculated as 1 minus the specificity.
Step 3: Calculate the probability of a false positive. Since the specificity is 95%, we convert this to a decimal: 0.95. Now, we subtract this from 1: 1 - 0.95 = 0.05.
Step 4: Interpret the result. The probability of a false positive result is 0.05, which means there is a 5% chance that the test will incorrectly indicate a person has the disease when they do not.

Prevalence – The proportion of a population found to have a condition.
Specificity – The ability of a test to correctly identify those without the disease (true negative rate).
False Positive Rate – The probability that a test incorrectly indicates the presence of a disease when it is not present.