Question

The following table shows the results of a medical test. Has Disease Does Not Have Disease Total Positive Test Result 499 40 539 Negative Test Result 20 214 234 Total 519 254 773 Use the preceding data to estimate each of the following. (Express each response as a percentage rounded to one decimal place.) a. What is the sensitivity of the test? Sensitivity is also known as the true positive rate of a test. In other words, what is the probability that a person tests positive given that they have the disease? % b. What is the specificity of the test? Specificity is also known as the true negative rate of a test. In other words, what is the probability that a person tests negative given that they do not have the disease? % c. What is the PPV (positive predictive value) of the test? In other words, what is the probability that a person has the disease given that they test positive?

Answer 1

a. Sensitivity: 96.2%

b. Specificity: 84.3%

c. PPV: 92.6%

Explanation:

a. Sensitivity = (Number of True Positive / Total Number with the Disease) * 100

b. Specificity = (Number of True Negative / Total Number without the Disease) * 100

c. PPV = (Number of True Positive / Total Number of Positive Test Results) * 100

Given the data in the table:

- True Positive (TP) = 499

- Total Number with the Disease = 519

- True Negative (TN) = 214

- Total Number without the Disease = 254

- Total Number of Positive Test Results = 539

Let's calculate each value:

a. Sensitivity = (499 / 519) * 100 ≈ 96.15%

b. Specificity = (214 / 254) * 100 ≈ 84.25%

c. PPV = (499 / 539) * 100 ≈ 92.57%