Question

80 volunteers take a meningitis test to help doctors see how accurate this test is at identifying whether someone has meningitis or not.

A positive result means the test has identified you as having meningitis.
Of the volunteers, only 8 people have meningitis.
The results show 2 people who have meningitis gets a negative result and 3 people who don't have meningitis get a positive result.
What was the accuracy of the test?

Answer 1

Out of the 80 volunteers, only 8 people have meningitis. Of these 8 people, 2 people got a negative result. This means that 6 out of 8 people with meningitis got a positive result, which is a sensitivity of 6/8 or 75%.

Out of the 72 volunteers who do not have meningitis, 3 people got a positive result. This means that 69 out of 72 people who do not have meningitis got a negative result, which is a specificity of 69/72 or 95.83%.

The accuracy of the test can be calculated using the formula:

Accuracy = (True Positives + True Negatives) / Total

True Positives = 6 (people with meningitis who got a positive result)
True Negatives = 69 (people without meningitis who got a negative result)
Total = 80 (total number of volunteers)

Accuracy = (6 + 69) / 80 = 0.938 or 93.8%

Therefore, the accuracy of the test is 93.8%.