Final answer:
Specificity is calculated by dividing the number of true negatives by the sum of true negatives and false positives. In this scenario, the specificity is 382/388.
Step-by-step explanation:
To calculate the specificity of a screening test, we need to know the number of true negatives and false positives. Specificity is the probability of a test giving a negative result when the patient is not infected, indicating the ability of the test to correctly identify those without the disease.
In the given scenario, 400 patients were screened, 24 tested positive, and of those, 18 were confirmed to have the disease. This leaves us with 6 false positives (24 positive tests - 18 with the disease). Of those who tested negative, 12 were false negatives (they had the disease but tested negative). To get the number of true negatives, we subtract the false positives and false negatives from the total number of patients: 400 - 6 - 12 = 382 true negatives.
Now, the specificity is the number of true negatives divided by the sum of true negatives and false positives. This is 382 true negatives / (382 true negatives + 6 false positives) = 382 / 388.
The specificity is therefore 382/388 which can be calculated to give a percentage or a proportion