Finding Sensitivity and Specificity of a test - Preventive & social medicine

 Case 

In a screening test, 60% of non healthy people turned out to be positive but 20% of healthy people also turned out to be positive. What is the sensitivity and specificity of this screening test?

Solution

Check for non healthy

If 60% of diseased are positive (true positive TP)

Then 40% diseased must be negative (false negative FN)

Check for healthy

If 20% healthy are positive (false positive FP)

Then 80% healthy are negative (true negative TN)

So sensitivity = TP / TP+FN 

= 60 / 60+40

= 0.6

To get it in percentage multiply it by 100 so sensitivity is 60%

So specificity = TN / TN+FP

= 80 / 80+20

= 0.8

To get it in percentage multiply it by 100 so specificity is 80%