Question

100 people are tested for disease. 30 people have the disease and 70 do not. There were 20 true positives and 37 true negatives.
Part 1: What was the sensitivity of the test? Be sure to give context.
Part 2: What was the specificity of the test? Be sure to give context.
Part 3: What was the positive predictive value of the test? Be sure to give context.
Part 4: What was the accuracy of the test? Be sure to give context.

Answer 1

100 people were Tested for the disease.

30 people have the disease and 70 do not. There were 20 true positives and 37 true negatives.

True positive (TP) = 20

True negative (TN) = 37

False positive (FP) = 30 - 20 = 10

False negative (FN) = 70 - 37 = 33

1) Sensitivity =

=

= 20/53 = 0.377

? Sensitivity is the ability of the test to correctly identify those with the disease i.e. true positive.

So the sensitivity of the test is 0.377

2) Specificity =

=

= 37/47 = 0.787

? Specificity is the ability of a test to correctly identify those without the disease i.e. true negative.

So the specificity of the test is 0.787

3) Positive predictive value =

=

= 20/57

= 0.351

? Positive predictive value is the proportion that the subjects with a positive screening truly have the disease.

So the positive predictive value is 0.351

4) Accuracy of the test

= Correctly predicted class   × 100% Total Testing class

=   TP + TN    × 100% TP + TN + FP + FN

=   20 + 37    × 100% 100

= 57 %

Accuracy is the percentage of correctly classified instances i.e. percentage of true results in the population.

The accuracy of the test is 57%