Question

The table below has probabilities for a given test to see if people have a certain disease. Based upon this table answer the questions that follow:

	Disease	Clear (no disease)
Positive test result (+)	.12	.08	.20
Negative test result (-)	.18	.62	.80
	.30	.70

1.        What is the positive predictive value?
2.       What is the negative predictive value?
3.        What is the false positive rate?
4.       What would you say about the quality of this test based on these results?

Answer 1

a:

Positive predictive value given the probability that a person actually have diseases among those for whom test gives positive result. So required value is

Positive predictive value= P(disease | test positive) = 0.12 / 0.20 = 0.60

b:

Negative predictive value given the probability that a person actually do not have diseases among those for whom test gives negative result. So required value is

Negative predictive value= P(no disease | test negative) = 0.18 / 0.80 = 0.225

c:

P(positive | no disease) = 0.08 / 0.70 = 0.1143

d:

Positive predictive value is 0.60 which is fairly good but false positive rate should be lesser than 0.1143. That is test is not very good.