C Suppose a diagnostc test for a certain condition has the following results: te

Question

C Suppose a diagnostc test for a certain condition has the following results: test actualYes 41 No 400 8559 1. What are the test's false positive and false negative rates? 2. What is the percent age of the sample having the condition? 3. A patient tests positive,s aware of the test's very low false positive rate, and asks "Doc, what are my chances? What do you tell the patient? What is her /his probability of actually having the condition? If they don't believe you, how do you explain? 4. Can you explain using the idea of conditional probability?

Explanation / Answer

Following table shows the row total and column total:

(a)

False positive means test gives positive results given that person do not have condition.

So

P(false positive) = P(+ | No) = 400 / 8959 = 0.0446

False negative means test gives negative results given that person have condition .

So

P(false negative) = P(- | Yes) = 1 / 41 = 0.0244

2)

P(condition X) = 41 /9000 = 0.0046 =0.46%

3)

P(Yes | +) = 40 / 440 =0.0909 =9.09%

That is if a person test positive then there is only 9.09% chances that person has condition.

Dr shoud suggest the patient for retest becuse chances of havig disease is low if he/she test positive.

4)

Conditonal probability shows that out of 440 positive results, only 40 have condition.

test + - Total actual Yes 40 1 41 No 400 8559 8959 Total 440 8560 9000

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