Although Western countries typ

  1. Although Western countries typically have low HIV prevalencerates (e.g., about 0.2% of the Australian population has HIV),clinics offering free HIV testing usually attract at-risk groupsamong whom the prevalence rate is much higher. Managers of such aclinic believe that 12% of their patients have HIV. The clinic usesa diagnostic test which returns a positive result in 98% of caseswhere the patient actually has HIV. Among patients without HIV, 96%of test results are negative. The following questions concerndiagnostic outcomes at this clinic.

    1. Use a contingency table to structure the above information aboutdiagnostic outcomes at this clinic. Complete all marginal totals aswell as the body of the table.

    2. What proportion of patients diagnosed as having HIV actuallyhave it?

    3. A randomly-selected patient has received a negative diagnosis.What is the chance that this patient does not have HIV?

    4. Among patients attending this clinic, what does the diagnostictest do better: show who has HIV, or show who doesn’t have it?Justify your answer.


A contigency table will be formed as below:

True Condition
Person has HIV Person does not has HIV



HIV + True Positive False Positive
HIV – False Negative True Negative

Suppose there are 10000 people coming to the clinic. Hence,people having HIV = 12% * 1000 = 1200.

Now, 98% of the people are diagnosed positive from the test fromthese 1200 people = 1176.

In this manner, the information is collected and gathered intothe following table:

True Condition
Person has HIV Person does not has HIV Total
Test Results HIV + 1176 352 1528
HIV – 24 8448 8472
Total 1200 8800 10000

(i) Proportion of people who are diagnosed as having HIVactually having it = 1176/1528 = 76.96%

(ii) The chance that a randomly selected patient who hasreceived a negative diagnosis does not has HIV = 8448/8472 =0.997

(iii) Let’s calculate each statistic:

Let’s say a person who has HIV. The chance that test will showhim HIV + is: 98%

Let’s say a person who does not have HIV. The chance that thetest will show him HIV – = 96%

Hence, the diagnostic test does better in showing who has HIVrather than showing who doesn’t as it is a better predictor in it(98%>96%)

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