On May 13, 2020, the New York Times published an article by Professors Todd Haugh and Suneal Bedi of Indiana University entitled, “Just Because You Test Positive for Antibodies Doesn’t Mean You Have Them.” Here is an excerpt from the article
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On May 13, 2020, the New York Times published an article by Professors Todd Haugh and Suneal Bedi of Indiana University entitled, “Just Because You Test Positive for Antibodies Doesn’t Mean You Have Them.” Here is an excerpt from the article:
“… the predictive value of an antibody test with 90 percent accuracy could be as low as 32 percent if the base rate of infection in the population is 5 percent. Put another way, there is an almost 70 percent probability in that case that the test will falsely indicate a person has antibodies.
The reason for this is a simple matter of statistics. The lower prevalence there is of a trait in a studied population —here, coronavirus infection — the more likely that a test will return a false positive. While a more accurate test will help, it can’t change the statistical reality when the base rate of infection is very low.”
Suppose we select one person at random from a population in which 5 percent of people are infected with
COVID-19, and give that person an antibody test. Assume that the antibody test is 90% accurate, meaning
that the test has a 10% false positive rate and a 10% false negative rate.
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Make a tree diagram to display the possible outcomes of this random process.
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Find the probability that the antibody test result is positive.
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Given that the antibody test result is positive, find the probability that the person has COVID-19. Compare your answer with the 32 percent predictive value stated in the news article.
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Explain the sentence in the article, “Put another way, there is an almost 70 percent probability…that the test will falsely indicate a person has COVID-19 antibodies.”
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