Researchers at the University of Washington and Harvard University analyzed
records of breast cancer screening and diagnostic evaluations ("Mammogram
Cancer Scares More Frequent Than Thought," USA Today, April 16,1998\()\).
Discussing the benefits and downsides of the screening process, the article
states that although the rate of falsepositives is higher than previously
thought, if radiologists were less aggressive in following up on suspicious
tests, the rate of false-positives would fall, but the rate of missed cancers
would rise. Suppose that such a screening test is used to decide between a
null hypothesis of \(H_{0}:\) no cancer is present and an alternative hypothesis
of \(H_{a}:\) cancer is present. (Although these are not hypotheses about a
population characteristic, this exercise illustrates the definitions of Type I
and Type II errors.)
a. Would a false-positive (thinking that cancer is present when in fact it is
not) be a Type I error or a Type II error?
b. Describe a Type I error in the context of this problem, and discuss the
consequences of making a Type I error.
c. Describe a Type II error in the context of this problem, and discuss the
consequences of making a Type II error.
d. Recall the statement in the article that if radiologists were less
aggressive in following up on suspicious tests, the rate of false-positives
would fall but the rate of missed cancers would rise. What aspect of the
relationship between the probability of a Type I error and the probability of
a Type II error is being described here?
