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 false-positives 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
H0: no cancer is present
and an alternative hypothesis of
Ha: 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?