Researchers at the University of Washington and Harvard University analyzed reco

Question

Researchers at the University of Washington and Harvard University analyzed records of breast cancer screening and diagnostic evaluations ("Mammo-gram Cancer Scares More Frequent thant 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 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 possible consequences of making a Type I error.

c. Describe a Type II error in the context of this problem, and discuss the possible consequences of making a Type II error.

d. What aspect of the relationship between the probability of Type I and Type II errors is being described by 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?

Explanation / Answer

a) Type I error. (Incorrect rejection of true null hypothesis)

b) Rejecting the null hypothesis, when it is actually true indicates that there is no cancer, but assuming it false, researcher rejects is. Consequence will be severe, as treatmnet corresponding to cancer might begin.

c) Type II error refer sfailure to reject a false null hypothesis. That is when cancer is present, it is concluded that no cancer. This is more severe than Type I error as timely treatment which might reduce th eintensity of cancer will not begin at all.

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