## Info

Values in the first column are probabilities of positive and negative test results for people with colorectal cancer; values in the second column are probabilities of positive and negative test results for people who do not have colorectal cancer (Hoffrage et al. 2000).

Values in the first column are probabilities of positive and negative test results for people with colorectal cancer; values in the second column are probabilities of positive and negative test results for people who do not have colorectal cancer (Hoffrage et al. 2000).

disease status is not known. Stated more personally, if your doctor did an occult-stool test and reported a positive result, what are the chances that you have colorectal cancer?

Based on the top row of Table 3.1, you might assume that your chances of having colorectal cancer in this case are pretty high because the probability of a positive test result in a person with colorectal cancer is much larger than the probability of a false positive (0.5 versus 0.03). However, the significance of this depends on the frequency of colorectal cancer in the general population, which is only about 0.3% (Hoffrage et al. 2000). Why is this important? The easiest way to see how this informat ion affect s the analysis is to imagine applying the probabilities in Table 3.1 to a large, hypothetical group of people. Suppose we consider a group of 10,000. If this group is representative of the general population, 30 would have colorectal cancer. Of these 30, 15 would have a positive occult-stool test and 15 would have a negative test, based on the first column of Table 3.1. Of the remaining 9,970 people who do not have colorectal cancer, we expect there to be about 299 who would have false positive tests (0.03 X 9970). These numbers are shown in Table 3.2. Looking at the first row of Table 3.2, we see that the expected total number

Table 3.2. Test results and disease status of 10,000 hypothetical individuals, where the frequency of colorectal cancer is 0.3%.

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