Simulation (2015 #4)
- Steve Phelps
A researcher conducted a medical study to investigate whether taking a low-dose aspirin reduces the chance of developing colon cancer. As part of the study, 1,000 adult volunteers were randomly assigned to one of two groups. Half of the volunteers were assigned to the experimental group that took a low-dose aspirin each day, and the other half were assigned to the control group that took a placebo each day. At the end of six years, 15 of the people who took the low-dose aspirin had developed colon cancer and 26 of the people who took the placebo had developed colon cancer. Do the data provide convincing statistical evidence that taking a low-dose aspirin each day would reduce the chance of developing colon cancer among all people similar to the volunteers? For a simulation, there will be two groups with 500 in each group. We will assume that the 15 people in the low-dose group would have developed cancer regardless of the treatment group they were in. We will also assume that the 26 people in the placebo group would have developed cancer regardless of the group they were in. Overall, there were 41 people who developed cancer. We will randomly sort the 1000 people into two groups (low-dose and placebo) and see where these 41 people end up. We will then compare the proportion of people in each group who developed cancer with the test statistic pplacebo - plow-dose and see where our test statistic 26/500 - 15/500 = 11/500 = .022 occurs in the distribution.