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M316 chapter 23

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Unformatted text preview: M316 Chapter 23 Dr. Berg Two Categorical Variables: The Chi‐Square Test The two‐sample z procedures of chapter 21 allow us to compare the proportions of successes in two groups. When there are more than two outcomes, or we want to compare more than two groups, we need a new statistical test. The new test addresses a general question: Is there a relationship between two categorical variables? Two‐Way Tables In Chapter 6 we used a two‐way table of counts to present data on two categorical variables. This is where we start. Example (23.1) Health Care: Canada and the United States Canada has universal health care. The United States does not, but often offers more elaborate treatment to patients with access. How do the two systems compare in treating heart attacks? A comparison of random samples of 2600 U.S. and 400 Canadian heart attack patients found that “the Canadian patients typically stayed in the hospital one day longer (P=0.009) than the U.S. patients but had a much lower rate of cardiac catheterization (25 percent vs. 72 percent, P<0.001), coronary angioplasty (11 percent vs. 29 percent, P<0.001), and coronary bypass surgery (3 percent vs. 14 percent, P<0.001).” The study then looked at many outcomes a year after the heart attack. There was no significant difference in the patients’ survival rate. Another key outcome was the patients’ own assessment of their quality of life relative to what it had been before the heart attack. Here are the data for the patients who survived a year: Quality of Life Canada United States M...
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