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Unformatted text preview: rs. 2 M316 Chapter 23 Dr. Berg b) Association does not prove causation. Explain how buying recycled filters might improve a person’s opinion of their quality. Then explain how the opinion a person holds might influence his or her decision to buy or not. You see that the cause‐and‐effect relationship might go in either direction. The Problem of Multiple Comparisons The null hypothesis in Example 23.1 is that there is no difference between the distributions of outcomes in Canada and the United States. Put more generally, the null hypothesis is that there is no relationship between two categorical variables, H0: there is no relationship between nationality and quality of life. The alternative hypothesis says that there is a relationship but does not specify any particular kind of relationship, Ha: there is some relationship between nationality and quality of life. Any difference between the Canadian and American distributions means that the null hypothesis is false and the alternative is true. The alternative hypothesis is not one‐sided or two‐sided. We might call it “many‐sided” because it allows any kind of difference. We could use the two‐sample t test for proportions on each category of the response variable and assign a P‐value to each, but we would run the usual multiple analysis risk that we would get a bogus result. When we do many individual tests or confidence intervals, the individual P‐values and confidence levels don’t tell us how confident we can be all of the inferences...
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