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CHAPTER 12

Analysis of Variance

So far, we have explored hypothesis tests that cope with at most two samples. Now, of course, they could be run multiple times—it would be trivial to extend loops and t.test to run through many iterations. However, that is a proposition fraught with risk. For a given = 0.05, suppose we wish to compare mean staph infection rates for eight regional medical centers. Then there are choose(8,2) = 28 total pairwise comparisons. Thus, the chance of at least one Type I error, supposing our eight samples are independent, is 1 – (.95)28 = 0.7621731 which is rather high. Analysis of variance (ANOVA) compares three or more ...

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