H 0 1 2 h 0 1 3 h 0 2 3 problems 3 separate

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Unformatted text preview: roup, then, to test if any of the groups have a different heart rate, we would consider the ‘overall’ null hypothesis H 0 : µ1 = µ2 = µ3 HA : at least one µi is different for i=1,2,3 7 6 Why not just do 3 pairwise comparisons? • H 0 : µ1 = µ2 • H 0 : µ1 = µ3 • H 0 : µ2 = µ3 Problems: • 3 separate p-values for 3 different tests don’t tell us how likely it is that three sample means ¯¯¯ (Y1, Y2, Y3) are spread apart as far as these by chance (i.e. when µ1 = µ2 = µ3). ¯ ¯ • It might be that Y1 = 73.48 and Y2 = 91.32 are significantly different when only looking at 2 populations, but not significantly different if we look at 3 populations – as more and more groups are added, we expect the gap between smallest and largest sample means to get larger (even if the population means are the same). 8 • The probability of a Type I error (rejecting H0 when it was true) for the whole set of three t-tests will be larger than α. – For example, ∗ Set the chance of making a Type I error on an individual t-test at α = 0.05 ∗ The chance of NOT making a mistake on an individual t-test is (1 − α) = 0.95 These t-tests are not independent, bu...
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This note was uploaded on 06/12/2013 for the course MATHEMATIC MAT7870 taught by Professor Sun during the Winter '13 term at Wayne State University.

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