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Unformatted text preview: Chapter 2: TwoSample Methods 8 Selecting Among TwoSample Tests Assumptions X 1 ,...,X m iid F 1 and Y 1 ,...,Y n iid F 2 ( F 1 and F 2 are continuous cumulative distribution) X 1 ,...,X m and Y 1 ,...,Y n are independent : the cdfs differ by F 1 ( x ) = F 2 ( x ) Testing H : = 0 The ttest if F 1 and F 2 are normal with equal variance the correct probability of a Type I error and the greatest power modest violations of the normality assumption have little effect on the probability of a Type I error of the ttest the robustness property for the probability of a Type I error: due to the CLT effect 5 to 10 samples from Uniform distribution around 20 sample from Exponential distribution when the underlying distributions are normal, the theoretical support for the optimality in terms of power The Wilcoxon RankSum Test vs. the tTest Wilcoxon Test advantages over the ttest, when the observations are usually large or small in comparison with the rest the data greater power for moderate to large samples and for distributions that are heavier tailed or skewed may be preferred on the basis of Type I error considerations the ttest greater power than the Wilcoxon test for small samples and for distributions that are lighttailed validity might be in question for very small sample, when sampling is from nonnormal distribution but the table critical values are used . 1 Relative Efficiency Two test ar the same level of significance m 1 + n 1 = N 1 m 2 + n 2 = N 2 with m 1 /n 1 = m 2 /n 2 choose N 1 and N 2 for two tests to have the same power Relative Effieicency of test 1 to test 2 eff(1 vs 2) = N 2 N 1...
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This note was uploaded on 07/22/2011 for the course STA 4502 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
 Staff

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