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# note06 - Chapter 2 Two-Sample Methods 8 Selecting Among...

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Chapter 2: Two-Sample Methods 8 Selecting Among Two-Sample 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 cdf’s differ by F 1 ( x ) = F 2 ( x − △ ) Testing H 0 : = 0 The t-test 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 t-test 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 Rank-Sum Test vs. the t-Test Wilcoxon Test advantages over the t-test, 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 t-test greater power than the Wilcoxon test for small samples and for distributions that are light-tailed validity might be in question for very small sample, when sampling is from non-normal distribution but the table critical values are used . 1

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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
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