Section 8.5

# Section 8.5 - Section 8.5 A Nonparametric Test The...

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Unformatted text preview: Section 8.5 A Nonparametric Test The two-sample t-test even for the normal populations may not be the best or the most powerful size α test. If the populations are not normal , we have better alternatives available. Maan-Whiteney Test (Wilcoxon’s Rank Sum Test) Assume the two populations have same shape and spread so that they differ only in location (mean or median ). The populations need not be normal. Take samples of size m and n respectively from the populations P 1 and P 2 ; combine them and assign them ranks 1, 2, …, ( n m + ) from the smallest to the largest. Assumption : Let { } m x x ,..., 1 be a random sample for continuous x ~ F with 1 μ and { } n y y ,..., 1 be random sample from continuous y ~ G with mean 2 μ . Assume both F and G have same spread and shape. 1 Consider testing 2 1 : μ μ = H . If H is true, the observations should be inter-mingled. Combine both the samples, order them from the smallest to the largest and assign them the ranks 1, 2, …, (m+n)....
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Section 8.5 - Section 8.5 A Nonparametric Test The...

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