1. Math
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  3. 1 you have two independent samples xi xn and yi...

Question: 1 you have two independent samples xi xn and yi...

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1. You have two independent samples, Xi,..., Xn and Yi,... , Ym drawn from populations with continuous distributions. Suppose the two samples are combined and the combined set of values are put in increasing order. Let Vr- 1 if the value with rank r in the combined sample is a Y and V,-0 if it is an X, for r-1, . . . ,N, where N-m+ n. Show that, if the two populations are the same then mn E(V) TES The general linear rank statistic is defined to be T-:-1 ary, where (ar) are given constants. Show that the mean and variance of the general linear rank statistic are mn E (T)- N 2arandVar (T) - Show that Wilcoxons W is a linear rank statistic. Use the formulae above to derive its mean and variance, under the null hypothesis that the populations are the same. Wilcoxons W is designed to test whether two populations differ in their location. How could W be adapted to test whether two populations with the same median differ in their variance?

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