# Mann-Whitney test pivotal quantity & randomized block design

 P: 11 Hi there, I have a question about an assignment I got from school. They were initially 12 assignments, I've finished 10 so far but I still can't figure how my last 2 assignments work. First there is the question; Prove that W1(δ) and U1(δ) are pivotal quantities, where W1(δ) = sum of ranks assigned to Y11-δ,.....,Y1n-δ and U1(δ) = W1(δ) - n(n+1)/2. I really don't understand how to prove that. I can imagine that proving that W is a pivotal quantity, will automatically result in U being a pivotal quantity since W is independent from parameter δ (is that the right parameter?). Second question is about randomized block design. The given question/assignment was; prove that SS=SSE+SST+SSB where; SSE=measures variability in populations SST=measures variability due to differences in populations SSB=measures variability between blocks (?) SS= measures total variability in data I decided that it would be a lot more convinient to prove SS-SST-SSB=SSE since their formula's aren't so complex as the one from SSE is Nevertheless it doesn't add up... When I simplefy them all (and with some help of reverse engineering -> simplefy SSE as well) I eventually end up with $$\Sigma\Sigma$$(YijYi$$\bullet$$-YijY$$\bullet$$j which should be equal to 2... (the bullets are supposed to be before respectively behind the j and the i in subscript) I worked it all out, if any of you would like to see scans/images of what I've written on paper to see what I've done, just ask. I think I've made a mistake in simplefying the initial errors before I all summed them up. Nevertheless, on request, I will post my complete 3-page (bad handwriting) simplification/solution so far... Please help me out on this, I'm going to get beserk in a matter of minutes cause the first 10 assignments already took me about 3 days to finish, but these 2 already took me a day and I still can't get how to prove them both... Kind regards, Sander