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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 W_{1}(δ) and U_{1}(δ) are pivotal quantities, where W_{1}(δ) = sum of ranks assigned to Y_{11}-δ,.....,Y_{1n}-δ and U_{1}(δ) = W_{1}(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 [tex]\Sigma\Sigma[/tex](Y_{ij}Y_{i[tex]\bullet[/tex]}-Y_{ij}Y_{[tex]\bullet[/tex]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

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# Mann-Whitney test pivotal quantity & randomized block design

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