Mann-Whitney test pivotal quantity & randomized block design

[Sander1337]

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,...,Y_1n-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

http://img4.imageshack.us/img4/2817/knipseli.jpg

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(Y_ijY_i\bullet-Y_ijY_\bulletj 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

 

[Sander1337]

Sorry for posting this in the wrong forum. I didn't knew wether this was a homework question or not, since I have a question about a method instead of about homework..

Please move post to right section if moderator thinks otherwise!