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MannWhitney test pivotal quantity & randomized block design 
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#1
Sep1309, 11:08 AM

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 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 SSSSTSSB=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 3page (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 


#2
Sep1309, 11:42 AM

P: 11

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! 


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