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Mann-Whitney test pivotal quantity & randomized block design

  1. Sep 13, 2009 #1
    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

    http://img4.imageshack.us/img4/2817/knipseli.jpg [Broken]

    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](YijYi[tex]\bullet[/tex]-YijY[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,

    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 13, 2009 #2
    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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