Mann-Whitney test pivotal quantity & randomized block design

In summary, the conversation is about a student struggling with two assignments from school. The first assignment involves proving that W1(δ) and U1(δ) are pivotal quantities, with W1(δ) being the sum of ranks assigned to Y11-δ,...,Y1n-δ and U1(δ) being W1(δ) - n(n+1)/2. The student is unsure of how to prove this and wonders if proving W as a pivotal quantity will automatically prove U as well. The second assignment is about proving that SS=SSE+SST+SSB in a randomized block design, with SSE measuring variability in populations, SST measuring variability due to differences in populations, and SSB measuring variability between
  • #1
Sander1337
10
0
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

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,

Sander
 
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  • #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!
 

1. What is the Mann-Whitney test?

The Mann-Whitney test, also known as the Wilcoxon rank-sum test, is a nonparametric statistical test used to compare two independent groups. It is used when the assumptions for parametric tests, such as the t-test, are not met.

2. What is the pivotal quantity in the Mann-Whitney test?

The pivotal quantity in the Mann-Whitney test is the difference between the two sample medians. This quantity is used to calculate the p-value, which determines the significance of the difference between the two groups.

3. What is a randomized block design?

A randomized block design is a type of experimental design where subjects are divided into groups, or blocks, based on certain characteristics. Within each block, subjects are randomly assigned to different treatments or conditions. This design is used to reduce the effects of confounding variables and increase the precision of the results.

4. How is the Mann-Whitney test used in a randomized block design?

In a randomized block design, the Mann-Whitney test is used to compare two treatments or conditions within each block. This allows for a more precise analysis of the effect of the treatment, as it controls for potential confounding variables within each block.

5. What are the advantages of using a randomized block design with the Mann-Whitney test?

The advantages of using a randomized block design with the Mann-Whitney test include increased precision of the results, reduced effects of confounding variables, and the ability to analyze the effect of the treatment within each block. This design also allows for a more efficient use of resources, as fewer subjects are needed compared to other experimental designs.

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