# hw4 - 2 { Y .j-Y .j } . Question 2: For the model in...

This preview shows pages 1–2. Sign up to view the full content.

MAT 3378 - Fall 2009 Assignment 5 : Deadline: Friday, July 16, 2009 (in class) Question 1: Consider a repeated measures design model: Y ij = μ .. + ρ i + τ j + ε ij , where the subject eﬀects are ρ i independent N (0 2 ρ ), the treatment eﬀects satisfy r i =1 τ j = 0, the random errors ε ij are independent N (0 2 ) and ρ i ij are independent, for i = 1 ,...,s and j = 1 ,...,r . (a) Give the covariance structure associated to this model. That is give the diﬀerent values taken by σ { Y ij ,Y i 0 j 0 } . (b) Using the covariances from part (a), show that 1. σ 2 { Y .j } = σ 2 ρ + σ 2 s . 2. for j 6 = j 0 : σ { Y .j , Y .j 0 } = σ 2 ρ s 3. for j 6 = j 0 : σ 2 { Y .j - Y .j 0 } = 2 σ 2 s (c) Let j 6 = j 0 . Using the results from part (b), argue that we can use s 2 { Y .j - Y .j 0 } = 2 MSE s as a point estimate for σ

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2 { Y .j-Y .j } . Question 2: For the model in Question 1, we can show that E { SSTR } = σ 2 ( r-1) + s r X j =1 α 2 i . (a) Suppose that we are considered with the power for the test for A main ef-fects. Suppose that σ = 10 . 5 and that we would like to detect a range in the A 1 main eﬀects of Δ = 20 units with high probability. Give the value of the non-centrality parameter for the corresponding non-central F distribution. (b) Refer to part (a), if α = 5%, the power of the test is the probability of which event? 2...
View Full Document

## This note was uploaded on 12/22/2011 for the course MAT 3378 taught by Professor G.lamothe during the Spring '11 term at University of Ottawa.

### Page1 / 2

hw4 - 2 { Y .j-Y .j } . Question 2: For the model in...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online