# ps09 - Statistics 403 Problem Set 9 Due in lab on Friday...

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

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: Statistics 403 Problem Set 9 Due in lab on Friday, November 19th 1. Suppose we are planning to collect paired data X i ,Y i with the goal of estimating EX- EY . We want to have 80% power to detect a raw effect size EX- EY = 1, and based on previous experience we are confident that SD( X ) ≈ 2 and SD( Y ) ≈ 3. However we do not know much about the correlation between X and Y . (a) What sample size is required if cor( X,Y ) = 0 . 3? (b) If we perform the study using the sample size from part (a), and the correlation coefficient is actually 0 . 5, then what power do we actually have? Solution: The expected test statistic is ET = √ n EX- EY SD( X- Y ) = √ n 1 √ 4 + 9- 12 r = q n/ (13- 12 r ) , where r = cor( X,Y ). Note that when r increases, ET increases, so the power increases. To get 80% power we solve . 8 = P ( T > 2) = P ( T- ET > 2- ET ) = P Z > 2- q n/ (13- 12 r ) . So we set 2- q n/ (13- 12 r ) =- . 84 (since- . 84 is the 20 th = (100- 80) th percentile of the standard normal distribution), and solve for n to get n = 2 . 84 2 (13- 12 r ) . Substitute r = 0 . 3 to get n = 76. To get the power when r = 0 . 5, we calculate P Z > 2- q 76 / (13- 12 · . 5) , and we get that the power is approximately 0 . 9....
View Full Document

## This note was uploaded on 02/06/2012 for the course STAT 403 taught by Professor Kerbyshedden during the Winter '12 term at University of Michigan-Dearborn.

### Page1 / 4

ps09 - Statistics 403 Problem Set 9 Due in lab on Friday...

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

View Full Document
Ask a homework question - tutors are online