This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Statistics 403 Problem Set 7 Due in lab on Friday, November 5th 1. Suppose we are planning to studying a treatment for depression. We will obtain base line depression scores X i , i = 1 ,..., 30 on a set of research subjects. Three months later, after the treatment is complete, we will obtain a new set of depression scores Y i , i = 1 ,..., 30 on the same subjects. We anticipate that the treatment will reduce average depression scores by 1 . 6 raw units. For power analysis, we assume that the pretreatment measures will have a standard deviation of 3 units, the posttreatment measures will have a standard deviation of 2 units, and the pretreatment and post treatment measures will be correlated 0 . 4 with each other. (i) What is the power for detecting the anticipated effect of 1 . 6 units when using a paired ttest; (ii) What would the power be if we used an unpaired ttest? Solution: The standard deviation of the D i = X i Y i values is q var( X ) + var( Y ) 2cov( X,Y ) = 3 2 + 2 2 2 . 4 3 2 = 2 . 86 . Thus the expected test statistic under the paired analysis is ET = 30 1 . 6 / 2 . 86 = 3 . 1 . This gives us a power of P ( T > 2) = P ( Z > 2 ET ) = P ( Z > 1 . 1) = 0 . 86 . Under the unpaired analysis, the expected value of the test statistic is ET = E X Y q 2 X / 30 + 2 Y / 30 = 1 . 6 q 3 2 / 30 + 2 2 / 30 = 2 . 43 , and the variance of the test statistic is var( T ) = var X Y q 2 X /n + 2 Y /n = n 2 X + 2 Y var( D ) 1 = n 2 X + 2 Y 2 X + 2 Y 2cov( X,Y ) n = 2 X + 2 Y 2cov( X,Y ) 2 X + 2 Y = 13 2 . 4 3 2 13 . 63 ....
View Full
Document
 Winter '12
 KerbyShedden
 Statistics

Click to edit the document details