Sounds like a contrast to me. Use a contrast or estimate in SAS to get the mean and a test of if it is equal to 0.
Paul R. Swank, Ph.D. Professor, Developmental Pediatrics Medical School UT Health Science Center at Houston -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]]On Behalf Of Paige Miller Sent: Thursday, June 27, 2002 2:05 PM To: [EMAIL PROTECTED] Subject: T-test on linear combination of means Suppose I have three (or more) samples, from three (or more) different populations. According to my subject matter expert, he wants to estimate a linear combination of the means, say for example 0.5*mu1 + 0.5*mu2 - mu3 where mu1, mu2 and mu3 are the population means. I know how to compute this estimate, it is done by simply replacing the population means with the sample means. If I assume the original populations are normal and that the population variances are equal, I can compute the variance of this linear combination. Pretty straightforward stuff. However, I want to create a t-test to test the null hypothesis that this linear combination of means is equal to zero, using an estimate of variance derived from the data, rather than a population variance, which is unknown. In doing so, I run into the mathematical difficulty that I do not know the proper degrees of freedom for this test. (And yes, I know that for the special case of estimating mu1 - mu2 there are textbook formulas for this t-test, however I really am interested in linear combinations of more than two means). I feel like I am missing something very obvious; however, if someone knows, or can point me to the proper formula for a t-test on a linear combination of means, it would be greatly appreciated. -- Paige Miller [EMAIL PROTECTED] http://www.kodak.com "It's nothing until I call it!" -- Bill Klem, NL Umpire "When you get the choice to sit it out or dance, I hope you dance" -- Lee Ann Womack . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . ================================================================= . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
