```Date: Thu, 7 Mar 2002 09:22:03 -0800 Reply-To: Cassell.David@EPAMAIL.EPA.GOV Sender: "SAS(r) Discussion" From: "David L. Cassell" Subject: Re: Weights in GLM and the estimated error variance Content-type: text/plain; charset=us-ascii Ulrike Groemping answered his own question: > Solved it myself now: > The weights have to sum to the sample size, for the standard deviation > to be realistically estimated. Technically, no. In order to keep the standard errors on the same scale, you would indeed want that the weights would sum to something around the sample size.. which is equivalent to saying that your analysis is on the population rather than a random subset thereof. That is what you wanted in your case. But, in most cases that isn't what is going on. The weights often represent a 'correction' to transform from the sample back to the population. A simple random sample of 10% of the population would have weights of 10: each sample unit represents 10 units of the actual population. So you need to expand the standard errors upward in order to reflect your uncertainty about the true population characteristics. If you look at the formulae for weighted variances [either the standard, which assumes simple random sampling and hence independence, or survey sampling formulae, which do not] you will see that there are a lot of "weight**2" stuck in there to get the unbiased estimators. That's what is happening inside proc glm too. HTH, David -- David Cassell, CSC Cassell.David@epa.gov Senior computing specialist mathematical statistician ```

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