Dear Neville,
Can you give more information? The usual formula for the variances ofa linear combination of independendent observations of the form
w1Y1+w2Y2+.......+wkYk
where w1 to wk are a series of weights summing to 1 and Y1 to Yk are a series of observations is
w1^2V1+w2^2V2+....+wk^kVk
where wi^2 is the square of weight i and Vi is the variance of observation i.
This formula is central to meta-analysis and used for both fixed effect and random effects approaches, the difference between the two being how the individual variances are calculated (purely internally in the fixed effects approach and partially externally in the random effects approach).
Certainly the formula is pretty easy to put into an Excel spreadsheet. You need a column for the weights, C1, a column for the square of the weights,C2= C1*C1 a column for the variances, C3 and then a column for the product C4=C2*C3 and you then sum this column
Stephen
Stephen Senn
Professor of Statistics
School of Mathematics and Statistics
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From: A UK-based worldwide e-mail broadcast system mailing list [[log in to unmask]] On Behalf Of Neville Calleja [[log in to unmask]]
Sent: 04 March 2011 14:35
To: [log in to unmask]
Subject: Variance/SE for a weighted mean
I would appreciate any assistance on the calculation of the variance of a weighted mean. I am using SPSS which uses the sum of weights as the denominator for the calculation of variance. I feel that this gives an underestimate of the variance, given that, at the end of the day, the unweighted sample size is what really matters. I'm aware of the WinCross and Mentor approaches which sound reasonable but I do not have access to these packages.
Can anyone suggest any way of calculating such a variance of a weighted mean/proportion? I'd be extremely appreciative if anyone could share any SPSS or STATA syntax that does this, or possibly even an Excel template.
Thanks
Neville Calleja
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