On Thu, 10 Oct 2002 11:37:01 -0400, Bruce Weaver <[EMAIL PROTECTED]> wrote:
> On Thu, 10 Oct 2002, Rich Ulrich wrote: > > > On Thu, 10 Oct 2002 14:05:08 +0200, Jan Malte Wiener > > <[EMAIL PROTECTED]> wrote: > > > > > hi, > > > hopefully a simple one -> > > > > > > let's assume i have data like this: > > > subject A: 1,0,1,1,0,1,1,1 -> mean=6/8=0.75 > > > subject B: 1,1,1 -> mean=3/3=1 > > > > > > weighted arithmetic mean of A+B-> (8*0.75 + 3*1)/11 = 0.82 > > > -> well that was easy, but what if i do have 20 subjects like this and i > > > want to compare their weighted arithmetic mean to the weighted mean of > > > another group of 20 subjects ?? i guess i need to weight every single > > > subject-mean before running any stat-test. and here is my problem: how > > > do i weight the individual subject means ?? > > > > Statistically speaking, that looks bad. You don't have > > this problem when comparing 20 vs 20 subjects, > > if you are doing an Analysis of variance in the usual, legal, > > legitimate way; you want to count each Subject once. > > Weighting creates a problem of logic in computing 'error'; > > it is a problem of whether the analysis is by ANOVA. > > > > If you still want to get the weighted average that you describe, > > use "WEIGHT" . > > > I just want to make sure I follow you here, Rich. You're talking about > WEIGHT as in a weighted regression (or GLM), right? (As opposed to WEIGHT > CASES BY some frequency count.) I presume one would weight each subject's > mean by the inverse of its variance, right? The question (and example) was about weighting by the frequency count. My answer was about the frequency count, and counting a subject several times is the sort of weighting that screws up any simple t-test, or correlation, etc. -- When a sample in survey research is 're-weighted' to match a population, there is a simple and crude approach which is sometimes adequate. Samples are weighted by proportion, and Ns are further tweaked so the original N results. The tests produced that way are approximately correct so long as the adjustments are not far from 1.0, and don't change (much) the effective standard errors. -- The example here has counts that (a) count one person more than once, so that the DF is grossly overstated, and (b) are notably unbalanced. You raise a different question. I have worried much less about what you mention, weighting by variance. But that, too, is more common when *testing* is not at issue (I think). Does my argument, now or earlier, overlook something? - I faced survey questions once or twice, long ago, and right now, I am working from memory and from extrapolation from research principles. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
