Date: Fri, 25 Oct 2002 10:21:36 +0200 Reply-To: Asesoría Bioestadística Sender: "SPSSX(r) Discussion" From: Asesoría Bioestadística Subject: Re: Some formulae needed Content-Type: text/plain; charset=us-ascii Hi everybody Thanks to all who replied, but, although the information provided will be useful for the reverse-sample size calculation ("What power had a study that failed to reach significance with n1 and n2 sample sizes..."), what I needed was the formula that calculates n1 and n2 under certain conditions (alfa and beta levels, difference worth detecting and estimated standard deviation). A modification of the 1:1 ratio formula (n1=n2=ng): ng>2*var*(Zalfa-Zbeta)^2/(Mean.diff)^2 Regards Marta "Burleson,Joseph A." ha escrito: > Thanks, Richard! I'd forgotten about the geometric, simple as it is. > > Now can anyone tell us why the harmonic is used instead of the geometric (I > don't know)? The harmonic clearly penalizes discrepancy more, e.g.: > > Overall N = 100, n1 = 30, n2 = 70 > > Arithmetic n-bar = 50 > > Geomertic mean n = 45.8 > > Harmonic n' = 42 > > -Joe Burleson > > -----Original Message----- > From: Richard Ristow [mailto:wrristow@mindspring.com] > Sent: Thursday, October 24, 2002 3:01 PM > To: Burleson,Joseph A.; SPSSX-L@LISTSERV.UGA.EDU > Subject: Re: Some formulae needed > > At 01:34 PM 10/24/2002 -0400, Burleson,Joseph A. wrote: > > >In Cohen's power book, the formula for finding the "harmonic" > >(geometric) mean is: > > > >n' = 2*(n1)*(n2)/(n1 + n2) > > > >Note that when n1 = n2, this becomes the same as the arithmetic mean: > > > >n-bar = (n1 + n2)/2 > > > >In effect, your "average" sample size per group incurrs a stiffer > >penalty the more discrepant the difference between the two group sizes. > > To correct the terminology: This IS the formula for the harmonic mean. > (The defining formula is > > 1/n' = (1/n1 + 1/n2)/2 > > but that's less convenient for calculation.) > > The GEOMETRIC mean is a different value: > > n' = SQRT(n1*n2)

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