```Date: Thu, 24 Oct 2002 15:27:00 -0400 Reply-To: "Burleson,Joseph A." Sender: "SPSSX(r) Discussion" From: "Burleson,Joseph A." Subject: Re: Some formulae needed Comments: To: Richard Ristow Content-Type: text/plain; charset="iso-8859-1" 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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