Date: Thu, 24 Oct 2002 15:27:00 0400
ReplyTo: "Burleson,Joseph A." <burleson@up.uchc.edu>
Sender: "SPSSX(r) Discussion" <SPSSXL@LISTSERV.UGA.EDU>
From: "Burleson,Joseph A." <burleson@up.uchc.edu>
Subject: Re: Some formulae needed
ContentType: text/plain; charset="iso88591"
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 nbar = 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.; SPSSXL@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:
>
>nbar = (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)
