Date:         Thu, 24 Oct 2002 15:00:33 -0400
Reply-To:     Richard Ristow <wrristow@mindspring.com>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Richard Ristow <wrristow@mindspring.com>
Subject:      Re: Some formulae needed
Comments: To: "Burleson,Joseph A." <burleson@up.uchc.edu>
In-Reply-To:  <7D25CCC35D3CD31192BF006008BFB1FE04F572C2@nsofs14.uchc.edu>
Content-Type: text/plain; charset="us-ascii"; format=flowed

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)