Date:         Fri, 25 Oct 2002 10:21:36 +0200
Reply-To:     Asesoría Bioestadística
              <bioestadistica@eresmas.net>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Asesoría Bioestadística
              <bioestadistica@eresmas.net>
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)