**Date:** Wed, 28 Apr 1999 10:57:03 -0400
**Reply-To:** "Bessemer, David W." <Bessemer@FTKNOXARI-EMH15.ARMY.MIL>
**Sender:** "SPSSX(r) Discussion" <SPSSX-L@UGA.CC.UGA.EDU>
**From:** "Bessemer, David W." <Bessemer@FTKNOXARI-EMH15.ARMY.MIL>
**Subject:** Re: General Statistics Question: How big a sample?
**Content-Type:** text/plain
On Tue, 27 Apr 1999 08:44:58 -0700, Mike Rosen wrote:
>What I'm asking for is a method for calculating (or at least estimating)
the
>required sample size to achieve a particular confidence interval for a
mean,
>given a (different) sample.

The method is provided by Stein's two sample procedure:

A first sample of size n(1) provides an estimate of variance (s^2).

The required second sample size is n(2) = (t^2)(s^2)/(d^2)

where t is the t-distribution value for alpha and n(1)-1 degrees of freedom,
and d is the half-width of the desired confidence interval.

Steel & Torrie (1960), Principles and Procedures of Statistics, NY:
McGraw-Hill
give an example and the original reference:

Stein, C. (1945) A two-sample test for a linear hypothesis whose power is
independent of the variance. Ann. Math. Stat., 16, 243-258.

S & T say that the method also applies to finding the C.I. for a mean
difference
by using the combined variance of the two subgroups in a first sample. If
the
variances in the groups differ, I think the best course of action is to use
Welch's
approximation to the t-distribution.

Dave
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David W. Bessemer
bessemer@ftknoxari-emh15.army.mil
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US Army Research Institute
Armored Forces Research Unit
ATTN: TAPC-ARI-IK (Bessemer)
Fort Knox, KY 40121-5620

Phone: (502) 624-4932/7046
FAX: (502) 624-8113
(DSN Prefix: 464)
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Any opinion stated in this message is
entirely my own, not an official position
of the US Army Research Institute.
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