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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?
Comments: cc: mike.rosen@EDS.COM
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 -------------------------------------------------------- David W. Bessemer -------------------------------------------------------- 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) -------------------------------------------------------- Any opinion stated in this message is entirely my own, not an official position of the US Army Research Institute. --------------------------------------------------------

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