Date:         Mon, 26 Sep 2005 23:18:24 -0700
Reply-To:     David L Cassell <davidlcassell@MSN.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         David L Cassell <davidlcassell@MSN.COM>
Subject:      Re: t test and normality
In-Reply-To:  <200509262055.j8QKboZ1007649@malibu.cc.uga.edu>
Content-Type: text/plain; format=flowed

Vadim.Pliner@VERIZONWIRELESS.COM replied:
>The two-sample t test is based on the assumption that both samples come
>at random from normal populations with equal variances. This assumption
>has nothing to do with the central limit theorem which states that the
>sampling distribution of the mean of the sample elements tends to a
>normal distribution. Fortunately, the t test is robust to departures
>from its theoretical assumptions, and the larger the samples, the more
>robust the test. PROC UNIVARIATE is a right way to test your samples
>for normality. If you are concerned your samples are markedly skewed,
>it may be safer to apply PROC NPAR1WAY which uses nonparametric
>Wilcoxon test.

Yes.  The 2-sample t test does that.

But the large-sample version, which is essentially a z-test, doesn't need an
underlying assumption of normality, because with the large sample sizes,
you get the Central Limit Theorem (unless there are some unusual properties
of the underlying distribution).  The t-test does have a basic problem with
large discrepancies in variance between groups, so the original poster needs
to be concerned with that.

David
--
David L. Cassell
mathematical statistician
Design Pathways
3115 NW Norwood Pl.
Corvallis OR 97330

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