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
Content-Type: text/plain; format=flowed
>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
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 L. Cassell
3115 NW Norwood Pl.
Corvallis OR 97330
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