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.

HTH, Vadim Pliner

kachi wrote: > HM, > > > > With large sample size as 1000 Proc ttest can be used > without testing for normality assumption due to the result > of Central Limit Theorem. This Proc takes care of varying > sample variances in the 2 groups and you read that line in > the output. > > The PROC UNIVARIATE checks whether each of your sample comes > from a parent Normal Distribution with Mean = 0. You can do > this PROC if you have a guess of the Population Mean and in > its absence, the sample mean may be used. > > If your interest is to test for normality then do as follows. > Let the observations of sample1 be x1, x2, .. x1000 and the > sample mean be M1. > Create y1 = x1 - M1, y2 = x2 - M1 .. y1000 = x1000 - M1. Then > use Proc Univariate to test weather y are distributed normally. > > This means that the sample1 has come from a parent Normal > Distribution with mean equal to M1. You may use some other guess > values for M1. Similarly you can answer for sample2. > > Hope this answers your question. > > Muthia Kachirayan > > > > > > > Date: Thu, 22 Sep 2005 13:36:54 -0700 > Reply-To: hmekouar@HOTMAIL.COM > Sender: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU> > From: hmekouar@HOTMAIL.COM > Organization: http://groups.google.com > Subject: Re: t test and normality > Comments: To: sas-l@uga.edu > Content-Type: text/plain; charset="iso-8859-1" > > Thanks so much. But, I used proc univariate to check normality and the > results suggested non normality. I am a bit confused. Once I have large > samples, by the central limit theoreme, should I assume normality even > if the proc univariate suggests non normality? > Thanks