Date:         Wed, 8 Dec 1999 15:00:25 -0500
Reply-To:     Alan Neustadtl <aneustadtl@socy.umd.edu>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Alan Neustadtl <aneustadtl@SOCY.UMD.EDU>
Subject:      Achieved Probability Explanation
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I have thought myself into a corner and hope someone can set me
straight.  In proc ttest, SAS presents the achieved probability of the
absolute value of the calculated t or greater.  The manual explains
that this is presented as a 2-tailed test.  In other words, you can
directly compare your alpha with the achieved probability.  If alpha ls
less than the achieved probability, you fail to reject the null in a
2-tailed test.  If alpha is greater, you reject the null.

To perform a 1-tailed test, you should cut the achieved probability in
half and compare your alpha with this value and make a decision similar
to the one above --if alpha is greater than p, reject the null
hypothesis; if alpha is less than p, fail to reject the null
hypothesis.

To make this concrete, assume a large sample that produces a calculated
t value of 1.96, and alpha equal to 0.05.  SAS reports Prob>|T| equal
to 0.0500.  Admittedly, this is at the borders, but for a 2-tailed
test, let's say that is is close enough that you fail to reject the
null hypothesis.  Alternatively, for a
1-tailed test, you would compare 0.05 to 0.025 and would reject the
null hypothesis.  I understand that this produces results as expected,
but I can't for the life of me grasp the underlying concept of why?

Any help is appreciated, and I apologize at th eoutset for being so
muddled!

Best,
Alan