```Date: Wed, 8 Dec 1999 14:29:31 -0700 Reply-To: Mark S Dehaan/MSD/LMITCO/INEEL/US Sender: "SAS(r) Discussion" Comments: To: Alan Neustadtl From: Mark S Dehaan/MSD/LMITCO/INEEL/US Subject: Re: Achieved Probability Explanation Comments: To: SAS-L@LISTSERV.VT.EDU Content-type: text/plain; charset=us-ascii Alan, I will try to explain in general terms. The p-value is simply how extreme the observed value (of the mean, or whatever) is on the hypothesized distribution (typically a normal distribution is assumed for most tests). Say your observed p-value is 0.03 This means that the mean falls on one tail or the other at the point such that there are .03 (3%) possible values more extreme, either less than if on the lower tail or greater than for the upper tail. The trick is that this p-value (for most tests) could be on either the low tail or the upper tail - you have to look at the mean or t-stat to see which end you are dealing with. For a one sided test you first see if the t-stat fell on the tail your alternative hypothesis addresses. For example your alternative hypoth may be that there is a positive difference. Then you should have a positive t-stat. If the statistic is on the wrong side then you can automatically assume that the null is accepted as the test stat value wasn't even on the correct end for your alternate hypothesis to be true. If it is on the correct tail for your alternate hypoth, then you would see if the p-value is smaller than your alpha. If so then your data is more extreme than your null would suggest and you reject the null and accept the alter. hypoth. Now a two sided test is simply two one sided tests with the total alpha divided in half for each test. That is you are interested in an extreme value AT EITHER TAIL, you don't care which. Each tail is equally important so you divide your alpha in half to compare each tail to. That is you compare the p-value for your data to half your overall alpha. You are checking how extreme the value was on either end. If I could draw a picture here it would be helpful. But I hope this somehow helps. Best wishes, Mark DeHaan Alan Neustadtl @LISTSERV.VT.EDU> on 12/08/99 01:00:25 PM Please respond to Alan Neustadtl Sent by: "SAS(r) Discussion" To: SAS-L@LISTSERV.VT.EDU cc: Subject: Achieved Probability Explanation 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 ```

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