Hi James M. Clark Professor of Psychology 204-786-9757 204-774-4134 Fax [email protected]
>>> Michael Palij <[email protected]> 21-Apr-12 4:36 PM >>> On Sat, 21 Apr 2012 08:01:57 -0700, Jim Clark wrote: [snip] >What I do know is that if you select a sample of N observations with mean M and >standard deviation S out of a population with mean MU and standard deviation >SIGMA, then: > >1. M will fall within MU +/- z(alpha/2)*SIGMA/sqrt(N) with probability = 1 - >alpha (hypothesis testing), and I believe this may be Fisher's position with respect to a one sample test. >2. Equivalently, MU will fall within M +/- z(alpha/2)*SIGMA/sqrt(N) with >probability = 1 - alpha (confidence intervals). If you have only one CI, your second point is wrong -- this is what Neyman was emphasizing when he said that for a given CI, it either contained the population parameter (Prob= 1.00) or it didn't (Prob= 0.00). JC: Sorry to disagree, but if 1 is true, 2 is also true. That is, if M is expected to fall within a certain distance of MU with a certain probability, then MU is expected to fall within that same distance of M with the same probability. In the latter case, it is the CI that varies from sample to sample with 1-alpha of the CIs containing MU, which is staying in position. Just as you only have one CI in 2, you only have one M in 1, so it is not obvious to me why CIs are prevented from being conceptualized as selected from a hypothetical sampling distribution (according to Neyman given Michael's summary) while Ms are not so constrained. To turn the issue around a bit, given the way I have phrased #1 (Hypothesis Testing), it is also true that for a given sample M, it will either be within a certain distance of MU or not. But so what? We still don't say that p of being in the rejection region is 0 or 1 based on the outcome for this one trial out of a hypothetical sampling distribution. Perhaps I'm too concrete a thinker, but if I randomly sample 100,000 times from a population and calculate the ps as described above, then both 1 and 2 MUST both hold true. It is simply impossible for them not to. Specifically, with respect to 2 and using z = 1.96 and sigma, then 95% of the CIs will contain MU, which means that MU falls within my CI 95% of the time. Take care Jim --- You are currently subscribed to tips as: [email protected]. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13090.68da6e6e5325aa33287ff385b70df5d5&n=T&l=tips&o=17416 or send a blank email to leave-17416-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
