```Date: Feb 28, 2013 7:04 AM
Author: Gaj Vidmar
Subject: Adjustment of alpha to sample size (Prof Rubin, Prof Koopman et al., could you help this amateur again?)

Some time ago I asked a question here about adjustment of alpha to sample size.I'm using it (broadly speaking, to roughly clarify) in the field of SPC/SQC("eclectic", "pragmatic", i.e., anything goes that allegedly works :)My sort-of-control-chart invloves prediction interval from regression(through origin, if anyone remembers or wants to search for the original post),where I adjust the confidence level (i.e., 1-alpha) so that there is alwaysone half of a point to be expected outside the limits(maybe bizzare or silly, maybe not -  let's leave that aside). So my formula is(1-aplha) = (n-0.5)/nAt first, I had called this approach (half seriously) idiot's FDR, but further readingconvinced me that albeit not entirely unrelated (as a concept),FDR is always and only about multiple test (to put it simply).Fortunately, I've found three Bayesian references that(at least my blockheadness guesses so)argue for this type of thinking (listed below; the closest to something I can at leastpartly understand is #3). Should be enough, especially because Bayesian is evenmore "in" than FDR (although I'm even more clueless about it, but the refereesdon't know that, and I'm skilled at conning scientific journal readers :o)However, in the newsgroup, Prof Herman Rubin had written that "The level shoulddecrease with increasing sample size. In low dimensional problems,with the cost of incorrect acceptance going as the k-th power of the error,the rate at which the level decreases should be about 1/n^((d+k/2)."So it would be wonderful if one of you wizzards came up with some "simplealgebra" (as it's so often said in the literature when the opposite is truefor mere mortals) that relates Prof Rubin's formula to mine!I can guess that "the level" refers to alpha and that my problem islow dimensional (1D). "Incorrect acceptance" most probably means"incorrect acceptance of the null hypothesis".And let's say I take k to be 2 (by analogy with the notorious Taguchi,or because quadratic loss sounds familiar to many people in many fields).So far so good; but what does d stand for??Fortunately (or un-, from a broader perspective) my paper (currently under review)should get accepted even without such ellegant justification. And all I can do toreturn the favour is an acknowledgement . (Needless to say, co-authorshipis not something that the two Profs I mention in the title -- and other newsgroup"heavyweights", especially the retired ones -- want or need, anyway).So, as usual, thanks in advance for any help.Gaj VidmarReferences:1. Seidenfeld T, Schervish MJ, Kadane JB. Decisions without ordering.In "Acting and Reflecting", Sieg W (ed). Kluwer: Dordrecht, 1990, 143-170.2. Berry S, Viele K. Adjusting the alpha-level for sample size.Carnegie Mellon University Department of Statistics Technical Report 1995; 635.http://www.stat.cmu.edu/tr/tr635/tr635.ps3. Berry S, Viele K. A note on hypothesis testing with random sample sizes and itsrelationship to Bayes factors. Journal of Data Science 2008; 6(1): 75-87.http://www.jds-online.com/file_download/159/JDS-380.pdf
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