20/08/2001 -- Errata -- A trivial numerical mistake has been found in the original Newton problem, where I have confused dice and coins... Nothing changes on the "variations over the problem", nor on the rest of the paper. I apologize for the mistake and thank Christoph Berger for having realized it. Hereafter follow (part of) the mails containing the details: ----------------------------------------------------------------- Date: Thu, 16 Aug 2001 14:47:46 +0200 From: Christoph Berger To: giulio.dagostini@roma1.infn.it Subject: Your paper Dear Giulio, I am just working through your contribution to the CERN workshop on confidence limits (CERN 2000-005, p 3) and already stumbled over the introductory Newtonian problem. The answer is I think the binomial distribution. But I can reproduce your numbers only with p=1/2 (i.e. tossing a coin) [omissis] Best regards Christoph ----------------------------------------------------------------- To : Christoph Berger Cc : Attchmnt: Subject : Re: Your paper ----- Message Text ----- Dear Christoph, THANKS A LOT for spotting the mistake! You are right. The numbers have been evaluated with the wrong p, as is indeed documented in the related Mathematica notbook publically available (see CLW stuff in http://www-zeus.roma1.infn.it/~agostini/prob+stat.html ) where I explicitely state to use N[PDF[BinomialDistribution[6, pn], 1]] and so on, with pn = 1/2. I think I was making some tests, and perhaps the final code that remained in the notebook was the solution of the equivalent coin problem. And when I wrote the digits on the paper, I did not pay enough attention. [omissis] Anyhow, nothing changes about the substance of the paper, and some of the arguments are even REINFORCED on the light of this real life example: - the condemned person is able to perceive levels of confidence, though he is not able to evaluate the percentage; - he will ask an expert person he trusts, and the expert's confidence will be his confidence; - but the expert could make a wrong calculation and state a number different from the one he would rationally believe... - experts might be dangereous, because their beliefs often become public opinion beliefs.. so we must be very carefull in providing CL's with are taken as confidences by the rest of the community (as in the case of leptoquarks or Higgs...). Best regards and thanks again, Giulio PS: the correct numbers I get are 0.402, 0.296 and 0.245, respectively. So, at least, the mistake had not, fortunatly, tragical consequences for the condamned person...