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Thanks Andy. Yes you are right - I should have specified the normal distribution. Best wishes, Tim [log in to unmask] <mailto:[log in to unmask]> Phone +44(0)20 7905 2666 Fax +44(0)20 7905 2381 Population, Policy and Practice Programme UCL Great Ormond Street Institute of Child Health, London WC1N 1EH, UK On 22/03/2019, 09:22, "Andrew Salmon" <[log in to unmask]> wrote: >Hi Tim >that feels right, but are the mean and variance uncorrelated? in >mathematical analysis the mean always seems to be related to the first >derivative of something or other, and the variance to the second. Not >only that, but in most parametric distributions, the mean and variance >incorporate the same parameter, with the normal distribution being the >exception? > >Or do I just need more coffee this morning...? > >Andy > >On Fri, 22 Mar 2019 at 09:04, Cole, Tim <[log in to unmask]> wrote: >> >> Sorry to come late to the party. >> >> It¹s worth stating that accuracy relates to the mean of a sample of >>values >> (in that bias is the difference between the sample mean and the true >> mean), whereas precision relates to the sample variance (or its >>inverse). >> Hence the two are uncorrelated by definition. >> >> Best wishes, >> Tim Cole >> >> [log in to unmask] <mailto:[log in to unmask]> Phone +44(0)20 7905 >> 2666 Fax +44(0)20 7905 2381 >> Population, Policy and Practice Programme >> UCL Great Ormond Street Institute of Child Health, London WC1N 1EH, UK >> >> ------------------------------ >> >> >> >> >Date: Thu, 21 Mar 2019 09:56:44 +0000 >> >From: Allan Reese <[log in to unmask]> >> >Subject: Precision & accuracy (MY conclusion) >> > >> >Thanks to all for comments. Martin Bland suggests, "The standard >> >statistical usage, as I understand it, is that precision refers to how >> >close repeated observations are to one another, and accuracy how far >> >they are from the true value." That, and similar comments, correspond >>to >> >the definitions in Kendall & Buckland (Dictionary of Statistical Terms, >> >4th ed), though I would use "reliability" for the former. As K&D >> >comment, the "precision" of an estimator varies with the square root of >> >the number of observations, but it's not quite the sense here. >> > >> >John Whittington sent me a great hint off-list, "Modern technology is >> >such that it is only too easy to produce such a device which displays >> >umptreen more DPs than is sensible in relation to the accuracy of the >> >measurement." That's what happen here. The device (digital calliper) >>has >> >a standard LED display that shows 2dp, but it was flimsily constructed >> >and flexed when applied to an object. There is no reason to believe the >> >measurements are biased, especially as the "accuracy" is quoted as +/-. >> >To my mind, it means a reading of, say 3.45 could mean anything from >> >3.25 to 3.65, so I have doubts even rounding to 0dp! >> > >> >Fortunately, the model I use is made of metal, has a quoted precision >>of >> >0.02 (and a 2dp display), so I'm happy rounding to 1dp. >> > >> >There is clearly much imprecision, and confusion, in the use of the >>word >> >"precision" with regard to measurement (recording), calculation >> >(numerical analysis), and general use in the language - Collins >> >Dictionary was no help at all! >> > >> >Allan >> > >> >> You may leave the list at any time by sending the command >> >> SIGNOFF allstat >> >> to [log in to unmask], leaving the subject line blank. You may leave the list at any time by sending the command SIGNOFF allstat to [log in to unmask], leaving the subject line blank.