Re: [R] OT: P(Z <= -1.46).
In the days when tables were calculated laboriously, it was common practice to introduce several deliberate rounding errors in every table. These were used to catch infringements of copyright (and recover reproduction fees). Because tables came (and probably still do come) from a very few sources, published tables in textbooks will be far from independent data points. I found several pointing back to Lindgren. I checked my and my Dept's tables. Most are for positive x: the Biometrika tables have 0.9278550, Fisher and Yates do not have pnorm (only qnorm), Hald has 0.92785, and Lindley & Scott have 0.9279. All the tables in Lindgren (1960) are credited apart from this one, and I surmise that may be a deliberate error in that table (but it may of course also be a computational inaccuracy: if it were a rounding of Hald I would expect it to be credited as such). On Sat, 25 Nov 2006, [EMAIL PROTECTED] wrote: > In checking over the solutions to some homework that I had assigned I > observed the fact that in R (version 2.4.0) pnorm(-1.46) gives > 0.07214504. The tables in the text book that I am using for the > course give the probability as 0.0722. > > Fascinated, I scanned through 5 or 6 other text books (amongst the > dozens of freebies from publishers that lurk on my shelf) and found > that some agree with R (giving P(Z <= -1.46) = 0.0721) and some agree > with the first text book, giving 0.0722. > > It is clearly of little-to-no practical import, but I'm curious as to > how such a discrepancy would arise in this era. Has anyone any > idea? Is there any possibility that the algorithm(s) used to > calculate this probability is/are not accurate to 4 decimal places? > > Could two algorithms ``reasonably'' disagree in the 4th decimal > place? > cheers, > > Rolf Turner > [EMAIL PROTECTED] > > __ > R-help@stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > -- Brian D. Ripley, [EMAIL PROTECTED] Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UKFax: +44 1865 272595 __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] OT: P(Z <= -1.46).
Duncan Murdoch <[EMAIL PROTECTED]> writes: > My copy of the CRC standard mathematical tables give 0.0721, without > citation. > > > Could two algorithms ``reasonably'' disagree in the 4th decimal > > place? > > One possible source for this error (if it is an error), would be someone > rounding to 5 places giving 0.07215, then rounding again to 4 places. > Is that reasonable? Wouldn't be surprised. I'm using an introductory textbook that has qnorm(.95) as alternatingly 1.64 and 1.65 in its tables, where the latter fairly clearly comes from rounding of 1.645 instead of 1.644854. -- O__ Peter Dalgaard Øster Farimagsgade 5, Entr.B c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~ - ([EMAIL PROTECTED]) FAX: (+45) 35327907 __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] OT: P(Z <= -1.46).
Based on integration it appears that .0721 is correct. > integrate(function(x) exp(-x^2/2)/(2*pi)^.5, -Inf, -1.46) 0.07214504 with absolute error < 1.2e-07 On 11/25/06, [EMAIL PROTECTED] <[EMAIL PROTECTED]> wrote: > In checking over the solutions to some homework that I had assigned I > observed the fact that in R (version 2.4.0) pnorm(-1.46) gives > 0.07214504. The tables in the text book that I am using for the > course give the probability as 0.0722. > > Fascinated, I scanned through 5 or 6 other text books (amongst the > dozens of freebies from publishers that lurk on my shelf) and found > that some agree with R (giving P(Z <= -1.46) = 0.0721) and some agree > with the first text book, giving 0.0722. > > It is clearly of little-to-no practical import, but I'm curious as to > how such a discrepancy would arise in this era. Has anyone any > idea? Is there any possibility that the algorithm(s) used to > calculate this probability is/are not accurate to 4 decimal places? > > Could two algorithms ``reasonably'' disagree in the 4th decimal > place? >cheers, > >Rolf Turner >[EMAIL PROTECTED] > > __ > R-help@stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] OT: P(Z <= -1.46).
On 11/25/2006 10:21 AM, [EMAIL PROTECTED] wrote: > In checking over the solutions to some homework that I had assigned I > observed the fact that in R (version 2.4.0) pnorm(-1.46) gives > 0.07214504. The tables in the text book that I am using for the > course give the probability as 0.0722. > > Fascinated, I scanned through 5 or 6 other text books (amongst the > dozens of freebies from publishers that lurk on my shelf) and found > that some agree with R (giving P(Z <= -1.46) = 0.0721) and some agree > with the first text book, giving 0.0722. > > It is clearly of little-to-no practical import, but I'm curious as to > how such a discrepancy would arise in this era. Has anyone any > idea? Is there any possibility that the algorithm(s) used to > calculate this probability is/are not accurate to 4 decimal places? A text I've used gives the 0.0722 value, citing the 1962 edition of Lindgren's Statistical Theory. So it's not completely certain that this is "in this era". You can see parts of the 1993 version of Lindgren on books.google.com, and it repeats the 0.0722 value, but without citation (at least in the parts that are online). My copy of the CRC standard mathematical tables give 0.0721, without citation. > Could two algorithms ``reasonably'' disagree in the 4th decimal > place? One possible source for this error (if it is an error), would be someone rounding to 5 places giving 0.07215, then rounding again to 4 places. Is that reasonable? Duncan Murdoch > cheers, > > Rolf Turner > [EMAIL PROTECTED] > > __ > R-help@stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
