[R] OT: P(Z <= -1.46).

[Duncan Murdoch]

On 11/25/2006 10:21 AM, rolf at math.unb.ca 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
> 					rolf at math.unb.ca
> 
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