[R] Precision - or lack there of

[John Sorkin]

Ducan,
First, thank you for your reply. 
As I previously noted in a reply to Peter Dalgaard, you, and he, are
correct. I missed something quite obvious. Sometimes it does not pay to
do statistics early in the morning! Again, many thanks,
John

John Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
Baltimore VA Medical Center GRECC,
University of Maryland School of Medicine Claude D. Pepper OAIC,
University of Maryland Clinical Nutrition Research Unit, and
Baltimore VA Center Stroke of Excellence

University of Maryland School of Medicine
Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524

(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)
jsorkin at grecc.umaryland.edu

>>> Duncan Murdoch <murdoch at stats.uwo.ca> 12/09/06 11:39 AM >>>
On 12/9/2006 9:26 AM, John Sorkin wrote:
> R 2.3.1
> Windows XP 
> 
> I am surprised at the lack of precision in R, as noted below. I
would
> expect the values to be closer to zero, particularly the later
examples
> where the sample size is quite large.

These are all cases where the theoretical distributions are easy to 
calculate, and the results you are getting are not particularly
unusual:
> 
>> mean(rnorm(500,0,1))
> [1] -0.03209727

 > pnorm(-0.03209727, sd=1/sqrt(500))
[1] 0.2364660

>> mean(rnorm(5000,0,1))
> [1] -0.005991322

 > pnorm(-0.005991322, sd=1/sqrt(5000))
[1] 0.3359104

[skipped some]

>> mean(rnorm(50000,0,1))
> [1] -0.0006160524
>> mean(rnorm(500000,0,1))
> [1] -0.001254309
>> mean(rnorm(5000000,0,1))
> [1] 0.0004633778
>> mean(rnorm(50000000,0,1))
> [1] -0.0001325764

 > pnorm(-0.0001325764, sd=1/sqrt(50000000))
[1] 0.1742618

> 
> I would appreciate any thoughts. Is the lack of precision due to
> running on a 32-bit system?

No, the lack of precision seems to be due to the distributions you are

sampling from.

Duncan Murdoch

> 
> Thanks,
> John
> 
> 
> John Sorkin M.D., Ph.D.
> Chief, Biostatistics and Informatics
> Baltimore VA Medical Center GRECC,
> University of Maryland School of Medicine Claude D. Pepper OAIC,
> University of Maryland Clinical Nutrition Research Unit, and
> Baltimore VA Center Stroke of Excellence
> 
> University of Maryland School of Medicine
> Division of Gerontology
> Baltimore VA Medical Center
> 10 North Greene Street
> GRECC (BT/18/GR)
> Baltimore, MD 21201-1524
> 
> (Phone) 410-605-7119
> (Fax) 410-605-7913 (Please call phone number above prior to faxing)
> jsorkin at grecc.umaryland.edu 
> 
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