[R] Precision - or lack there of

[Duncan Murdoch]

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
> 
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