R help - Jan 2008 - Different results in calculating SD of 2 numbers

Hi all,

Can anyone tell me why I am getting different results in calculating SD of 2
numbers ?
> (1.25-0.95)/2
[1] 0.15
> sd(c(1.25, 0.95))
[1] 0.2121320          # why it is different from 0.15?

Regards,

Send instant messages to your online friends http://uk.messenger.yahoo.com 
	[[alternative HTML version deleted]]

Ron Michael <ron_michael70 at yahoo.com> writes:
> Can anyone tell me why I am getting different results in calculating
> SD of 2 numbers ?
>
>> (1.25-0.95)/2
> [1] 0.15
Because this is not the SD?  Try
> (1.25-0.95)/sqrt(2)
:-)
>> sd(c(1.25, 0.95))
> [1] 0.2121320          # why it is different from 0.15?
-- 
Bj?rn-Helge Mevik

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at
r-project.org] On Behalf
> Of Ron Michael
> Sent: Wednesday, January 16, 2008 12:15 AM
> To: r-help at stat.math.ethz.ch
> Subject: [R] Different results in calculating SD of 2 numbers
> 
> Hi all,
> 
> Can anyone tell me why I am getting different results in calculating SD of
2 numbers ?
> 
> > (1.25-0.95)/2
> [1] 0.15
Because the above is not the standard deviation of two numbers.  The sample
based estimate of the population standard deviation of a set of numbers (which
is what sd() computes) is

(sum((x-mean(x))^2 )/(length(x)-1))^.5

which for your two numbers would be

( (1.25 - 1.1)^2 + (.95 - 1.1)^2 )^.5
> > sd(c(1.25, 0.95))
> [1] 0.2121320          # why it is different from 0.15?
> 
> Regards,
> 
Hope this is helpful,

Dan

Daniel Nordlund
Bothell, WA  USA

>>>>> "RM" == Ron Michael <ron_michael70 at
yahoo.com>
>>>>>     on Wed, 16 Jan 2008 00:14:56 -0800 (PST) writes:
    RM> Hi all,
    RM> Can anyone tell me why I am getting different results in calculating
SD of 2 numbers ?

    >> (1.25-0.95)/2
    RM> [1] 0.15
    >> sd(c(1.25, 0.95))
    RM> [1] 0.2121320          # why it is different from 0.15?

because  1 is different from 2 !
If 2 was 1, than sqrt(2) == 1 as well, but actually I don't
think the universe and we all would exist in that case ....

Martin Maechler, ETH

And another problem, in addition to the points made by others, is that
the formula for the SD gives a biased estimate (it underestimates it) of
the population SD for small n when sampling from a normal distribution.
When n is about twelve or so or more, the bias can usually be ignored
(it is about 2.2%), but when you have only two numbers, the correction
factor is about 1.25.

The approximate correction formula, as I understand it, is
(n-.75)/(n-1), so if n = 2, then it is 1.25/1, but this is not exact.
The "real" formula is more complex (not difficult, but involves the
gamma function) and my reference to it is not at this office, or I would
give it.

HTH,

Ben 

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On Behalf Of Ron Michael
Sent: Wednesday, January 16, 2008 2:15 AM
To: r-help at stat.math.ethz.ch
Subject: [PS] [R] Different results in calculating SD of 2 numbers

Hi all,

Can anyone tell me why I am getting different results in calculating SD
of 2 numbers ?
> (1.25-0.95)/2
[1] 0.15
> sd(c(1.25, 0.95))
[1] 0.2121320          # why it is different from 0.15?

Regards,

Send instant messages to your online friends
http://uk.messenger.yahoo.com 
	[[alternative HTML version deleted]]

______________________________________________
R-help at r-project.org 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.