Re: [Phys-l] Basic statistics

["Folkerts, Timothy J" <FolkertsT@bartonccc.edu>]

> I suggest we not make up new names until doing a little research on 
> accepted names used by NIST, CDC, professional statisticians, etc.

I agree completely - there are already plenty of common terms out there that we can use. 


> The problem is that "standard deviation of the mean" is a mixed breed. 
> It's a mixture of "standard deviation" and "standard error of the mean." 

In my mind, "standard deviation of the mean" is a perfectly fine, unmixed breed - although perhaps it should be called the "standard deviation of the meanS".  Any time you find the standard deviation, you are finding the standard deviation of some particular set of numbers.  The "standard deviation" is more precisely the standard deviation calculated from many individual data points, which could logically be called "the standard deviation of the individuals".  The "standard deviation of the means" is exactly that - the standard deviation calculated from many values of the mean (where each value of the mean is in turn calculated from a different sample). 

On the other hand, "standard error of the mean" is both 1) common) and 2) less likely to get confused with the term "standard deviation", so it will likely remain standard nomenclature.

* * * from NIST * * *
Standard Error:  The standard deviation for a statistic's sampling distribution.

* * * * * * * * 

This would imply that "standard" error" is the same as "standard deviation", but it is restricted to use with a statistic (a value calculated from sample data - NIST again), rather than individual data points.  You can have the standard error of the mean, or the standard error of the standard deviation (which can itself be enlightening), or the standard error of any other value calculated from a smaple.   


And as a somewhat obscure aside:
"Central Limit Theorem states that regardless of the shape of the 
frequency distribution of observations of the original population, the 
frequency distribution of sample means of repeat random samples of size 
n tends to become normal as n increases."

There are actually a few distributions for which this is NOT true.  The Cauchy Distribution (also known as the Lorenz distribution) is one such example - the standard deviation is not finite and that messes up the Central Limit Thm.


Tim F