* * * Ludwik said: * * *
I suggest that, at least on this list, we start using the word
"errance" instead of "standard deviation of the mean". By errance, E,
we mean s/sqr(n), where s is a standard deviation from a representative
sample of size n.
* * * end quote * * *
I suggest we not make up new names until doing a little research on
accepted names used by NIST, CDC, professional statisticians, etc.
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."
We don't need a substitute for "standard deviation of the mean." We
just need to quit using it because it's not commonly-used wording for
anything I am aware of.
Since I have a foot both in physics and chemistry, I am familiar with
statistics in analytical chemistry, and all my analytical chemistry
books discuss the two separate ideas as "standard deviation" and
"standard error of the mean." Also, below is cut and pasted from CDC
(Centers for Disease Control) Division of Epidemiology.
* * * from CDC * * *
Definitions
Standard Deviation (SD) is a measure of the variation or spread of the
distribution about the mean of an observation of a characteristic in the
collection of all values of that observation in a population or sample.
Standard Error of the Mean (SEM) is the standard deviation of means of
repeated samples of the same size from a population. It is an estimate
of how closely the sample mean represents the population mean.
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.
Why use SEM?
To establish a confidence level of how accurately a sample mean
represents the population mean
* * * end quote * * *
I believe a little research will show the wording from CDC and from my
analytical chemistry books is well established in other fields. Perhaps
this is true in physics also, but the discussion here is shaking my
"confidence" in that.
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu