I don't dispute that "standard error of the mean" is indeed the
"standard deviation of means." (Note common usage tends to say "of
means" rather than "of the mean," for what it's worth.)
The reason I called it a mixed bread is because it intermixes the two
most widely accepted phrases of "standard deviation" and "standard error
of the mean." And, as Tim Folkerts implied, sticking the word
"deviation" in the later is likely to cause confusion because you have
to be more careful to listen to the whole phrase to distinguish which is
being talked about. If everyone used "standard deviation" and "standard
error of the mean" you would immediately know which is being used as
soon as you heard the second word.
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu