Dear Tipsters,
One reason we use the standard deviation is that it comes from the
family of functions called moments about the origin of the
distribution:
Moment (r) = E[(X - mean) to power r]
(sorry that the program does not give proper symbols)
So the first moment = E[X - mean] = E(x) - E(mean) = mean -mean = 0
The second momen = E[(X - mean)squared] = variance
The third mean reflect symmetry or skewness.
My faithful Garrett (1958; Statistics in Psychology and Education,
5th ed. Longmans) observes that the SD is more "stable" than the AD
because it less affected by sampling errors. Indeed, he does
not give the formula for thr SE of the AD.
However, he adds that the different measures of variability (range,
AD, SD and Q -quartile deviation) have their uses and he that in
some cases extreme deviations may unduly influence SD.
It is also a fact that SD serves is many other stats., such as
correlation, t etc.
Sincerely,
Stuart
___________________________________________________
Stuart J. McKelvie, Ph.D., Phone: (819)822-9600
Department of Psychology, Extension 2402
Bishop's University, Fax: (819)822-9661
3 Route 108 East,
Lennoxville, e-mail: [EMAIL PROTECTED]
Quebec J1M 1Z7,
Canada.
Bishop's University Psychology Department Web Page:
http://www.ubishops.ca/ccc/div/soc/psy
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