Judith--
Here 'tis.
sum (x-xbar)^2
= sum (x^2 - 2 x xbar + xbar^2)
= sum x^2 - sum 2 x xbar + sum xbar^2
now because 2 and xbar are constants
=sum x^2 - 2 xbar sum x+ sum xbar^2
now because sum x = n xbar
=sum x^2 - 2 xbar n xbar + sum xbar^2
=sum x^2 - 2 n xbar ^2+ sum xbar^2
now because sum of a constant = n times that constant
=sum x^2 - 2 n xbar^2 + n xbar^2
=sum x^2 -n xbar^2
now because xbar = sum x / n
=sum x^2 - n( sum x)^2 / n^2
=sum x^2 - ( sum x)^2 / n
--Russ
_________________________________________________________________
Russell T. Hurlburt, Ph.D. Email: [EMAIL PROTECTED]
Professor of Psychology Telephone: (702) 895-0194
University of Nevada, Las Vegas Fax: (702) 895-0195
4505 S. Maryland Parkway
Las Vegas, NV 89154-5030 USA
http://www.nevada.edu/~russ
Info about Comprehending Behavioral Statistics (2nd ed.)
is at http://psychology.wadsworth.com/authors/hurlburtr/cbs.html
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Judith wrote:
SS = the sum of the squared scores minus the sum of the scores squared,
divided by the number of scores.
Does anyone know the mathematical proof for this formula's equivalence to
the definitional formula?
The definitional formula being:
SS = The sum of the squared deviations from the mean
