I am looking for the formula to complete the Brown and Forsythe Test
for homogeneity of variance and an example of someone else completing
the test by hand.

Hi michellec513-ga 
This paper gives the formula and an example.
http://www.psych.nyu.edu/cohen/eps12dr1.pdf 
Let me know if you find it useful.
Regards
Sukhjeet

Thank you -- it seems to provide information for the ANOVA F test that
Brown and Forsythe proposed; however, this has been my own problem in
searching in that I keep finding this test, which statistically
packages actually do for you.  Unfortunately, the test I am looking
for by them tests for the homogeneity of variances.  From what I have
seemed to find out, this test compares variances by using medians;
however, I can't seem to find an example of the formula and how one
would use it.  A popular test for homogeneity of variance that is used
is the Levene's Test, however, my professor would like me to use the
Brown and Forsythe test instead.  I hope this helps.  Thank you again
for the link.