The Journal of Finance
between-groups to the within-groups sums-of-squares. When this ratio of the
form.
8=1 p=l
where
G =: Number of groups
g = Group g, g = 1 . . . G
Ng = Number of firms in group g
ypg = Firm p in group g, p = 1 . . . Ng
fg = Group mean (centroid)
y = Overall sample mean
is maximized, it has the effect of spreading the means (centroids) of the G
groups apart and, simultaneously, reducing dispersion of the individual points
(firm Z values, ypg) about their respective group means. Logically, this test
(commonly called the "F" test) is appropriate because one of the objectives of
the MDA is to identify and to utilize those variables which best discriminate
between groups and which are most similar within groups.
The group means, or centroids, of the original two-group sample of the form
1 V
are
Group 1 = —0.29 F = 20.7
Group 2 = +S.02 Fs.go (.01) = 3.34