Probabilities in the Problem of Classification - Probabilistic Composition of Preferences, Theory and Applications - page 92

X X

m

WPseudoF ¼ w j ð B j =ð r 1 ÞÞ=ð Wj =ð n i r ÞÞ

j ¼ 1 i

for

w j denoting the weight assigned to the jth criterion,
B j denoting the variance of the conditional expectation for the jth criterion and
W j denoting the expected value of the conditional variance for the jth criterion.
Thus,

" ! ! # ! !

:

X

w j X

X n i

2

X

m r

2

r

WPseudoF ¼ n i c ij c j = c iaj c ij = ð r 1 Þ= n i r

j ¼ 1 i ¼ 1 i ¼ 1 a ¼ 1 i

cation in Table 8.3 , the means and sums of
squares for the four classes and the seven criteria

Table 8.7 presents, for the classi

employed in the computation ofW.
Presents also the general means and the sums of squares relatively to these global
means after replacing the original values by themeans of the classes

—

— employed in the

computation of B.
Table 8.8 presents the values of PseudoF and WPseudoF derived from the values
of Table 8.7 and for the case of Car11 and Car13 being moved from classes 2 and 4

Table 8.7 Means and sums of squares for cars classification
Beauty

Comfort Consumption Power Price Reliability Safety

Class 2
Means

1 0.75 0.25 0.5 0.5 0.5 0.5

Sums of
Squares

0 0.75 0.75 1 1 1 1

Class 3
Means 0.67 1.00 1.00 0.33 1.00 0.67 0.33

Sums of
Squares

0.67 0.00 0.00 0.67 0.00 0.67 0.67

Class 4
Means 0.70 0.40 0.20 0.70 0.40 1.00 1.00

Sums of
Squares

2.10 2.40 1.60 2.10 2.40 0.00 0.00

Class 5
Means 0.33 1 1 0.33 0.33 1 1

Sums of
Squares

0.67 0 0 0.67 0.67 0 0

Global
means

0.7 0.65 0.45 0.55 0.5 0.85 0.8

Interclasses
squares

0.77 1.40 2.60 0.52 0.93 0.88 1.53