CHAPTER V.
MANIFOLD CLASSIFICATION.
1. The general principle of a manifold classification—2-4. The table of
double-entry or contingency table and its treatment by fundamental
methods—5-8. The coefficient of contingency—9-10. Analysis of
a contingency table by tetrads—11-13. Isotropic and anisotropic
distributions—14-15. Homogeneity of the classifications dealt with
in this and the preceding chapters: heterogeneous classifications.
1. CrassiricaTiON by dichotomy is, as was briefly pointed out in
Chap. I § 5, a simpler form of classification than usually occurs
in the tabulation of practical statistics. It may be regarded as
a special case of a more general form in which the individuals or
objects observed are first divided under, say, s heads, 4; 4, . . ..
A, each of the classes so obtained then subdivided under ¢ heads,
B,, B,....B, each of these under heads, C,, Cy ..... . C,, and
so on, thus giving rise to s. ¢. . . . . . ultimate classes altogether.
2. The general theory of such a manifold as distinct from a
twofold or dichotomous classification, in the case of n attributes
or characters ABC .... XN, would be extremely complex: in the
present chapter the discussion will be confined to the case of two
characters, 4 and B, only. If the classification of the 4’s be s-
fold and of the B’s t-fold, the frequencies of the st classes of the
second order may be most simply given by forming a table with
s columns headed 4, to 4, and ¢ rows headed B; to B. The
number of the objects or individuals possessing any combination
of the two characters, say 4,, and B,, ¢.e. the frequency of the
class 4,,B,, is entered in the compartment common to the mth
column and the mth row, the st compartments thus giving all
the second-order frequencies. The totals at the ends of rows
and the feet of columns give the first-order frequencies, <.e. the
numbers of 4,’s and B,’s, and finally the grand total at the
right-hand bottom corner gives the whole number of observations.
Tables I. and II. below will serve as illustrations of such tables
of double-entry or contingency tables, as they have been termed
by Professor Pearson (ref. 1).
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