V.—MANIFOLD CLASSIFICATION. 71 
the great majority of the tables, and accordingly its origin 
demands explanation. Were such a table treated by the method 
of the contingency coefficient, or a similar summary method, 
alone, the peculiarity might not be remarked. . 
13. It may be noted, in concluding this part of the subject, 
that in the case of complete independence the distribution of 
frequency in every row is similar to the distribution in the row 
of totals, and the distribution in every column similar to that in 
the column of totals ; for in, say, the column 4, the frequencies 
are given by the relations — 
4, 4, 4, 
(4,8) = 2B), (4,8) = C42) B,), (4.8) = By, 
and so on. This property is of special importance in the theory 
of variables. 
14. The classifications both of thissand of the preceding chapters 
have one important characteristic in common, viz. that they 
are, so to speak, “homogeneous”—the principle of division 
being the same for all the sub-classes of any one class. Thus 
A’s and o’s are both subdivided into B’s and f’s, 4,’s, 4s. . .. 
A/s into Bs, By’s . ... Bs, and so on. Clearly this is necessary 
in order to render possible those comparisons on which the 
discussions of associations and contingencies depend. If we 
only know that amongst the 4’s there is a certain percentage 
of B's, and amongst the a’s a certain percentage of (C’s, there 
are no data for any conclusion. 
Many classifications are, however, essentially of a heterogeneous 
character, e.g. biological classifications into orders, genera, and 
species; the classifications of the causes of death in vital 
statistics, and of occupations in the census. To take the last 
case as an illustration, the first “order” in the list of occupations 
is “General or Local Government of the Country,” subdivided 
under the headings (1) National Government, (2) Local Govern- 
ment. The next order is “Defence of the Country,” with the sub- 
headings (1) Army, (2) Navy and Marines—not (1) National 
and (2) Local Government again—the sub-heads are necessarily 
distinct. Similarly, the third order is “Professional Occupations 
and their Subordinate Services,” with the fresh sub-heads (1) 
Clerical, (2) Legal, (3) Medical, (4) Teaching, (5) Literary and 
Scientific, (6) Engineers and Surveyors, (7) Art, Music, Drama, 
(8) Exhibitions, Games, etc. The number of sub-heads under 
each main heading is, in such a case, arbitrary and variable, 
and different for each main heading; but so long as the 
classification remains purely heterogeneous, however complex