; THEORY OF STATISTICS. 
it may become, there is no opportunity for any discussion 
of causation within the limits of the matter so derived. It is 
only when a homogeneous division is in some way introduced 
that we can begin to speak of associations and contingencies. 
15. This may be done in various ways according to the 
nature of the case. Thus the relative frequencies of different 
botanical families, genera, or species may be discussed in 
connection with the topographical characters of their habitats— 
desert, marsh, or moor—and we may observe statistical associa- 
tions between given genera and situations of a given topographical 
type. The causes of death may be classified according to sex, 
or age, or occupation, and it then becomes possible to discuss 
the association of a given cause of death with one or other 
of the two sexes, with a given age-group, or with a given 
occupation. Again, the classifications of deaths and of occupations 
are repeated at successive intervals of time; and if they have 
remained strictly the same, it is also possible to discuss the 
association of a given occupation or a given cause of death with 
the earlier or later year of observation—i.c. to see whether the 
numbers of those engaged in the given occupation or succumbing 
to the given cause of death have increased or decreased. But 
in such circumstances the greatest care must be taken to see 
that the necessary condition as to the identity of the classifications 
at the two periods is fulfilled, and unfortunately it very 
seldom is fulfilled. All practical schemes of classification are 
subject to alteration and improvement from time to time, and 
these alterations, however desirable in themselves, render a 
certain number of comparisons impossible. Even where a 
classification has remained verbally the same, it is not necessarily 
really the same; thus, in the case of the causes of death, 
improved methods of diagnosis may transfer many deaths ‘from 
one heading to another without any change in the incidence 
of the disease, and so bring about a virtual change in the 
classification. In any case, heterogeneous classification should 
be regarded only as a partial process, incomplete until a 
homogeneous division is introduced either directly or indirectly, 
e.g. by repetition. 
REFERENCES. 
Contingency. 
(1) PEARSON, KARL, ‘On the Theory of Contingency and its Relation to 
Association and Normal Correlation,” Drapers’ Company Research 
Memoirs, Biometric Series i.; Dulau & Co, London, 1904. (The 
memoir in which the coefficient of contingency is proposed.) 
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