THEORY OF STATISTICS.
investigation of the motion of molecules”! have become part of
the ordinary language of physicists. We find a work entitled
“the principles of statistical mechanics”? and the Bakerian
lecture for 1909, by Sir J. Larmor, was on “the statistical and
thermodynamical relations of radiant energy.”
7. It is unnecessary to multiply such instances to show that the
words statistics,” “statistical,” no longer bear any necessary
reference to “ matters of state.” They are applied indifferently in
physics, biology, anthropology, and meteorology, as well as in the
social sciences. Diverse though these cases are, there must be
some community of character between them, or the same terms
and the same methods would not be applied. What, then, is this
common character ?
8. Let us turn to social science, as the parent of the methods
termed statistical,” for a moment, and consider its characteristics
as compared, say, with physics or chemistry. One characteristic
stands out so markedly that attention has been repeatedly
directed to it by “statistical” writers as the source of the peculiar
difficulties of their science—the observer of social Jacts cannot ex-
pervment, but must deal with circumstances as they occur, apart
Jrom his control. Now the object of experiment is to replace the
complex systems of causation usually occurring in nature by
simple systems in which only one causal circumstance is permitted
to vary at a time. This simplification being impossible, the
observer has, in general, to deal with highly complicated cases of
multiple causation—cases in which a given result may be due to
any one of a number of alternative causes or to a number of
different causes acting conjointly.
9. A little consideration will show, however, that this is also
precisely the characteristic of the observations in other fields to
which statistical methods are applied. The meteorologist, for
example, is in almost precisely the same position as the student
of social science. He can experiment on minor points, but the
records of the barometer, thermometer, and rain gauge have to be
treated as they stand. With the biologist, matters are in some-
what better case. He can and does apply experimental methods
to a very large extent, but frequently cannot approximate
closely to the experimental ideal ; the internal circumstances of
animals and plants too easily evade complete control. Hence a
large field (notably the study of variation and heredity) is left,
in which statistical methods have either to aid or to replace the
methods of experiment. The physicist and chemist, finally,
1 Clerk Maxwell, “Theory of Heat” (1871), and ‘‘On Boltzmann’s
Theorem ” (1878), Camb. Phil. Trans., vol. xii.
2 By J. Willard Gibbs (Macmillan, 1902),
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