mathematically; it is possible to express in figures the exact
relations between the occurrence of one phenomenon and
the occurrence of another. The number which expresses this
relation is called the coefficient of correlation. This
coefficient expresses relationship in terms of the mean values of the
two series of phenomena by measuring the amount each individual
phenomenon varies from its respective mean. Suppose,
for example, that in correlating crime and unemployment,
the coefficient of correlation were found to be .47. If in
every case of unemployment crime were found and in every
case of crime, unemployment, the coefficient of correlation
would be +1. If crime were never found in unemployment,
and unemployment never in crime, the coefficient of correlation
would be -1, indicating a perfect inverse relationship.
A coefficient of 0 would indicate that there is no relationship.
The coefficient of .47 would accordingly indicate a significant
but not a "high" correlation between crime and unemployment.

We cannot consider here all the details of statistical methods,
but attention may be called to a few of the more significant
features of the process. Statistics is a science, and consists
in much more than the mere counting of cases.

With the collection of statistical data, only the first step has been
taken. The statistics in that condition are only raw material showing
nothing. They are not an instrument of investigation any more
than a kiln of bricks is a monument of architecture. They need to
be arranged, classified, tabulated, and brought into connection with
other statistics by the statistician. Then only do they become an
instrument of investigation, just as a tool is nothing more than a
mass of wood or metal, except in the hands of a skilled workman.[1]

[Footnote 1: Mayo-Smith: _Statistics and Sociology_, p. 18.]

The essential steps in a statistical investigation are: (1) the
collection of material, (2) its tabulation, (3) the summary,
and (4) a critical examination of the results. The terms are
almost self-explanatory. There are, however, several general
points of method to be noted.

In the collection of data a wide field must be covered, to be
sure that we are dealing with invariable relations instead of
with mere coincidences, "or overemphasizing the importance
of one out of a number of cooeperating causes." Tabulation
of the data collected is very important, since classification of
the data doe