CHAPTER IX.
CORRELATION.
1-3. The correlation table and its formation—4-5. The correlation surface—
A-7. The general problem—8-9. The line of means of rows and the
line of means of columns: their relative positions in the case of
independence and of varying degrees of correlation—10-14. The
Hi SE coefficient, the regressions, and the standard-deviations of
arrays—15-16. Numerical calculations—17. Certain points to be
remembered in calculating and using the coefficient.
1. IN chapters VL.-VIII. we considered the frequency-distribu-
tion of a single variable, and the more important constants
that may be calculated to describe certain characters of such
distributions. We have now to proceed to the case of two
variables, and the consideration of the relations between them.
2. If the corresponding values of two variables be noted
together, the methods of classification employed in the preceding
chapters may be applied to both, and a table of double entry or
contingency-table (Chap. V.) be formed, exhibiting the frequencies
of pairs of values lying within given class-intervals. Six such
tables are given below as illustrations for the following
variables : —Table I., two measurements on a shell (Pecten).
Table IL, ages of husbands and wives in England and Wales in
1901. Table IIL, statures of fathers and their sons (British).
Table IV., fertility of mothers and their daughters (British
peerage). Table V., the rate of discount and the ratio of reserves
to deposits in American banks. Table VIL, the proportion of
male to total births, and the total numbers of births, in the
registration districts of England and Wales.
Each row in such a table gives the frequency-distribution of
the first variable for cases in which the second variable lies
within the limits stated on the left of the row. Similarly, every
column gives the frequency-distribution of the second variable
for cases in which the value of the first variable lies within the
limits stated at the head of the column. As “columns” and
“rows” are distinguished only by the accidental circumstance
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