APPENDIX II. 
THE MEANING OF CORRELATION. 
In Chapters III. and IV.* an attempt has been made to 
ascertain the relationship between (1) yield of wheat per acre 
and rainfall in certain months of the year, and (2) the price 
of wheat in New Zealand and the total supply for New 
Zealand respectively. 
The methods of ascertaining this relationship are many 
and varied, but in the text they have been restricted to three, 
two of which are of common usage, viz., the comparison of 
two series of figures or the representation of these by graphs. 
But it is always difficult to establish a causal connection 
between two groups of phenomena by these means only. 
Consequently it has been found necessary to make use of a 
statistical device which may present difficulties to those who 
are not familiar with statistical method. If it can be proved 
that some causal connection exists between two groups or 
series of data, then the series are said to be correlated. The 
degree of correlation cannot be ascertained with exactitude 
by the mere visualizing of series of figures or their graphic 
representation. A more accurate measurement is required, 
and this is best found in the application of the theory of 
mathematical probability to the problem. This can be done 
best by calculating the co-efficient of correlation, from which 
it can be ascertained accurately the degree to which the 
series are related. No attempt will be made here to state 
the whole theory of correlation, or to explain fully the method 
of calculating the coefficient of correlation. This brief state- 
ment is intended to serve as a guide to those who are un- 
familiar with the use of statistics, and, in particular, with 
the methods of correlating two groups of phenomena. 
It is obvious that it would avail little to attempt to 
correlate two groups of data between which there was no 
evident causal connection. In the cases to which the theory 
has been applied in the text, the data are suggestive of causal 
correlation, and if the coefficient of correlation conforms to 
the tests which are set out below, then it may be concluded 
that such causal connection does exist. Obviously, we may 
suppose that there is some organic relationship between the 
price of wheat and the supply. To prove this we proceed as 
follows. 
The two series of data are tabulated in parallel columns.t 
Then for each series the standard deviation is calculated. This 
is found by, (1) finding the average of the whole series; 
(2) ealeulating the deviations from this average with the 
correct sign prefixed for each item in the series; (3) squaring 
*See page 67. tSee page 299, 
