APPENDIX II. 



THE MEANING OF COEEELATION. 



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) calculating the deviation* from this average with the 

 correct sign prefixed for each item in the series; (3) squaring 



*See page 67. f See page 299. 



