HISTORY OF WHEAT PRODUCTION IN NEW ZEALAND 121 



Following out this suggestion the co-efficient of corre- 

 lation* of the two series was calculated. Index numbers 

 of supply and price were taken for the years 1869-1914, 

 the base period being 1890-99. The annual average in 

 each case during this period was equated to 100 and then 

 corresponding numbers were taken out for each year. 

 The next step was to find the mean for each series, and 

 then the deviations from the mean in each case. By 

 squaring these deviations and taking the square root of 

 the mean of the squares in each case the standard 

 deviation was found. The co-efficient of correlation was 



then taken from the following formula : - , where 



n Zi ZQ 



x and y are the deviations of the two series from the 

 mean with due regard to sign, n is the number of terms 

 and zi and z* the standard deviations. This gave a 

 co-efficient of correlation of 440. The probable error 



l-r a 



was then found by using the formula - where r is 



the co-efficient of correlation and n is the number of 

 terms. The probable error was -079. 



Despite the fact that the co-efficient of correlation is 

 not high, correlation may be regarded as a practical 

 certainty, for the co-efficient is almost six times as 

 great as the probable error, Dr. Bowley's criterion of 

 correlation. 



The correlation co-efficient is relatively high when all 

 circumstances are considered. Many outside influences 

 operate to interfere with the natural tendency of supply 

 to act on price and vice versa. Thus our price is 

 determined not so much by the local supply but largely 

 by the English price. f In the earlier years of the period 

 the gold supplies played a large part in determination of 



*The subject of correlation is explained briefly in Appendix 

 II. 



tFor a complete treatment of price determination see Chapter 

 VII. 



