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 
21 22 
a and y are the deviations of the two series from the 
mean with due regard to sign, ” is the number of terms 
and z and z the standard deviations. This gave a 
co-efficient of correlation of -440. The probable error 
2 
was then found by using the formula t 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.t 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 
{For a complete treatment of price determination see Chapter 
VII. 
