RURAL ECONOMICS 1 833 



rainfall. Agaia Lenoir (i) has worked out the coefficient of correlation 

 between the production and the price of wheat in France with the follow- 

 ing results : 



From 1847 to 1870 the coefficient of correlation was . . . 0.75 



" 1871 " 1885 " " "... 0.56 



" 1885 " 1905 " " "... 0.34 



showing that as the cereal market tends to become world wide, so the in- 

 fluence of the home production on prices tends to diminish. 



With regard to the interpretation of agricultural experiments, it should 

 be borne in mind that they hardly ever manage to isolate the action of the 

 factors under investigation, for the experiments usually deal with plants 

 and animals whose functions do not lend themselves to study under rigidly 

 homogeneous conditions. As a case in point the probable error (2) was 

 worked out for two of Wagner's series of results dealing with manurial expe- 

 riments. (Table VIII). The mean increase in yield with nitrate of soda 

 is 6.4 kg., while the probable error is 0.66 .showing that the increase is dtie 

 to the manitring and not to incidental causes. 



From another set of results Wagner estimates the mean relative effi- 

 cienc}^ of ammonia nitrogen (nitrate nitrogen being taken as 100), from 

 series showing considerable variation as follows : 



Relative efficien cy 

 Mean Highest and lowest 



— figures 



Wheat 87 13 to 107 



Rye 76 52 " 109 



Barley . 72 42 " 109 



Oats 90 61 " 12.1 



These figures were worked otit by Gregoire (3), taking into accotmt 

 the unit price of the two manures, and the results are given in Table VIII, 

 from which it is much easier to judge of relati\'e economic advantages of 

 the two forms of nitrogen. 



The probable error is also employed to determine : 



i) The minimum amount of data required for the statistical study 

 of a problem, using the foimtila n -- cp^/E'^ which is obtained from that of 

 the probable error [E] and from the mean of a series of terms E = (pn where 

 9 = probable error of each term and n — number of terms ; 



(1) M. l,ENOiR. Ivtude sur la tormation des pri.v. Paris, 1913. 



(2) Probable error, E^ = o,.i8l/-^^^^^ + ''^^'^^^' 







where S(^i^) !i"'l JLi^.J^) 'i^e the sum of the deviations squ^-ircd and n^, Hj are the number 

 of terms. 



(3) A. Gregoire, I,es recherches agronomic|ues et I'interprctation de leurs rcsultats. An- 

 nales de Gembloux 1912, pp. 52-58. 



