282 Journal of Agricultural Research vo1.xix,no. ? 



Ample illustration of the arithmetical routine has been given in the 

 original paper. 



The formulae employed assume the symmetry of the correlation sur- 

 face. It has been shown elsewhere (4) that spurious values of the cor- 

 relation coefficient may arise in such cases. Since both p^p^ and <rp a^ 



take the maximum values when, because of the symmetry of the correla- 

 tion surfaces, pi = p2, o'i = o'2> i^ is clear that the limiting value of the 

 spurious correlation will be o. 



Thus it is possible that heterogeneity exists even when rp p =0, but a 



field can not be considered homogeneous if rp p has a value which is 



statistically significant in comparison with its probable error. 



Practically, little difficulty will arise from this source, and it can 

 usually be easily avoided by the exercise of a little care in the selection 

 of the proper grouping in doubtful cases. 



According to the foregoing conception the relationship between the 

 yield of associated plots is expressed on the universally comparable 

 scale of r, ranging from o to ±1. 



When symmetrical tables are used — that is, when each plot is used 

 once as a first and once as a second member of the associated pair — 

 Pi = p2, <Tp =o-p , and the regression slope is identical with the correlation 



coefficient. 



Thus, if one ultimate plot, p^, of a combination plot be known, the 

 most probable deviation of another plot will be p2 — p= (Pi-py- 



Concretely, if the yield of a first plot of a combination plot be 10 

 pounds above the average of the field as a whole and if the interplot 

 correlation be r^ p = 0.60, the most probable yield of a second plot will 



be 6 pounds above the average. 



Similar reasoning applies throughout. Those who have difficulty in 

 thinking in terms of correlation coefficients can most easily grasp the 

 significance of the results by remembering that in this case the correla- 

 tion coefficients multiplied by 100 gives the most probable percentage of 

 deviation of the yield of an associated plot when the deviation of one 

 plot of the group from the general average is known. 



INFLUENCE OF SOIL HETEROGENEITY ON YIELD OF FIELD CROPS 



In the paper in which these formulae were suggested it was shown that 

 yield of straw and grain and the nitrogen content of wheat, yield of 

 roots and tops of mangolds, and yield of timothy hay are markedly 

 influenced by irregularities in the carefully selected fields upon which 

 plot cultures have been carried out by agriculturalists. 



We have now to ascertain whether this is a general phenomenon or 

 whether it is merely a chance result of these particular cultures. The 

 suggestion has been made that the latter is the case, that with the exer- 

 cise of a little care uniform fields may be secured, and that substratum 



