July i, 1920 



Universality of Field Heterogeneity 



307 



the field we have merely to determine the correlations between the 

 percentages of water content of associated plots. These are 



The correlations are of a very substantial order, ranging from 0.317 

 to 0.704. Notwithstanding the fact that there are only 88 stations 

 upon which the probable errors are based, the constants may in every 

 case be considered significant in comparison with their probable errors. 



Thus, notwithstanding the fact that we are dealing with a field only 

 150 by less than 264 feet, 1 there is a marked and statistically significant 

 heterogeneity in respect to so important a factor in plant growth as 

 soil moisture at each level in the upper 6 feet of soil. 



This result seems of very real importance in its relation to the practical 

 phases of plot-test work. It shows beyond all dispute that at least 

 under soil conditions such as are found at the San Antonio Experi 

 mental Farm, substratum heterogeneity may be very great at levels 

 of the soil which are ordinarily left entirely out of account in the selec 

 tion of fields which are to be used for plot tests but which are not below 

 the extensions of the roots of the deeper-penetrating crops and not too 

 deep to serve as reserves of soil moisture for the higher layers of the soil 

 in the case of crops which draw their water from more superficial levels. 



It is of some interest to determine whether the correlations at one 

 level in the field may be looked upon as sensibly higher than those at 

 other levels. We have, therefore, determined the differences between 

 the correlations at the different depths. These are given with their 

 probable errors, and in relation to their probable errors, in Table IV. 



In the table the positive signs indicate higher correlations at lower 

 levels. Of the 10 possible comparisons between the correlations of the 

 first 5 feet, all but one show greater heterogeneity at the lower levels. 

 The sixth foot seems to be somewhat more homogeneous than the second 

 to the fifth foot. A number of the differences are apparently significant 

 in comparison with their probable errors. Thus there is apparently a 

 real difference in the amount of heterogeneity of this field at different 

 levels. Heterogeneity is least at the surface and greatest at a depth of 

 4 feet. 



The significance of this result will perhaps be apparent at once. A 

 field might be reasonably uniform for the surface foot of soil and hence 



1 The total length is 264 feet, but this is reduced by discarding the right file. 



