July 1, 1920 Universality of Field Heterogeneity 311 



The coefficients show that for both the upper and lower soil layers 

 there is a correlation of about medium value between adjacent samples 

 for the residual nitrate in the soil. These coefficients are unquestion- 

 ably significant in comparison with their probable errors. 



While the coefficients for nitrogen produced from soil nitrogen after 

 incubation are both positive in sign, neither can be considered statis- 

 tically trustworthy in comparison with its probable error. When 

 nitrogen is added to the soil, in the form of either ammonium sulphate 

 or of blood, the correlations between the nitrogen produced on incubation 

 are larger. All are positive in sign, and three of the four may be reason- 

 ably considered statistically significant. 



Thus it is clear that this plot, only 100 feet in diameter, shows distinct 

 heterogeneity in residual nitrate and in the amount of nitrification 

 occurring on incubation after the addition of nitrogen. 



SUMMARY AND CONCLUSIONS 



The purpose of this paper, which is one of a series on the statistical 

 phases of the problem of plot tests, is to show the extent to which the 

 heterogeneity of experimental fields may influence plot yields. 



By heterogeneity we understand differences in capacity for crop 

 production throughout the field of such a magnitude as to influence in 

 like maimer, but not necessarily to like degree, the yield of adjacent 

 small plots. Thus, variability of plot yields does not necessarily indicate 

 the heterogeneity of the fields upon which tests are made but may be 

 due to other factors. 



Heterogeneity is measured by a coefficient which shows the degree of 

 correlations between the yields of associated ultimate plots, grouped in 

 combination plots. 



This coefficient has been determined for a relatively large series of 

 experimental fields widely distributed throughout the world and planted 

 to a considerable variety of crops, for which a number of diff"erent kinds 

 of yields have been measured. The results show that in every field the 

 irregularities of the substratum have been sufficient to influence, and 

 often profoundly, the experimental results. 



It might be objected that by chance, or otherwise, the illustrations 

 are not typical of what ordinarily occurs in plot cultures. But the 

 series considered practically exhaust the available data for such pur- 

 poses. Furthermore the records are in large part drawn from the 

 writings of those who are recognized authorities in agricultural experi- 

 mentation and who have given their assurance of the suitability of the 

 fields upon which the tests were made. 



For example, Mercer and Hall (75) state the purpose of their research 

 to be — 



to estimate the variations in the yield of various sized plots of ordinary' field crops 

 which had been subjected to no special treatment and appealed to the eye sensibly 

 uniform. 



177285°— 20 3 



