28o Journal of Agricultural Research voi. xix, No. ? 



with reasonable precautions reliable results will be obtained. If, on the 

 other hand, the application of such a criterion shows a high degree of 

 irregularity in fields selected for their uniformity by experienced agri- 

 culturalists, it is evident that very special precautions must be taken 

 to obtain trustworthy results. Some quantitative measure, and some 

 probable error of this measure, of the amount of irregularity of the soil 

 of a field, as shown by actual capacity for crop production, and not 

 merely a demonstration of its existence is, therefore, required. 



The purpose of this paper is to show by the analysis of the actual 

 yields of test plots reported by agricultural experts that the securing of 

 fields suitable for a direct comparison of yields is, practically speaking, 

 an impossibility. The results show that unless special precautions are 

 taken irregularities in the field may have greater influence upon the 

 numerical results of an experiment than the factors in crop production 

 which the investigator is seeking to compare. 



The results of this study may seem to be altogether negative — destruc- 

 tive rather than constructive. The unbiased student must, however, 

 admit that a full evaluation of all the sources of error is an essential 

 prerequisite to constructive work. Furthermore, large expenditures of 

 public funds are being devoted to fertilizer tests, variety tests, and rota- 

 tion experiments. It is preeminently worth while to ascertain to what 

 extent results derived from methods now in use may be considered 

 reliable. 



Subsequent papers will treat other phases of the problem. 



FORMULAE 



A criterion of field homogeneity (or heterogeneity) to be of the greatest 

 value should be universally applicable, be comparable from species to 

 species, character to character, or experiment to experiment, and be 

 easy to calculate. 



In 1 91 5 the suggestion was made (5)^ that we may proceed as follows: 

 Suppose a field divided into N small plots, all sown to the same variety of 

 plants. lyCt p be the yield of an individual plot. The variability of p 

 may be due purely and simply to chance, since the individuals of any 

 variety are variable and the size of the plots is small, or it may be due in 

 part to the diversity of conditions of the soil. If irregularities in the 

 experimental field are so large as to influence the yield of areas larger 

 than single plots,^ they will tend to bring about a similarity of adJQining 

 plots, some groups tending to yield higher than the average, others lower. 



Now let the yields of these units be grouped into m larger plots, C„, 

 each of n continguous ultimate units, p. The correlation between the 



1 Reference is made by number (italic) to " Literature cited, " p. 313-314. 



2 Irregularities of soil influencing the plants of only a single small plot may in most work be left out of 

 account, since they are of the kind to which differences between individuals are to a considerable extent 

 due and are common to all the plots of a field. 



