260 University of California Publications in Agricultural Sciences [Vol.3 



the probable error of the difference between the mean of the sixteen 

 samples taken purely at random, and the entire number of determina- 

 tions made, to be .20 ± .15 milligrams, with a coefficient variability of 

 34.4 ± 4.5 per cent as contrasted with 25.9 ± 2.1 per cent for the total 

 number. The difference between the number of samples considered 

 here and the total number is not significant with the incubated blanks, 

 but with the ammonium sulfate samples the probable error of the 

 difference between the means is 0.66 ± .33, and with dried blood 

 2.0 ± 1.1. The chances are somewhat less than 2 to 1 that the differ- 

 ences between the sixteen samples here considered and the total eighty- 



one samples are significant. It is evident that calculations made from 

 the mean of sixteen samples are of a higher degree of accuracy than 

 when only ten samples are used, but the number is still too few to give 

 results of a high order of reliability, and could by no means be taken 

 as truly representative of the entire area under consideration. 



Other numbers and other groupings may be selected and the mag- 

 nitude of their means and their accompanying probable errors and 

 coefficients of variability computed from the data reported in tables 

 1 to 4. 



Effect of Distance upon Variability 



To determine whether or not the distance apart the samples were 

 taken is a factor of importance in sampling, the arrangement given in 

 table 11 has been made. The results shown in the table are for residual 



