1918] 



Waynick: A Statistical Study of Nitrification in Soil 



25 < 



qualitative relations hold as between the various treatments in every 

 ease except the incubated subsoil samples which are somewhat less 

 variable than tbe surface samples. AVilh the other three series, the 

 subsoil samples still show a much higher coefficient of variability than 

 the surface samples, as do the samples treated with fertilizers in the 

 laboratory in contrast with the untreated field samples. The per- 

 centage probable errors or laboratory errors are shown in column 

 three, while the corrected figures for the field samples are given in 

 column four. 



Referring again for a moment to table 6, it is evident that the 

 laboratory error increases as the square root of the number of deter- 

 minations made, so that the mean of any number of readings on the 

 colorimeter becomes less reliable, the fewer the number, exactly as the 

 mean of a fewer number of samples is less accurate than the mean 

 of a larger number. In other words, the curves of the errors of the 

 various determinations are parallel, as will be seen by reference to 

 figure 2. This fact must be kept in mind in considering the results 

 given in the following section. 



Results of Random Samplings 



It is of very direct interest to consider for a moment the accuracy 

 of the mean of a limited number of samples taken at random. Ten 

 surface samples are included in the first group (table 9) and sixteen 

 in the second (table 10). since about these numbers of samples have 



TABLE 8 



Summary of Statistical Data after Making Allowance for 



Laboratory Error 



Coefficient Corrected 



of variability coefficieTit 



(laboratory of Laboratory 



error) variability error 



Per cent Per cent Per cent 

 Residual nitrate. 



Surface 4.8 ± 0.2 21.1± 2.1 0.3 



Subsoil 18.5± 1.0 32.9± 3.4 1.2 



Tncubated blanks. 



Surface 3.8± 0.2 27.4±1.7 0.3 



Subsoil 9.2± 0.5 25.5± 2.1 0.7 



Ammonium sulfate. 



Surface 2.6± 0.1 26.8± 1.6 0.2 



Subsoil 4.6± 0.2 36.1 ±2.4 0.4 



Blood. 



Surface 0.6± 0.03 26.5± 1.5 0.05 



Subsoil 1.2±0.10 48.2±3.1 0.09 



THE 



Corrected 

 probable 

 erro c of 



mean 

 Per cent 



1.5 



3.1 



2.0 

 1.4 



1.8 



3.0 



1.9 

 3.9 



