1918] WaynicJe: A Statistical Study of Nitrification in Soil -4. 



acid method is not of moment in this connection, because neither very 

 low nor very high amounts of nitrate were ever determined and all 

 of the determinations are directly comparable one with the other, since 

 exactly the same procedure was followed in every case. 



It must be emphasized that no attempt has been made to segregate 

 the causes of variation and the results as given are the summation of 

 all the factors which are of importance in causing differences between 

 samples. All the work was done in a careful manner with due atten- 

 tion to detail, no new or modified procedure being attempted. The 

 results of this study, therefore, are intended to serve as a basis for 

 interpreting the mass of data which has already been obtained by soil 

 biologists and to emphasize the extreme importance of applying statis- 

 tical methods to results secured in the future before their value as 

 contributions to science or practice can be recognized. 



Calculations 6 



The amounts of nitrate found are reported in tables 1 to 4. follow- 

 ing, the individual determinations always being given. The mathe- 

 matical treatment will be discussed briefly from the data given in 

 table 1, the discussion being applicable to all the tables as well. 



The mean as given is obtained by dividing the sum of all the 

 determinations by the number of determinations. This figure repre- 

 sents, therefore, a hypothetical composite sample of all the samples 

 taken. The deviation from the mean of any determination is found 

 by taking the difference between the mean and the individual result. 

 The mean deviation of a series of determinations is an expression of 

 the average amount any single observation taken at random is likely 

 to differ from the mean of the series. This figure may be either plus 

 or minus, but as the sign is of no importance as regards subsequent 

 calculations, it is not recorded but may easily be found by inspection. 

 The standard deviation (a) is found, after the manner usual in statis- 

 tical investigations, by squaring the deviation of each determination 

 from the mean, taking the sum of the squares thus found, dividing this 

 figure by the total number of determinations made and taking the 

 square root of the quotient. The percentage ratio of the standard 

 deviation to the mean expresses the coefficient of variability {C.V.) 

 for a given series of determinations. It is an expression of the per- 

 centage deviation on either side of the mean, within which approxi- 

 mately two-thirds of the determinations may be expected to lie. The 



