26 PRINCIPLES OF SOIL MICROBIOLOGY 



The probable error of the standard deviation is obtained from the 



O" 



formula ± 0.6745 /— • The coefficient of variability (C.V.) is the 

 V2n 



percentage ratio of the standard deviation (<r) from the mean. The 



C.V. 

 probable error of the coefficient of variability = ±0.6745 ,-■-• By the 



use of formulae for the calculations of the errors of observation, the 

 error of the mean arithmetical value of the plate counts can be deter- 

 mined. 44 



By taking several representative soil samples and by using several 

 plates, the error can be reduced to a minimum. A combination of five 

 soil samples and ten plates, for each soil to be tested, will reduce the 

 error for bacterial numbers to 1.8 per cent and for actinomyces to 2.7 

 per cent. 45 The same is true of fungi; when a low dilution (1000) is 

 combined with an acid medium, and 5 to 10 plates are used for each 

 sample, the error may be reduced to 2 per cent. 



It is of interest to note here that in order to determine accurately the 

 average value of hygroscopic moisture in the soil, Floess 46 found that 

 fifty soil samples, taken at definite distances in the field, are required. 

 The probable error was calculated from the formula : 



[v] • 0.845 

 r = 



■\/n (n - 1) 



Where [v] is the sum of all individual variations from the mean and n 

 the number of observations. 



Under ideal conditions, the bacterial counts on parallel plates will 

 vary in a manner similar to samples from a Poisson series. 47 The 

 accuracy can thus be determined with precision and the mean count of a 

 number of plates is a direct measure of the bacterial population capable 

 of developing on the plate. Agreement with the theoretical distribu- 

 tion may be tested by means of the index of dispersion. 



44 Davenport, C. B. Statistical methods. Wiley, New York. 1914. Barlow, 

 P. Tables of squares, cubes, square roots, cube roots, reciprocals. Spon. 

 London. 1914. 



45 Waksman, 1922 (p. 20). 



46 Floess, R. Die Hygroskopizitatsbestimmung, ein Masstab zur Bonitierung 

 des Ackerbodens. Landw. Jahrb. 42: 255-289. 1912. 



47 Fischer, R. A., Thornton, H. G., and Mackenzie, W. A. The accuracy of the 

 plating method of estimating the density of bacterial populations. Ann. Appl. 

 Biol. 9: 325-359. 1922. 



