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



negligible, for all practical purposes, when the probable error of the 

 sampling is of as great a magnitude as 0.1 milligram. It must be 

 recognized that the mean of the number of samples so calculated may 

 be found to have a greater or less probable error in practice so that 

 a greater number of samples than calculated should be taken. This 

 relation has already been brought out in the previous section, where 

 it was shown that the fewer the samples, the less representative 

 of the total area they became. By an inspection of table 12, it 

 is evident that the number of samples necessary to secure the degree 

 of accuracy which we established for the residual nitrate samples must 

 be very greatly increased, when we are dealing with ammonium sulfate 

 or blood treated samples. 



It will be remembered that throughout the discussion, we have con- 

 sidered the probable error of the mean of any given series of samples 

 directly, so that we have but an even chance that the mean for any 

 given number of determinations made will be of significance. It is 

 usual to consider about three times the probable error as a significant 

 difference between two given means, hence if we are to establish this 

 standard as regards the number of samples taken, we must increase 

 all the figures given by three times.* It is obvious that such a number 

 of samples in the case of dried blood, for instance, would be far beyond 

 practical limits as regards the making of the determinations. The 

 chances are that the use of a fewer number of samples means a low 

 degree of reliability for any determinations made. If soil biologists 

 are to continue to make beaker tests with fertilizers, the results must 

 be interpreted from this viewpoint. 



* By multiplying the probable error found by 3.17 the chances are thirty to 

 one that a difference greater than the figure so found is significant. 



