1918] Waynick: A Statistical Study of Nitrification in Soil 261 



nitrate in the surface samples only. The first group of determinations, 

 from numbers two to seventy-two, inclusive, by intervals of ten, were 

 recorded from samples lying within a radius of five feet of number 

 one. The mean of the eight readings is 3.20 ± .14 milligrams or 0.5 ± 

 .15 milligrams above the mean for the whole number of samples. The 

 coefficient of variability is. however, relatively low. 



The second group of determinations from numbers six to seventy- 

 six, varying as those of the group above, are of the samples on the 

 circle with a radius of twenty-five feet from the center. The mean of 

 this group of eight determinations is 2.40 ± .14 milligrams or 0.3 ± .15 

 below that of the established mean as already given. The coefficient 

 of variability in this case is nearly the same as for the total of eight y- 

 one samples, however. 



The last group of determinations represents the nitrate found in 

 the samples taken as the fifty-foot radius. The mean of the eight 

 determinations is 2.50 ± .20 milligrams ; 0.70 ± .24 milligrams and 

 .10 ± .24 milligrams. In two cases, the differences are significant; in 

 the third, the probable error is greater than the difference and holds 

 between the most widely separated samples taken on the twenty-five 

 and fifty-foot radii. Even though only eight samples are considered 

 in any one group, the conclusion seems justified that the distances 

 apart samples are taken is of little importance, except in so far as their 

 distribution be uniform over the area to be sampled. A small area of 

 an apparently uniform field may lead to very erroneous results, as 

 evidenced by the high figures obtained for the mean of the determina- 

 tions made upon the samples on the five-foot radius. It is, of course, 

 taken for granted that we are dealing in every instance with a field 

 suitable for experimental work and hence not marked by changes in 

 the soil apparent to the eye. 



Estimate of the Number of Samples Required for any 

 Given Degree of Accuracy 7 



It is very desirable to know just how many samples it is necessary 

 to use to secure the degree of accuracy deemed desirable for the work 

 in hand. By the use of the probable error and the standard deviation 

 found from any representative number of samples, an estimate of the 

 number of samples which will give a lower or higher degree of accuracy 

 than the number used may be computed. For example, in the ease of 



