per load becomes the sampling unit rather than the total load volume. The 

 same principles of determining sample size apply regardless of the unit 

 used.i/ 



REQUIRED SAMPLE SIZE 



In any sampling process, three factors determine sample size: (1) the 

 desired accuracy at a prescribed level of probability, (2) the total number of 

 sampling units in the population, and (3) the variation among sampling units. 

 The first of these is established by policy, and the second is estimated from 

 the cruise. The variation must be determined from a representative sample of 

 20 to 30 units, from which an adjustment factor and its standard error are 

 computed. 



The adjustment factor, in this case, can be considered a regression 

 coefficient, "b," which is the ratio of I(y), the sum of the Forest Service 

 scaled volumes, to £(x), the sum of the company scaled volumes of the same 

 loads, or 



b = l&i 



n 



2( X ) 



The accuracy of "b M is pertinent to the problem, and this is determined, 

 of course, by the standard error of "b" for a particular situation. The 

 method of calculating the standard error of "b" is expanded in the appendix 

 to this report where the factor "C" is used as a measure analagous to the com' 

 mon coefficient of variation. The required sample size, "n," for different 

 accuracies, sale sizes, and variations can be computed in the conventional 

 manner. (See appendix for equations and numerical example.) 



After computing the required sample size, "n," a sampling scheme can be 

 worked out to collect this sample in an unbiased, random fashion during the 

 course of the sale. The final adjustment factor is then based on all the 

 sample loads. 



Table 1 shows the required sample size for various values of "C," for 

 accuracies, M E," of 0.01 to 0.04, and for total number of units of 200 to 

 2,000, computed at approximately the 95-percent probability level. Interme- 

 diate values not shown in the table can be determined by plotting sample size 

 over the variable in question (using values from the table) while holding the 

 other two variables constant. After fitting a free-hand curve through the 

 plotted points, interpolated values can be read from the curve. Other values 

 can be computed, of course, by means of the equations shown in the appendix. 



1/ This assumes that the same accuracy standard by volume applies to all 

 species. A more refined method of sampling where limits of accuracy are set 

 on value rather than volume is beyond the scope of this paper. 



-2- 



