The most obvious factor which influences allowable error is the total 

 value of the sale. It is reasonable that a lower percentage error should 

 be the goal on a high-priced sale than would be allowed on a low-priced 

 sale. This fact is true whether the sale is high-priced because of its 

 size or its quality. 



Natural variation among the sampling units (logSj, trees, or truck- 

 loads),, commonly expressed as the coefficient of variation, is a second 

 factor which influences the acceptable sampling error. Uniform material, 

 that is material whose volumes have a low coefficient of variation, re- 

 quires less intensive sampling to achieve a given accuracy than highly 

 variable material. For this reason, greater sampling accuracy can be 

 justified for uniform material before reaching the point of diminishing 

 returns . 



The cost of measuring a sampling unit (log, tree 5 or truckload) is 

 a third factor which has an important influence on the magnitude of the 

 acceptable sampling error , If scaling is costly, the point of diminish- 

 ing returns will be reached sooner (resulting in a larger allowable error) 

 than if scaling is cheap „ It is assumed, of course, that the oost per 

 unit does not change with different sampling rates = 



Finally, the number of sampling units in the sale influexices the 

 size of sample required to meet a given accuracy o Sample size must be 

 increased (although not directly) as the total n'jmber of units increases o 

 Usually, however, for a given total sale value j the sale with the larger 

 number of units will have the lower coefficient of variation. Further- 

 more, the larger number of units for a given total value will usually 

 indicate smaller units with correspondingly lower scaling costs per unit. 

 Because of these two compensating factors, number of units can be omitted 

 in the calculation of allowable error. Having decided on an acceptab!ie 

 error, however, the total number of sampling units in a sale must be used 

 as one of the variables in deciding actual sample size and sampling rate, 



2/ 



Blythe— first calculated the point of diminishing returns In comput- 

 ing sample size in log scaling. Figure 1 employs Blythe "s formula in an 

 alinement chart and is extended to include the calculation of allowable 

 error. Three variables, (a) measuring cost per unit (in dollars), (b) 

 the coefficient of variation of volumes among the" sampling units, and 

 (c) total sale value are included in the alinement chart. Instructions 

 for using the chart are printed with the figure. 



Having decided upon a suitable allowable sampling error and knowing 

 the coefficient of variation cf the material and the total number of units 

 in the sale, the required sample size can be found from the appropriate 

 graph in figure 2, 



2/ Blythe, R, H, Jr, The economics of sample size applied to the scaling 

 of sawlogs , Biometrics Bull,, 1; 67-70, 1945, 



-2- 



