Whenever the use of sampling is considered, the all-important question 

 of accuracy standards must be defined. Sampling cannot yield completely 

 accurate results, but the results can be evaluated and are assured with 

 various probabilities to be within certain limits of accuracy. Further- 

 more, these limits can be narrowed to any desired amount by adjusting 

 the sample size for a given set of conditions. In sample tree measure- 

 ment on a given timber sale, some predetermined accuracy goal must be 

 established in order to determine the sampling rate. 



The accuracy objective should not be a fixed percentage for all condi- 

 tions. The wide range in stumpage values as well as timber sale 

 volumes reo^uires that an appropriate accuracy standard be determined 

 for each sale. A million board feet of western white pine sold for 

 about ^25,000 at 1950 prices. A sampling error of only two percent 

 in the volume determination on such a sale would mean a gain or loss 

 of ip500. A million board feet of Douglas-fir and larch, on the other 

 hand, might sell for aa little as $5,000, and, for the same actual 

 monetary risk as in the white pine sale, a sampling error of 10 percent 

 could be allowed. Yet it is not reasonable that an error as large as 

 10 percent should be used in selecting a sampling rate because with 

 very little more expense, the error could be greatly reduced© 



Sample sizes (or sampling costs) do not bear a straight line relation- 

 ship to accuracy attained, as Figure 1 illustrates. That is, the cost 

 of reducing a sampling error from 10 to 9 percent, for example, is 

 much less than reducing it from 3 to 2 percent. For this reason the 

 cost of achieving a given accuracy, rather than the percentage of 

 accuracy, should be in proportion to the value of the sale. An appro- 

 priate sampling accuracy must be based upon both total sale value and 

 sampling costs. 



A practical method of determining sample size based on sale value and 

 scaling costs has been described, (1_, 2) The method offers a solution 

 to finding the point of diminishing returns in sample scaling — that 

 is, the point Vvfhere additional scaling in the sample would not reduce 

 the possible error by as much as the extra scaling cost. By the 

 diminishing returns principle, accuracy percentages will vary from 

 sale to sale depending upon stumpage rates, scaling costs, and timber 

 volume in the sale. From the seller's standpoint, the diminishing 

 returns principle is a good approach to the accuracy problem. The 

 volume is measured as accurately as is economically possible. Hovjever, 

 the buyer usually has a different vievjpoint. He is not burdened with 

 the cost of achieving the accuracy and consequently v;ants the standard 

 as high as possible to safeguard his purchase. A compromise betvjeen 

 the seller's and the buyer's objectives may be necessary. 



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