A99.9^ 

 F764Dn 



JAMES C. SPACE 



Iktermountain forest and range 



O^den.Utah 



EXPERIMENT STATION 



No. 14 



1X5 J> 



December^ ,1954 



> 



yVHAT IS AN ACCEPrABIiE ALDOWABLE ERROR AND SAMPLE SIZE -r J 



IN SAMPLE LOG SCALING OR TREE MEASURING 



Donald W. Lynch 

 Division of Forest Management Research 



-X) 

 -< 



When a sampling technique of any kind is substituted for complete ^ / 

 measurement, one accepts the fact that a certain sampling error exists,— 

 If the sample has been chosen in strictly random fashion one knows, for a 

 given probability, exactly what the limits of the sampling error will be. 

 In other words the error will lie somewhere within these plus or minus 

 limits. As the sample size is increased, approaching 100 percent tally as 

 a limit, the sampling error approaches zero. The error does not approach 

 zero, however, in direct proportion to the increase in sample size. For 

 example, a small increase ii! sample size is required to reduce a sampling 

 error from 5 percent to 4 percent, whereas a very large increase is re- 

 quired to reduce it from 2 percent to 1 percent. It follows, then, that 

 a point of diminishing returns will be reached where a further increase 

 in the sample size is not justified by the concomitant decrease in sam- 

 pling error (or increase ir sampling accuracy). 



In scaling sawlogs, for example, the use of sampling methods means 

 a willingness on the part of the seller tc risk a possible monetary loss 

 rather than to spend additional funds for a more accurate scale. Several 

 factors v/ill determine how large the risk should be or whether it should 

 be taken at all . 



1/ Sampling error in sample log scaling or tree measuring is the differ- 

 ence between the volume estimated by the sampling method and the volume 

 obtained by complete measurement expressed as a percentage of the latter. 

 It is assumed that the complete measurement is without error ^ which, of 

 course, is not strictly true. In log scaling, for example, a scale of 

 sound material is considered satisfactory if it is within 2 percent of a 

 check scaler's volume for the same logs, whereas a scale of defective 

 material is often accepted at a nigher discrepancy than 2 percent. 



