STRATIFIED R^l^IDOM SAMPLING 



Stratified sampling is the most efficient device for reducing the 

 variation in tree volumes within a sample. Stratifying consists 

 of dividing a population^ in this instance trees, into strata of 

 similar volume. A sample is then dravm independently from, each 

 stratum. The variation is composed only of the variation of the 

 individuals within a stratum and all variation betvjeen strata is 

 eliminated. 



Large trees 



The average timber sale contains a few scattered large trees, the 

 total number of vjhich is small compared to the entire number, yet 

 TJhose volumes are a large part of the whole. By eliminating these 

 trees from the sample, a large part of the variation can be elimi- 

 nated. A sample drawn from the remaining trees can be smaller than 

 before, yet provide the required accuracy. The volume of the large 

 trees can be obtained by a 100-percent tally, which is entirely 

 independent of the sample, and their volumes can merely be added on 

 after calculating the volume of the remaining trees from the sample. 

 Furthermore, the volume of the large trees vjill be free of sampling 

 error, so the sampled trees can have a larger allowable error than 

 has been established for the final result . The number of trees 

 measured in the sample, plus the number of the large trees measured, 

 will be less than the number necessary in a sample randomized over 

 the entire stand. 



To show the advantage of a complete measurement of large trees, a 

 portion of the scale books were sampled in this manner. The results 

 vjere compared with ordinary random sampling. Table 1 shows the 

 number of trees required by the two methods for a sampling accuracy 

 of 2.5 percent. The last column of the table lists the totals of 

 the sample trees and the large trees. In each instance, the total 

 is less than the first sample shown in column 2, which covered the 

 entire range of tree sizes. A reduction in trees comes by cutting 

 dovm the variation, as shown by the coefficients of variation in 

 the table, and by eliminating all sampling error from large trees. 

 An obvious question is; How large is a "large" tree? This cannot 

 be ansvjered definitely. The dividing point between "large" and 

 "small" trees can be determined for each sale only by a trial method 

 vjhich is rather laborious. (See iippendix VI.) If too many large 

 trees are measured, their number plus the sample trees is greater 

 than a sample of the entire range of sizes. 



-11- 



