using class values instead of actual dimensions in 

 Huber's formula. This will happen only if the dj's and 

 h 's sum to zero for fixed D and H . This will occur with 

 greater probability for large n; that is, for trees with 

 many segments or for estimating volume for a group of 

 trees. 



The study in this paper compares volume estimates 

 from visual segmentation with volume estimates ob- 

 tained from exact measurements of segments from trees 

 destructively sampled. 



FIELD DATA COLLECTION 



In 1980, volume samples were collected for 248 pinyon 

 and juniper trees on lands in Nevada managed by the 

 U.S. Department of the Interior, Bureau of Land 

 Management (BLM). An additional 55 trees were sam- 

 pled in 1981 on BLM lands in Nevada and Utah. From 

 two to six trees were selected at each of the 61 loca- 

 tions. The locations were a small subsample of the BLM 

 woodland inventory. The sampling was done as a secon- 

 dary task of a U.S. Department of Agriculture, Forest 

 Service. Forest Survey quality control crew. Because of 

 this, no attempt was made to design the subsample, 

 other than to distribute it throughout the inventory 

 area. 



In 1980, trees within the locations were selected in 

 proportion to crown area using transects (Meeuwig and 

 Budy 1981). Because the first year's sample was weak in 

 the larger diameter classes, those taken during the 1981 

 field season were purposely selected in larger diameter 

 classes. Individual tree measurements included diameter 

 at root collar (DRC), number of stems, crown widths, 

 total height, and location description data (USDA Forest 

 Service 1982). Volume measurements of each tree were 

 obtained by (1) visual segmentation and (2) destructive 

 segmentation. 



For visual segmentation, numbers of stem segments 

 were counted in classes of 2-inch midpoint diameter by 

 2-foot length. The estimator proceeded in a systematic 

 fashion from the base of a tree upward, recording each 

 segment in the appropriate class (see appendix). Two or 

 three visual volume estimates were done for each tree, 

 two by a U.S. Forest Service (FS) quality control crew 

 and usually one by a BLM crew. In 1981, when the last 

 55 trees were sampled, only the FS crew members made 

 visual volume estimates. 



Destructive segmentation involved cutting down trees 

 in order to measure diameter and length dimensions for 

 each segment. Segment lengths were chosen to roughly 

 parallel the visual method, although an exact rule was 

 not established. Tapers of segments were to be less than 

 15 to 20 percent. Segment length, diameter (outside 

 bark) at both ends, and diameter at the midpoint were 

 recorded for each segment. The destructive segmentation 

 provided data to compute accurate volume estimates for 

 comparison with the visual segmentation estimates. 



DATA ANALYSIS AND RESULTS 



We investigated three aspects of visual segmentation: 

 (1) its accuracy for estimating volume of individual trees. 



j 



j 



(2) its usefulness for volume equation development, and ' 



(3) the consequences of applying volume equations based 



on visual segmentation data. ^ 



Testing for Accuracy 



Before testing, the data were grouped by species, tree ' 

 size, and estimator group (field crews). Two species— 

 singleleaf pinyon iPinus monophylla Torr. & Frem.) and 

 juniper (Juniperus osteosperma [Torr.] Little)— were 

 represented. Four-inch diameter classes were selected to 

 minimize effect of tree size on the comparisons, as trees 

 ranged from 3 to over 20 inches DRC. There were up to 

 three visual volume estimates and a destructive volume ' 

 estimate for each tree. The crews doing the visual 

 estimating were placed into three groups and called FSl, 

 FS2. and BLM. FSl was the same estimator for all 

 samples. FS2 included two estimators, one of whom did I 

 only 55 of 303 trees. The BLM group included as many ■ 

 as 15 estimators. All estimators attended the same train- \ 

 ing sessions. 



Test statistic— The statistic used to make the compar- 

 isons within groups was the average difference Idiff) \ 

 between visual and destructive volume estimates: 



£_(v^ I 



1=1 n j 



where 



diff = average difference between visual and destruc- 

 tive estimates 



v. = visual volume estimate of the ith tree 



dj = destructive volume estimate of the ith tree 



n = sample size for a group. 

 The visual (v^) and destructive (d^) volume estimates were 

 computed by Huber's and Newton's cubic-foot log for- 

 mulas, respectively (Husch and others 1982, p. 101). 

 Different formulas were used because slightly different 

 measurement procedures were used for visual and de- 

 structive volume estimates. Husch points out that 

 Newton's formula is the most flexible and best formula 

 available for logs measured at three diameter points. 

 Because the destructive samples had three diameter i 

 measurements, Newton's formula was selected. On the j 

 other hand, the visual estimates had only one diameter I 

 measurement and were limited to Huber's formula. The ' 

 difference between the formulas was fairly negUgible. as 

 shown by figure 1. The difference, however, is given in ' 

 table 1 for later use in interpretation of results in ■ 

 table 2. ' 



Background on tests.— Testing for accuracy of a statis- 

 tic or estimator actually involves testing two 

 components— bias and precision. Bias is the expected 

 difference between any statistic and its true value. In 

 our case, diff is the statistic of interest and its true 

 value is zero. A biased statistic from a sample survey | 

 cannot be improved by increasing sample size. Precision i 

 describes how widely a statistic can fluctuate around its 

 true value. The variance of diff is a measure of precision 

 for our statistic. An imprecise statistic can usually be 

 improved by increasing sample size. 



Student's t-test can be used to compare visual volume 

 estimates with destructive estimates from the same 

 trees to determine bias, although it is a poor test for 



2 



