The pivotal-quantity method (Mood and others 1974, 

 p. 379) was used to derive the following 95 percent confi- 

 dence interval: 



a,.„ 1.96 J diffsq -I 

 ' \ 0.025:n J 



< DIFF < 



95% 



where 



= values obtained from a chi-square table at the 

 0.025 and 0.975 probability levels for n degrees of 

 freedom 



n 



diffsq = L (V -d,)-. 

 i — 1 



Accuracy test results.— Results on the accuracy of 

 visual segmentation are given in table 2 for each of the 

 three estimators. The mean differences (diff) are mostly 

 negative and range from —3 to —7 percent for the 

 pinyon and juniper totaled over all diameter classes. 

 Median, maximum, and minimum differences are also 

 given. The median tends to be closer to zero than the 

 mean. The maximum and minimum illustrate the ex- 

 tremes that can result from visual segmentation. 



According to the t-test confidence intervals, the mean 

 population difference (of visual minus destructive esti- 

 mates) could be zero for most diameter class groups. The 

 most noteworthy exceptions are for totals having mean 

 differences larger than —6 percent. For individual 

 diameter classes —10 to —13 percent differences are 

 required in order to have t-test significance. 



The chi-square test, on the other hand, shows that the 

 mean population differences would rarely include zero. 

 This conservative test is more sensitive to the large vari- 

 ation found in each individual visual estimate. 



These results indicate that visual segmentation tends 

 to be unbiased (according to t-test) but is inaccurate 

 (according to chi-square test) for estimating volume for a 

 single tree. In the table 2 confidence interval tests, sub- 

 stituting mean percent differences given in table 1 for 

 zero does not significantly alter results. However, our 

 use of Newton's formula to compute volume in destruc- 

 tive segmentation probably contributes somewhat to the 

 negative values consistently observed in table 2 for the 

 mean difference between visual and destructive 

 segmentation. 



Volume Equations 



The visual segmentation method was not intended to 

 provide accurate volume predictions for single trees. We 

 primarily devised it to provide large amounts of inexpen- 

 sive data for volume equation development. Neter and 

 Wasserman (1974) point out that measurement errors in 

 a dependent variable used for regression modeling will 

 present no problems if the errors are random. In our 

 case, this means the visual estimates must vary in a ran- 

 dom manner. This assumption can easily be examined by 

 comparing regression volume equations developed from 

 both the visual and destructive sample data. 



A simple regression model using only DRC and height 

 as predictor variables was selected for the comparison. 

 Other variables were available, but they added little to 

 the predictive power of DRC and height. Combining 

 DRC and height into one variable, DRC squared times 

 height (DRSQH) worked well. A natural log transforma- 

 tion of the data was made to minimize the increasing 

 variance of the volume data with increasing tree size and 

 to satisfy general linear model theory requirements for 

 hypothesis testing. The log-transformed model may not 

 be the best approach for developing pinyon-juniper vol- 

 ume equations, but it was adequate for our evaluation of 

 visual segmentation. 



In figures 2 and 3, regression equations in natural log 

 units for all groups are compared against the 95 percent 

 confidence bands for individual predictions from destruc- 

 tive sample data. It is hard to distinguish differences 

 between the four regression lines, as all lie well within 

 the 95 confidence bands. However, results expressed in 

 the log-transformed units can be deceptive for making 

 inference in cubic feet. 



Destructive 

 segmentation 

 regression 



95^'o confidence 

 interval for 

 destructive 

 segnnentation 

 regression 



T 



7 



LOG DRC (IN) SQUARED TIMES HEIGHT (FT) 



Figure 2. — Pinyon destructive segmentation 

 data in log units witti regression line (solid 

 line) and 95 percent confidence bands (for 

 individual predicted values) fit to data. Three 

 dasfied lines representing regression equa- 

 tions for visual estimates are overlaid. 



10 



5 



