Table 2.— Comparison between visual segmentation and destructive segmentation using the difference statistic (diff). The confidence intervals (CI's) 

 contain the mean difference (DIFF) unless a 1-in-20 chance in sampling has occurred 



Diameter 





Number 







Volume difference 



t-test 



Chi-squared 



class 



Estimator 



of trees 



Mean Volume difference 



Mean Medium 



Minimum 



Lower CI 



Upper CI 



Lower CI 



Upper CI 



Inches 









Percenf 









Ft^ 













Juniper 















3- 6.9 



BLM 



8 



-0.04 



-6 



-0.03 



0.51 



-0.78 



-0.34 



0.27 



-0.09 



0.13 



3- 6.9 



FS1 



23 











-.05 



.94 



-1.22 



-.17 



.16 



-.03 



.04# 



3- 6.9 



FS2 



23 



-.06 



-14 



-.06 



.25 



-.74 



-.15 



.02 



-.08 



-.04* 



7-10.9 



BLM 



18 



-.09 



-4 



.18 



1.58 



-4.48 



-.76 



.59 



-.19 



.13 



7-10.9 



FS1 



51 



-.17 



-9 



-.05 



1.58 



-4.92 



-.42 



.09 



-.19 



-.12*# 



7 - 10.9 



FS2 



51 



-.16 



-9 



-.07 



1.08 



-4.96 



-.39 



.08 



-.18 



-.12-?± 



11 -14.9 



BLM 



18 



-.09 



-2 



-.44 



4.16 



-2.99 



-.87 



.69 



-.22 



.15 



11-14.9 



FS1 



35 



-.73 



-13 



-.67 



3.49 



-3.09 



-1.24 



-.21 



-.80 



-.61 •# 



1 1 - 14.9 



FS2 



35 



-.40 



-7 



-.17 



2.89 



-4.63 



-.89 



.09 



-.47 



-.30*# 



15-18.9 



BLM 



10 



-.53 



-7 



-.49 



.78 



-2.14 



-1.27 



.21 



-.68 



-.14*= 



15-18.9 



FS1 



19 



.78 



9 



-.05 



21.03 



-2.40 



-1.64 



3.20 



.39 



1.53*# 



15-18.9 



FS2 



19 



.88 



11 



.36 



7.28 



1 Qn 



Oft 



no 



.oy 



^ oc * 



>19 



BLM 



7 



-1.33 



-7 



.43 



5.10 



-8.78 



-5.51 



2.86 



-2.14 



1.21 



^ ^ n 

 >19 



rol 



1 1 



1.39 



7 



.73 



14.48 



-5.98 



-3.32 



6.10 



.53 



3.47'# 



-in 



ceo 



1 1 



-2.09 



-11 



-1.56 



11.03 



n QQ 



— y.oo 



C AC 



— b.Ub 



-1 QQ 

 1 .OO 



-2.85 



- .27*# 



Total 



BLM 



61 



-.30 



-5 



-.02 



5.10 



-8.78 



-.78 



.19 



-.35 



-.22' = 



1 otai 



rol 



-f on 



Toy 



-.03 



-1 



-.07 



21.03 



-5.98 



-.50 



.45 



-.06 



.02 



1 otai 



ceo 



^ on 



ijy 



-.21 



-5 



-.09 



Pinyon 



11.03 



— y.oo 



— .0/ 



■1 A 

 .14 



— .<i4 



- .18*Tr 



3- 6.9 



BLM 



27 



.03 



5 



.05 



.52 



-.43 



-.04 



.11# 



.02 



.05*7? 



3- 6.9 



FS1 



53 



.06 



10 



.03 



.64 



-.49 







.12# 



.05 



.07*# 



3- 6.9 



FS2 



53 



-.04 



-7 



-.01 



.43 



- .97 



-.09 



.01 



-.05 



-.03*# 



7-10.9 



BLM 



33 



-.24 



-6 



-.25 



1.69 



-2.62 



-.62 



.14 



-.29 



-.16*# 



7-10.9 



FS1 



60 



.14 



4 



-.11 



4.82 



-2.27 



-.16 



.44 



.11 



.19*# 



7 - 10.9 



FS2 



60 



-.39 



-10 



-.13 



1.10 



-3.86 



- .65 



-.13*# 



-.42 



-.35*# 



11-14.9 



BLM 



20 



-.62 



-6 



-.43 



3.36 



-5.16 



-1.47 



.24 



-.76 



-.35*# 



11-14.9 



FS1 



31 



-1.12 



-10 



-1.12 



4.63 



-7.84 



-2.10 



-.14* 



-1.27 



-.88*# 



11 - 14.9 



FS2 



31 



-1.41 



-13 



-1.63 



2.06 



-5.67 



-2.11 



- .71 *# 



-1.53 



- 1.21 *# 



15-18.9 



BLM 



8 



-2.96 



-13 



-2.59 



3.83 



-13.69 



-8.20 



2.27 



-4.05 



.15 



15-18.9 



FS1 



16 



-.26 



-1 



-.71 



10.85 



-10.01 



-3.31 



2.79 



-.76 



.78 



15-18.9 



FS2 



16 



-1.42 



-5 



-1.35 



5.81 





— o.^^ 



-'+VJ 





— . / J TT 



> 19 



BLM 



1 



7.68 



13 



7.68 



7.68 



7.68 







.91 



27.72*# 



>19 



FS1 



3 



-6.19 



-12 



-4.85 



-4.80 



-8.93 



- 12.09 



-.30*# 



-8.60 



8.96 



>19 



FS2 



3 



-1.89 



-4 



-2.08 



.61 



-4.20 



-7.88 



4.10 



-2.90 



4.48 



Total 



BLM 



89 



-.40 



-6 



-.03 



7.68 



-13.69 



-.90 



.11 



-.44 



-.34-5 



Total 



FS1 



163 



-.28 



-4 



-.03 



10.85 



-10.01 



-.65 



.09 



-.31 



-.25*# 



Total 



FS2 



163 



-.60 



-8 



-.11 



5.81 



-9.23 



-.84 



-.35-# 



-.62 



-.58*# 













Pinyon and juniper 













Total 



BLM 



150 



-.36 



-6 



-.03 



7.68 



-13.69 



-.71 



-.01* 



-.38 



-.32*# 



Tota|2 



FS1 



302 



-.16 



-3 



-.05 



21.03 



-10.01 



-.46 



.13 



-.18 



-.15-# 



Tota|2 



FS2 



302 



-.42 



-7 



-.11 



11.03 



-9.88 



-.63 



-.21 *# 



-.43 



-.41*# 



'Ninety-five percent confidence interval does not contain zero. 



#Ninety-five percent confidence interval does not contain tfie negative value from table 1. 



^Mean percent difference Is tfie mean volume difference divided by tfie mean volume computed by Newton's formula. 



^his total for number of trees does not equal the totals in figure 1 and table 1 because of a data collection error in omitting visual segmentation of one tree. 



precision. Freese (1960) suggests a chi-square test if both 

 bias and precision are of concern. 



All statistical analyses are done in terms of 95 percent 

 confidence intervals instead of testing single point esti- 

 mates. Confidence inter^^als give more information than 

 simple tests that just accept or reject a hypothesis. 

 Also, confidence intervals allow the reader to select 

 either zero or a value from table 1 as the test criterion. 

 A 95 percent confidence interval can be interpreted as 

 an interval having a 19-in-20 chance for containing the 

 true population value. 



The t-test for paired differences is given in Steel and 

 Torrie (1960) and can be expressed in terms of a 95 per- 

 cent confidence interval: 



Prob {[diff - (too25:n-iSd)] ^ DIFF < 



[diff + (to.025:n-lSd)]) = 95% 



where 



t = the value obtained from a t-table at a = 0.025 

 probabihty level for n— 1 degrees of freedom 



= the standard error of the mean difference idiff) 

 n = the sample size of the groups of differences being 

 tested 



DIFF — the expected (true population) value of diff (it 

 is either zero or the values in table 1). 



Freese (1960) gave a computing formula for the chi- 

 square test, but not in the form of a confidence interval. 



4 



