Table 1— (con.) 



Mean Mean Median Maximum Minimum 



Diameter Number diameter volume volume volume volume Lower CL Upper CL Lower CL Upper CL 

 class of trees difference difference^ difference difference difference t-test t-test cfii-square chi-square 



Aspen 



5-6.9 



104 



.04 



2.5 



1.5 



49.5 



-29 



.74 



4.34* 



2.38 



2.74* 



7-8.9 



134 



.02 



.7 







14.8 



-9.8 



.03 



1.33- 



.63 



.75* 



9-10.9 



65 



.05 



1.1 



.9 



19.5 



-25 



-.24 



2.41 



.95 



1.28* 



11-12.9 



31 



.07 



1.1 



.7 



11.2 



-2.7 



.11 



2.14- 



.97 



1.37* 



13-14.9 



12 



.11 



1.4 



1.3 



3.9 



-2.4 



.27 



2.46* 



1.12 



1.95* 



15-16.9 



2 



.02 



.2 



.2 



.5 







-2.65 



3.11 



.06 



1.26* 



17-18.9 



1 



-.28 



-3.0 



-3.0 



-3.0 



-3.0 







-5.57 



4.76 



Total 



349 



.04 



1.4 









.72 



2.00* 



1.33 



1.40* 



Douglas-fir 



5-6.9 



4 



.09 



3.4 



2.6 



11.3 



-2.8 



-6.01 



12.78 



1.59 



12.26* 



7-8.9 



2 







.1 



.1 



3.0 



-2.8 



-37.04 



37.56 



-1.40 



9.57 



9-10.9 



1 



































11-12.9 



1 



-.20 



-3.1 



-3.1 



-3.1 



-3.1 







-5.77 



4.93 



13-14.9 



2 



.06 



.8 



.8 



1.0 



.5 



-2.33 



'3.86 



.35 



3.34* 



15-16.9 



3 



.10 



1.1 



.4 



3.0 







-2.83 



5.09 



.49 



5.16* 



17-18.9 



2 



.33 



3.3 



3.3 



4.2 



2.4 



-7.63 



14.23 



1.56 



14.25* 



19-20.9 



1 



































23-24.9 



1 



.47 



3.6 



3.6 



3.6 



3.6 







.42 



12.85* 



Total 



17 



.10 



1.5 









-.23 



3.26 



1.20 



2.14* 



'The 95 percent confidence limit does not include zero. This means there is a statistically significant difference between volumes computed with English 



and metric diameter measurements. 



n MV.-EV. . MV; = volume in cubic feet computed with metric diameter. 



1 I I where* 



Mean volume difference= L x 100/n 



i =1 EVj EVj = volume in cubic feet computed with English diameter. 



The average difference between metric and English 

 diameters was mostly less than one-tenth inch, which 

 corresponds to a Uttle more than 1 percent bias. This 

 positive bias is the expected result of using diameters 

 measured at 1.3 m in volume equations developed for 

 1.37 m diameter measurements. The confidence limits in- 

 dicate that the bias is most Likely a population 

 characteristic of about 1 to 2 percent. 



Because most volume equations probably predict 

 within 10 to 20 percent of the true value, a correction of 

 1 percent bias between metric and EngUsh 

 measurements provides only a minor improvement in 

 precision. Table 2 shows that a single correction for all 

 species measured in Grand County, Colorado, is suffi- 

 cient. The full and reduced model concept from Graybill 

 (1976) was used to make this determination. The full 



Table 2.— Results of testing six individual equations against the combined equation for 

 predicting English d.b.h. from metric measurements 



Source of Degrees of Sum of ^ , 



, , Mean square F— value 



variation freedom squares 



Total n = 1,783 



Combined equation p = 12 



Individual equations p - q = 2 



Combined minus 



Individual q = 10 



Error variance n - p = 1,771 



221.188.6943 

 221,157.3758 

 221,157.2334 



.1424 

 31.3185 



■0.01424 

 .01768 



0.8054 nsi 



"iThe .05 significance level is 1.83 for an F-value with 10 and 1,771 degrees of freedom. Hence, the 

 hypothesis is accepted and each of the individual equations can be represented equally well by the com- 

 bined equation. 



4 



