The equation for the average basal area of a diameter class assumes that the trees in a 

 diameter class are uniformly distributed over the 1/10-inch subclasses of the class. As 

 previously shouTi, this assumption could not be disproven and therefore would appear correct. 



An Initial Evaluation of the Log of Basal Area Growth Equations 



An unanswered question is whether basal area growth for even- and uneven-aged stands is 

 logically interrelated. As mentioned previously, the problems with the data used in this 

 study and the lack of normality make a statistical answer to this question intractable. I 

 thought, however, that an initial comparison between the two blackjack pine equations could 

 be made in such a fashion as to shed light on the performance of each model. A second compari- 

 son and a selection of a final blackjack pine model were reserved until validation. 



To make this initial comparison, the data used to develop the equations were divided into 

 four sets: virgin uneven-aged data, managed uneven-aged data, managed even- and uneven-aged 

 data, and managed even-aged data. The residuals about each final log of basal area growth 

 equation were then computed separately for each of the data sets originally used to develop 

 the particular equation. From this information, a mean squared error (MSE) , average residual, 

 and percent average residual (expressed as percent of the mean log of basal area growth) were 

 computed for each data set. The results are in tables 6 through 9. 



Table 6 . --Comparison of actual log of basal area growth data from virgin, uneven-aged plots 

 to log of basal area growth predicted by various equations developed using data 

 from those plots indicated 



Plots used Number of Mean squared Average Percent 



Vigor class in equation observations error residual average 



development residual 



Blackjack pine 



All 





8,197 



1 , 



.572575 



+ 0, 



.000013 



-0. 



,000462 



Blackjack pine 



Uneven- 



-aged 



8,197 



1 , 



,573900 



+ 



.000028 





,000994 



Blackjack pine 



Virgin 

 uneven- 



-aged 



8,197 



1 , 



.534644 



+ 











Yellow pine 



Uneven- 



-aged 



3,762 



6, 



.310643 



+ 



.000261 





,000076 



Yellow pine 



Virgin 

 uneven- 



> 



-aged 



3,762 



6. 



.273243 



+ 











Table 7 . --Comparison of actual log of basal area growth data from managed, uneven-aged plots 



to log of basal area growth predicted by various equations developed using data from 

 those plots indicated 



Vigor class 



Plots used 

 in equation 

 development 



Number of 

 observations 



Mean squared 

 error 



Average 

 residual 



Percent 

 average 

 residual 



Blackjack pine 



All 



19,069 



0.940228 



-0.007303 



+0.257221 



Blackjack pine 



Uneven-aged 



19,069 



.938867 



- .000012 



+ .000423 



Blackjack pine 



Managed , 

 uneven-aged 



19,069 



.935147 











Yellow pine 



Uneven-aged 



794 



1.840926 



- .001237 



+ .058064 



Yellow pine 



Managed , 

 uneven-aged 



794 



1.800258 











11 



