number of alternatives, none of them proved either applicable or useful (see appendix I for 

 further details on tests examined or tried) . A test not examined in this study but which 

 could prove useful in future studies is described by Freese (1960) . 



The lack of a useful statistical test, therefore, necessitated a subjective evaluation of 

 the validation runs. This decision led to an additional problem: how to conveniently sum- 

 marize, for reporting and comparative purposes, the large amount of detailed individual 

 subplot validation information produced in validating for the uneven-aged plots. After 

 consideration, I concluded that two statistics adequately reflected the average behavior 

 exhibited by just the validation subplots. These statistics were computed by first averaging 

 across all the plot's subplots the predicted and actual diameter distribution for each growth 

 period, combining blackjack and yellow pine in the process. Next, the mean difference be- 

 tween average actual and average predicted diameter distributions (the first statistic) and 

 the variance of these differences (the second statistic) were computed across diameter 

 classes for each plot and growth period. 



Use of averages incorporating both the model building and the validation data sets would 

 appear to violate the fourth rule of validation (that is, the validation data should be indepen- 

 dent of the model building data) . But the apparent violation is not serious because much of 

 the basic validation information produced and examined (but not reported here) for decision- 

 making pertained to just the subplots from the validation data set. 



For the even-aged validation data, the mean difference across diameter classes, between 

 the actual and predicted diameter distribution for each individual plot and growth period and 

 the variance of these differences were used as summarization statistics. Statistics produced 

 from average diameter distributions across all plots are meaningless for the even-aged data 

 set . 



Results of Validation 



PREDICTED UPGROWTH; ACTUAL MORTALITY. CONVERSION. INGROWTH 



The first set of validation runs used predicted upgrowth and actual mortality, cutting, 

 conversion, and ingrowth rates to assess the predictive capabilities of the various upgrowth 

 models . 



In addition to the two blackjack pine basal area growth equations tested, two methods for 

 applying the equations were also tested. One method used the average basal area growth for 

 the diameter class to advance the trees, and the other divided the diameter class into three 

 more classes and then used estimates for the lower, middle, and upper basal area growths of 

 the diameter class to advance each third separately. The combination of basal area growth 

 equations and advancement techniques resulted in the evaluation of four different upgrowth 

 models . 



For simplicity, the actual mortality, conversion, and cutting rates were expressed as 

 proportions rather than number of trees. This approach has the advantage of eliminating the 

 problems associated with removals being larger than the number of trees in a diameter class. 

 The method, however, exaggerates differences between predicted and actual upgrowth because 

 any difference between the resulting predicted and actual diameter distributions will result 

 in different numbers of trees being removed due to mortality, cutting, or conversion. 



Examining these runs revealed that, on the uneven-aged plots, the blackjack pine basal 

 area growth equation developed with both even- and uneven-aged data (BJBAGl) behaved the same 

 as the equation developed with just the uneven-aged data (BJBAG2) . As a result, BJBAGl was 

 adopted as the final basal area growth equation for blackjack pine. 



In addition, the upgrowth rate appeared too high. This led to an immediate suspicion of 

 the proposed correction for log bias because of the magnitude of that correction (a 35 percent 

 increase for blackjack pine and 140 percent increase for yellow pine) and because the justifi- 

 cation for that correction was not too firm. Therefore, I decided to try two additional 



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