APPENDIX B 



DISTRIBUTION OF TREES WITHIN A DIAMETER CLASS 



The uniformity of tree distribution within a diameter class is likely to be influenced by 

 the combination of diameter class size and the number of trees in the diameter class. The 

 fewer the number of trees in a class, the more difficult it would be to prove nonuniformity; 

 and the number of trees in a class is, in part, determined by the diameter class size. 

 Therefore, the smaller the diameter class size, the higher the probability that the assumption 

 of uniformity can be met. 



To test for uniformity, about one-fourth of the subplots reserved for model building were 

 randomly selected ftom both the uneven- and even-aged plots. All applicable measurement 

 periods on the selected subplots were examined, and those 1-inch diameter classes with five or 

 more trees in them were then chosen for testing. 



A chi-square "goodness-of -f it" test was selected because it is appropriate for testing 

 the distribution of a discrete random variable (the number of trees in a class) . For diameter 

 classes with five to nine trees in them, the diameter class was divided into five equal sub- 

 classes, and for diameter classes with 10 or more trees, the number of subclasses was 10. 

 The expected number of trees in each subclass was computed by dividing the total number of 

 trees in the class by the appropriate number of subclasses. 



The decision to use two sizes of subclasses was based on the suggestion by Snedecor and 

 Cochran (1967) that the expected value in any subclass should be greater than or equal to one. 

 Since the number of trees in a diameter class is usually low in the Southwest, the inclusion 

 of the five-to-nine size group spreads the testing over more diameter class sizes. For example, 

 of the 2,195 diameter classes with trees examined in this phase, 1,481 had less than five 

 trees, 417 had five to nine trees, and the remaining 297 diameter classes had 10 trees or more 

 (table 22) . 



Table 22 . --Results of testing within diameter class dia^rihution for each plot by number of 



trees in diameter class 



Plot 





Number 



of diameter classes 







1 to 4 trees 



5 



to 9 trees 



10+ 



trees 



Uniform 



Nonuniform 



Uniform 



Nonuniform 



61 



499 



147 



1 



39 



2 



62 



415 



79 







8 







71 



257 



98 







94 



2 



72 



299 



87 







101 







Taylor Woods 



11 



5 







49 



-> 



Total 



1,481 



416 



1 



291 



6 



Testing was done at the 99 percent level of significance in order not to reject the null 

 hypothesis of a uniform distribution unless marked deviations were found. The degrees of 

 freedom for the test were computed as the number of subclasses minus one because it was not 

 necessary to estimate distribution parameters. Results of the tests are found in table 22. 



Of the 714 diameter classes tested, only seven were not uniformly distributed. While it 

 was earlier hypothesized that the within diameter class distribution might depend upon number 

 of trees in the class and perhaps stand structure, the results indicate that these factors are 

 not as important as first thought. For example, on the even-aged plots tested, 20 of the 21 

 diameter classes with 50 or more trees in them were uniformly distributed, indicating that the 

 within diameter class distribution is not closely correlated with the number of trees or 

 structure of the stand. 



49 



