Application and Reliability 



Table 1.— Range of stump diameters, in inches, 

 for 17 northeastern tree species 





Range of 

 stump diameters 



Spruce and fir 



4.7-22.8 



Southern hard pines^ 



3.8-26.0 



Northern hard pines'' 



2.4-18.8 



Eastern white pine 



5.1-33.0 



Eastern hemlock 



5.9-26.5 



Othpr '?oftwood«5 



2.1-24.1 



Red maple 



3.5-38.5 



Sugar maple 



4.5-42.7 



Birch and elm 



4.6-34.0 



Hickory 



4.9-35.7 



Beech 



6.2-42.8 



Ash, aspen, and basswood 



5.3-38.8 



Yellow-poplar 



6.4-45.5 



Black cherry 



6.1-34.0 



White oak 



4.0-43.0 



Red oak 



5.6-48.5 



Other hardwoods 



2.7-36.8 



^Includes loblolly, shortleaf, pond, and Virginia pine. 

 ^Includes pitch and red pine. 



Equation Development 



The equations were developed 

 by using simple linear regression 

 because the simple linear models are 

 as reliable as the more complex mod- 

 els in predicting d.b.h. from stump 

 diameter (Bylin 1982). The form of the 

 equation used is y = a + bx; where y 

 is the predicted d.b.h. in inches and 

 X is the stump diameter (inside the 

 bark) in inches. 



The trees were initially grouped 

 to represent species most commonly 

 harvested throughout the Northeast. 



Some of the species with small sam- 

 ple sizes were combined with species 

 with similar equations (not signifi- 

 cantly different at the 0.05 level of 

 significance). The result was a group 

 of 17 northeastern species (Table 2). 



Sometimes it is difficult to iden- 

 tify the species from only the stump. 

 In these instances, a general soft- 

 wood or hardwood equation can be 

 useful. Therefore, I developed a sec- 

 ond set of equations that grouped all 

 of the softwood species together and 

 all of the hardwood species together 

 (Table 3). 



To use these equations, the 

 species or species group must be 

 identified (softwood or hardwood if 

 species is unknown), and stump di- 

 ameter must be measured to the 

 nearest 0.1 inch inside the bark. On 

 irregularly shaped stumps, it is some- 

 times necessary to take more than 

 one diameter measurement. Where 

 the stump is fluted or flared, measure- 

 ments should be taken across the 

 widest and narrowest diameters, and 

 then averaged. It is not necessary to 

 measure the height of the stumps. 

 Once the stump diameter is measured, 

 d.b.h. can be predicted. For example, 

 the predicted d.b.h. for a spruce tree 

 with a 14-inch stump diameter mea- 

 sured in the future would be: 



y° = 0.96596 + (0.79667) (14.0) 

 = 12.1 inches 



Knowing the prediction interval 

 is as important as being able to pre- 

 dict the d.b.h. based on the stump 

 diameter, especially where there is 

 a legal question. The variance of the 

 predicted d.b.h. gives a range tojudge 

 the value of timber loss. With the 

 values from Tables 2 and 3, the pre- 

 diction interval can be calculated by: 



where s^ = mean square error of the 

 sample 

 n = number of observations 

 in the sample 

 x° = stump diameter to be 

 measured in the future 

 x = mean stump diameter of 

 the sample 

 CSS = corrected sum of squares 

 of X = ns^(x) 



For a 14-inch stump diameter, the 

 variance around the expected d.b.h. 

 would be: 



v(y°) = 1.03742 X 



/ _1_ (14.0-11.8)A 

 ^ 337 3,445.6 / 



2 



