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Standard Error of Height Estimation 

 INVENT allows the user to double sample within each cluster for tree 

 height. For each species where three or more height trees are measured 

 within the stratum, a regression relationship between height and the inverse 

 of d.b.h. is analysed. When calculating volume for a tree whose height was 

 not measured, the regression equation is used to generate a height for that 

 tree. If the user were required to measure the heights of all trees on 

 some of the clusters while measuring no heights on the remaining clusters, 

 the volume standard error could be calculated using techniques developed by 

 Donald Bruce (1961) and Floyd A. Johnson (1958). Bruce 's method is outlined 

 in Appendix B, page 53. Johnson's method is an application of double 

 sampling with ratio of means estimation and this method is presented in 

 Appendix B, page 52. Neither method Is applicable if the user is free to 

 subsample a portion of the trees within each cluster. A new statistical 

 technique was developed to approximate the standard error of the resulting 

 volume estimate. 



The authors believe that this new technique is far more efficient in 

 field application. It allows the user to sample heights more intensely on 

 the more valuable species. It provides far more flexibility than the 

 traditional approach. 



H = height D = d.b.h. T = // trees sampled t = // height trees sampled 

 Regression Model : H = B^ + B^ ^"n"^ "*" ^ 



„ ^ /-u^ c2 MSE 

 Variance (H) = S„ = — — - 

 u t 



where MSE = mean square error of the regression (for 



computational formula see Neter and Wasserman, 

 1974, p. 45). 



^H 

 Standard Error (H) = SE„ = — 2_ (iqO) 



" H 



SE is calculated for every species where three or more height trees 

 H 



are measured. It is also necessary to calculate SE^ for the Softwood, Hard- 

 wood and All Species summary volumes. The method used is from Neter and 



