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UBC Theses and Dissertations

Using the jackknife technique to approximate sampling error for the cruise-based lumber recovery factor Jahraus, Karen Veronica


Timber cruises in the interior of British Columbia are designed to meet precision requirements for estimating total net merchantable volume. The effect of this single objective design on the precision of other cruise-based estimates is not calculated. One key secondary objective, used in the stumpage appraisal of timber in the interior of the province, is estimation of the lumber recovery factor (LRF). The importance of the LRF in determining stumpage values and the fact that its precision is not presently calculated, prompted this study. Since the LRF is a complicated statistic obtained from a complex sampling design, standard methods of variance calculation cannot be applied. Therefore, the jackknife procedure, a replication technique for approximating variance, was used to determine the sampling error for LRF. In the four cruises examined, the sampling error for LRF ranged from 1.27 fbm/m³ to 15.42 fbm/m³. The variability in the LRF was related to the number of sample trees used in its estimation. The impact of variations in the LRF on the appraised stumpage rate was influenced by the lumber selling price, the profit and risk ratio and the chip value used in the appraisal calculations. In the cruises investigated, the change in the stumpage rate per unit change in the LRF ranged between $0.17/m³ and $0.21/m³. As a result, sampling error in LRF can have a significant impact on assessed stumpage rates. Non-sampling error is also a major error source associated with LRF, but until procedural changes occur, control of sampling error is the only available means of increasing the precision of the LRF estimate. Consequently, it is recommended that the cruise design objectives be modified to include a maximum allowable level of sampling error for the LRF.

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