STUDY L/STHODS 



COIiECTION OF DATA 



Samples v/ere collected from scale books of tree measured sales on the 

 Bltterroot, Cabinet, Coeur d'Alene, Colville, Flathead, Kaniksu, 

 Kootenai, and Lolo National Forests. Only a limited number of scale 

 books "were available because tree measurement is relatively ne"j in 

 the Northern Regiono The samples covered as v/ide a range of conditions 

 as possible. Twenty-four samples from ponderosa pine sales, 22 from 

 Douglas-fir, 21 from western larch, 3 from western Virhite pine, and 3 

 from Engelmann spruce ivere collected. In taking the samples from the 

 scale books, rates of one in five to one in ten were used, depending 

 upon the size of the sale. In every case, a sufficiently large sample 

 was drawn to give a reliable estimate of the standard deviation of 

 the tree volumes. Unlike collecting the sample in the woods, mechanical 

 sampling from scale books can be considered unbiased. 



A total of 41 lists of paired markers' and checkers' volumes covering 

 different species and conditions were collected to study check scaling 

 requirements. As data from check scales were even less available than 

 tree measured scale books, the desired range in defect conditions could 

 not be entirely covered . 



FIRST SAIIPLE ANALYSIS 



The amount of variation in the volumes of trees on a timber sale is 

 the most important factor in determining sample size for a given accu- 

 racy. The other main influencing factor is the total number of trees 

 in the sale. The importance of volume variation can be appreciated by 

 considering the hypothetical case where all trees in the sale have 

 exactly the same volume. If the volume of only one tree is measured 

 and all the trees are counted, a perfect estimate of the volume is 

 obtained. However, tree volumes do vary, and so the sample of volumes 

 must be increased as the variation increases in order to get a reliable 

 estimate of the whole. Variation is commonly measured by the standard 

 deviation. (Formula shown in Appendix 11.) 



Small trees have numerically smaller standard deviations than large 

 trees. Hovjever, the relative variation, that is, the ratio of the 

 standard deviation tc tte arithmeti cal mean commonly referred to as the 

 coefficient of variation , was found to be rather uniform over the 

 entire range of tree volumes. (See Appendix III.) The usual range 

 of the coefficient of variation v/as found to be from 60 to 80 percent, 

 with an occasional value as low as 40 percent or as high as 90 percent. 

 The variation and mean volume for a sale are estimated from the sample. 

 Multiplying the mean volume by the total number of trees in the sale 

 gives an estim^ate of the total volurae. The standard error of the 



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