RELATIVE GAIN IN ESTIMATING VOLUME 



In volume estimation the most effective schemes are those which reduce variation within 

 and increase variation between classes. Since the number of field samples required to obtain 

 a mean of given reliability is directly related to the variance, each sampling scheme can be 

 evaluated by dividing its pooled within- stratum variance by that of the unstratified sample. When 

 the resulting percentage is subtracted from one, the remainder is an estimate of the reduction 

 in needed field samples. The most efficient scheme is the one with the lowest variance ratio 

 and therefore the greatest reduction in field plots. 



For this analysis all methods are considered proportional sampling, that is, strata areas 

 are assumed to be proportional to the number of field samples classified in them. Then: 



the total variance of the unstratified sample . 



the pooled within- stratum variance obtained by weighting the 

 variance of each stratum by the percent of the total area 

 occupied by the stratum . 



the variance ratio obtained by dividing the pooled variance by 

 the unstratified variance . 



the expected percentage reduction in required field plots . 



While this is not an absolute measure of sampling efficiency, it is a relative and reasonably 

 simple method of rating a large number of stratification schemes for comparison. 



The various field stratification schemes are listed in table 1 for comparison with the 

 aerial photo and map schemes listed in table 2. The number of strata, variance ratio, expected 

 reduction in field plots, and rank is shown for each scheme. 



Those schemes 4, 5, and 6 (table 2), based on cubic-volume classes, are better than any 

 other photo scheme and even better than any usable ground scheme shown in table 1 . Referring 

 again to table 2, photo scheme 5, based on cubic volume in 1,000-foot classes and topographic 

 site, ranks first but cubic volume alone in either 500- or 1 , 000-cubic-foot classes is nearly as 

 good. To get adequate sampling in each class the number of classes should be kept quite low, 

 and for this reason the scheme using 1 , 000-cubic-foot classes alone would probably be the most 

 practical even though it ranks third. 



Table 2 indicates that, compared with volume classes, much less gain can be expected 

 from stand-size and crown-cover classification and still less from species and topographic site. 

 Crown cover, using only three classes, appears to be worthless in volume estimating. In general, 

 classifications taken from existing type maps appear even less useful. Since these maps were 

 prepared by photo interpretation, but not measurement, we must assume that subjective photo 

 methods complicated by drafting limitations, add up to much poorer stratification than would be 

 possible from use of aerial photo volume tables. 



Comparison of the ratings shown in tables 1 and 2 indicates stratification by means of 

 ground measurements results in stand- size and density strata only a little better than those 



S 2 = 



S 2 



LOO -) P, S; 2 



7 



