-61- 



Slmple Random Sample 



Sample size from simple random sampling is estimated by the following 



equation: ^ 



r t CV ,^ 

 n = I — ] Equation 1 



where t is a t-value, CV is the coefficient of variation, and E is the 

 allowable error in percent. 



The t-value depends on the confidence level desired. The approximate 

 t-values for the most widely used confidence levels are: 



Confidence level 



(percent) t-value 



80 1.3 



90 1.7 



95 2.0 



99 2.7 



The coefficient of variation is a measure of the variability among 

 volume estimates in a forest based on a particular technique of sampling. 



Assume that from past experience a forester estimates that the 

 coefficient of variation is 50 percent when he samples with a 10 B.A.F. 

 prism. He wants to estimate the volume on a tract with an allowable error 

 of 10 percent at the 95 percent confidence level. That is, he wants the 



chances to be 95 in 100 that his estimate after completing the inventory 



3 

 is within 10 percent of the actual volume. 



The sample size by Equation 1 is estimated as follows: 



, = [_E_C^L]' = [^iP^]' = 100 points 



Thus, the forester must select 100 points. 



2 



The estimate of sample size using simple random and the subsequent estimates 

 using stratified random sampling can be adjusted by the equation 



n = 



a 1 + P/100 



where P is the percent cruise. This additional refinement in estimating 

 sample size is generally not necessary except on small tracts. 



3 

 To be within 10 percent of the actual volume implies that errors such as tree 



measurement errors, errors in estimating form class, and errors in volume 



equations are negligible. 



