M-,. = — = -z = proportion of area of subcompartment "t" that is in the 



flu ri * 1 



k 



"h" stratum 



t ^k^ik^hik 

 k 



Note that the denominator is proportional to the total acreage of stratum "/i"' in 

 subcompartment ' If acres by management class are the feature being compiled, 

 would be unity for stands in that class and zero otherwise. ^ 



St ration Means 



An estimate for stratum means will be developed first for the general case in which 

 subcompartments are selected with arbitrary probabilities. The simplification that 

 results from defining the selection probability to be proportional to acres in the sub- 

 compartment will then be demonstrated. 



Let P_- be N times the probability that subcompartment "i" would be drawn for any 

 any one of the N sample units. Then ^P^ = N where "i" ranges over all subcompartments 



in the forest. The expression for the stratum mean is then: 



y TVA, .M, . J A ../P. 



- I M,. I A. ./J. 



% k 



Expression (3) is a fraction in which the numerator is an estimate of the total 

 {character} in stratum The denominator is the corresponding estimate of tlie area 



in the stratum. Because both numerator and denominator are estimated using the same 

 sampling units, their covariance should help to reduce the variance of the ratio. 

 If Vj^ is defined to be proportional to the total forest acreage in the tth sub- 

 compartment ^-11^' 'then (3) reduces to: 

 k 



y TVA. . ' M. . 



V 



If the proportions Afi^ are established from absolute measures of acreage of each 

 stand, then (3) can also be expressed as: 



____ hifr ik hik 



^ k 



Likewise, an expression exactly equivalent to (4) can be obtained by omitting the 

 value of from (3a) . 



13 



