To illustrate the computation of the appropriate mean-square deviation_^ the 

 formul^a for Gov (Z^,y, ) will be used. The c£rrespondin^ fo^rmulae for Var (J, ) or 

 Var (Z,) are obvious by recalling that Var (J,) = Gov (Y, ,7,). 



Gov 



1 



N-l 



r N 



N I 

 ■ i=l 



(8) 



A sample estimate of the variance for double sampling designs is computed from an 

 approximation given by Gochran (1963, p. 333). Let 



~ I ^hr^ ~ total photo- interpreted points in compartment "p" 



P h P 



^^p = I ^hp^^^h^^p ^'^s^age of {character} per acre in compartment "p" 



Then 



I 



p h 



^'\p ' W ' hp - 



(9) 



The finite population correction designated as by Gochran has been omitted in 

 expression (9) because the sampling, although usually systematic, should be 

 considered as occurring with replacement. As discussed previously, obtaining F^^ 

 from a systematic sample will cause the variance estimate above to be too large if 

 the interpretation points are so close together that their serial correlation is 

 substantial . 



The variance estimate (9) assumes that the stratum areas are estimated by the 

 same sampling intensity in all compartments. For those compartments containing sub- 

 compartments for which stratum areas can be determined more exactly, it would seem 

 reasonable to determine the total areas from the sums of the known areas (dividing by 

 acres per photo point) plus the usual sample of photo points for the remainder. 

 Generally, this combination of areas will provide a more accurate estimate, although 

 the variance computation will not show the improvement. 



The variance of the grand totals can be calculated as the sum of the 

 compartment variances. Forest totals could be estimated somewhat more precisely if 

 counts of photo points and acres were totaled over the compartments first and these 

 totals used in place of X-p, T-g, and F/^p the formulae for the compartment total and 

 its variance. However, an important feature of this inventory design is its capabilit 

 for including the results of additional stand examinations as they are accomplished. 

 These additional data will be entered at the compartment record level. Hence, compila 

 tion procedures will be more easily handled if totals and variances are aggregated 

 upward from that level. 



In a similar way, statistics for various combinations of compartments can be 

 compiled readily by adding totals and variances for the included compartments. 



16 



