Variance of Population Total 



The variance of the population total is estimated from a sample drawn with PPSORT 

 by the expression— 



Var 7 = (Z?2 - Var b) TS + n TP 



in which 



b = 



a2= 



n 





n n 





Z 

 i=l 



Y. - 



^ 



(I Y./P.) I 

 t=l j=l 



P./n 



J 



n 





n 





Z 

 i=l 



P.2- 



% 



CEP. 

 J = l ' 





n 





n 





n 



n 



I (Y./P.)^ 

 t=l 



r E y./Pj2/n - [ E Y. - 

 j-1 ' ' i=l ^ 



( Z Y./P.) Z P./n] 

 i=l ^ ^ j = l 



n-2 



n n 

 Var b = a^/ Z P.2 - ( Z P.)'^/n 

 ^=l ^=l 



= probability with which the sample cluster of n units was selected 

 for measurement 



N = total number of units in the population to be sampled 



N n N n 



TS = 1 { 1 P ./n - 1 s . I P ./n)^ 



k=l ^ i=l ^ j=l ^ i=l 



N 



TP = 1 - Z s 2 

 k=l ^ 



The last two values are calculated by PPSORT. 



This expression is appropriate when the trend of Y„-/P^- is linear with respect to 

 P^. If the sample indicates that the trend is curvilinear, the variance will be over- 

 estimated unless the formula is modified as described in the following section. 



■^The factor {N-l)/N in Hartley's expression is replaced here by the exact value 

 (1 - ^s-,2) because it is readily available when PPSORT is used. 



4 



