Notation
Number of first-stage strata: L
Number of second-stage strata in a primary sampling unit (PSU) i: Pi
Number of units in stratum h of the first stage: Nh
Number of units sampled in stratum h of the first stage: nh
Probability of selection of a first-stage unit:
Number of second-stage units in stratum j of PSU i: Mhij
Number of units sampled in stratum j of PSU i: mhij
Interest variable: yhijk
Total number of units in the population: Z
Formulae
1. Total of stratum h calculated from PSU i
2. An estimate of yh
is given by
and
3. An estimate of y is given by
and
Notation
Number of strata: L
Number of units in stratum h: Nh
Number of units sampled in stratum h: nh
Interest variable: yhi
Formulae
An estimate of y is given by
and
where
The final estimate for a total is simply the sum of the total of the area frame and of the total of the lists.
Similarly, the final variance estimate of a total is simply the sum of the variance of the area frame and the variance of the lists.
The average (for a given domain) for units in both the area frame and the lists is the total of the variable of interest over the estimated number of units in the domain.
The variance of an average (for a given domain) is the total variance of the variable of interest over the square of the estimated number of units in the domain.
The final estimate (area frame and list) for an average is simply the sum of the variable of interest totals over the sum of the estimated number of units in the domain.
The final estimate of the variance of an average is the sum of the variances of the variable of interest totals over the sum of the estimated number of units in the domain.