Notations of Survey Data

Suppose in a complex survey with H strata and t_h selected PSUs in stratum h for h = 1,...,H, a total of n_hα individual records are sampled from the α^th PSU for α = 1,...t_h in the h^th stratum.  Therefore, the total sample size is

$$n={\sum}_{h=1}^H{\sum}_{\alpha=1}^{t_{h}}n_{h\alpha}.$$

Assume there are \(J\) mutually exclusive social groups in the population with \(J\geq2\).  Let p_j be the population share in group j and μ_j be the average health status in group j  for j = 1,...,J.

Let y_hαi be the health status for individual i in the α_th PSU in the h^th stratum, w_hαi  be the survey weight value for individual i in the α^th PSU in the h^th stratum and \(\delta_{h{\alpha}i}^{j}{\in}(0,1)\) be the membership indicator (=1 if individual-hαi belongs to group j; 0 otherwise).