2006 HCSDB Adult Sampling Report - Tricare

(G.4).96042n= B1 ⎛ .96041+ ⎜2N ⎝ B⎞⎟⎠where .9604 was obtained from z.975 P (1- P) with P = 0.5. The formula (G.4) can then beapplied to determine the sample size to achieve B in estimating stratum-level estimates.Recall that the 2006 HCSDB employs a stratified sample design. Since we wish to estimate theproportion of beneficiaries from domain d having a certain characteristic. An estimate of theproportion Pd can be obtained as the weighted sum of stratum-level proportion estimates:(G.5)pd=NHdh∑ p ,dhh=1 Ndwhere N dh is the population size of domain d for stratum h, Ndis the sum of N dh over all strata,and p is the estimated proportion for the h-th stratum. Since the sampling is independentdhacross strata, the variance of estimated proportion p dis the sum of stratum-level variances:(G.6)Vd=⎛--2⎛h h h hN h ⎞ N n P (1- P )∑⎜⎟h∈d⎝d⎠⎜ ⎟ n hhN N 1⎝⎞⎠where nh is the sample size in stratum h and Ph is the stratum-level proportion for stratum h.Like the single stratum case, all stratum-level proportions are assumed with 0.5, and thus theformula (G.6) can be reduced to the following:(G.7)Vd=2⎛h hN h ⎞ ⎛ N - n ⎞.∑⎜⎟h∈d⎝d⎠⎜ ⎟h h-N N 1 n⎝⎠25The minimum sample size satisfying the requirements for a predetermined half-length interval Bdis:(G.8)n⎛ N h N⎞h⎜∑Ph(1- Ph)⎟⎝ N N - 1⎠B 1 ⎞+ Ph(1- Ph)- 1⎟⎝ ⎠h∈dd hd =22d N h ⎛2 ∑ 2 ⎜z1- α /2 h∈dNd N h2G-2