Stata requires that there be a single fpc value in each stratum, so your "6 different fpc values" wouldn't work-you have only one stratum for the first stage
PSUs. Ouyang, Schreuder, and Boes (1997) suggest that \(fpc = (1-\dfrac{n}{N)}\) is a conservative compromise for a single stage sample. I recommend that you use that at each stage. So: 6/11 at Stage 1 and so on. Luckily it will make little difference because the two choices at each stage have similar values.
Reference:
Ouyang, Z., Schreuder, H. T., & Boes, D. C. (1997). Finite population corrections of the Horvitz-Thompson estimator and their application in estimating the variance of regression estimators. USDA Forest Service Research Paper, RM-RP-329
PSUs. Ouyang, Schreuder, and Boes (1997) suggest that \(fpc = (1-\dfrac{n}{N)}\) is a conservative compromise for a single stage sample. I recommend that you use that at each stage. So: 6/11 at Stage 1 and so on. Luckily it will make little difference because the two choices at each stage have similar values.
Reference:
Ouyang, Z., Schreuder, H. T., & Boes, D. C. (1997). Finite population corrections of the Horvitz-Thompson estimator and their application in estimating the variance of regression estimators. USDA Forest Service Research Paper, RM-RP-329
