# ss2s4p: Sample Sizes in Two-Stage sampling Designs for Estimating... In samplesize4surveys: Sample Size Calculations for Complex Surveys

## Description

This function computes a grid of possible sample sizes for estimating single proportions under two-stage sampling designs.

## Usage

 1 ss2s4p(N, P, conf = 0.95, delta = 0.03, M, to = 20, rho) 

## Arguments

 N The population size. P The value of the estimated proportion. conf The statistical confidence. By default conf = 0.95. delta The maximun margin of error that can be allowed for the estimation. M Number of clusters in the population. to (integer) maximum number of final units to be selected per cluster. By default to = 20. rho The Intraclass Correlation Coefficient.

## Details

In two-stage (2S) sampling, the design effect is defined by

DEFF = 1 + (\bar{m}-1)ρ

Where ρ is defined as the intraclass correlation coefficient, \bar{m} is the average sample size of units selected inside each cluster. The relationship of the full sample size of the two stage design (2S) with the simple random sample (SI) design is given by

n_{2S} = n_{SI}*DEFF

## Value

This function returns a grid of possible sample sizes. The first column represent the design effect, the second column is the number of clusters to be selected, the third column is the number of units to be selected inside the clusters, and finally, the last column indicates the full sample size induced by this particular strategy.

## Author(s)

Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>

## References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

ICC
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 ss2s4p(N=100000, P=0.5, delta=0.05, M=50, rho=0.01) ss2s4p(N=100000, P=0.5, delta=0.05, M=500, to=40, rho=0.1) ss2s4p(N=100000, P=0.5, delta=0.03, M=1000, to=100, rho=0.2) ############################ # Example 2 with Lucy data # ############################ data(BigLucy) attach(BigLucy) N <- nrow(BigLucy) P <- prop.table(table(SPAM))[1] y <- Domains(SPAM)[, 1] cl <- Segments rho <- ICC(y,cl)\$ICC M <- length(levels(Segments)) ss2s4p(N, P, conf=0.95, delta = 0.03, M=M, to=30, rho=rho)