# S.STPPS: Stratified Sampling Applying PPS Design in all Strata In TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population

## Description

Draws a probability proportional to size simple random sample with replacement of size m_h in stratum h of size N_h

## Usage

 `1` ```S.STPPS(S,x,mh) ```

## Arguments

 `S` Vector identifying the membership to the strata of each unit in the population `x` Vector of auxiliary information for each unit in the population `mh` Vector of sample size in each stratum

## Details

The selected sample is drawn according to the cumulative total method (sequential-list procedure) in each stratum

## Value

The function returns a matrix of m=m_1+\cdots+m_h rows and two columns. Each element of the first column indicates the unit that was selected. Each element of the second column indicates the selection probability of this unit

## Author(s)

Hugo Andres Gutierrez Rojas hagutierrezro@gmail.com

## References

Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas.

`E.STPPS`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46``` ```############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # The auxiliary information x <- c(52, 60, 75, 100, 50) # Vector Strata contains an indicator variable of stratum membership Strata <- c("A", "A", "A", "B", "B") # Then sample size in each stratum mh <- c(2,2) # Draws a stratified PPS sample with replacement of size n=4 res <- S.STPPS(Strata, x, mh) # The selected sample sam <- res[,1] U[sam] # The selection probability of each unit selected to be in the sample pk <- res[,2] pk ############ ## Example 2 ############ # Uses the Lucy data to draw a stratified random sample # according to a PPS design in each stratum data(Lucy) attach(Lucy) # Level is the stratifying variable summary(Level) # Defines the sample size at each stratum m1<-70 m2<-100 m3<-200 mh<-c(m1,m2,m3) # Draws a stratified sample res<-S.STPPS(Level, Income, mh) # The selected sample sam<-res[,1] # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data) # The selection probability of each unit selected in the sample pk <- res[,2] pk ```