# T.SIC: Computation of Population Totals for Clusters In damarals/TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population

## Description

Computes the population total of the characteristics of interest in clusters. This function is used in order to estimate totals when doing a Pure Cluster Sample.

## Usage

 `1` ```T.SIC(y,Cluster) ```

## Arguments

 `y` Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample `Cluster` Vector identifying the membership to the cluster of each unit in the selected sample of clusters

## Value

The function returns a matrix of clusters totals. The columns of each matrix correspond to the totals of the variables of interest in each cluster

## Author(s)

Hugo Andres Gutierrez Rojas hugogutierrez@usantotomas.edu.co

## 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.

`S.SI, E.SI`
 ``` 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 47 48``` ```############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector y1 and y2 are the values of the variables of interest y1<-c(32, 34, 46, 89, 35) y2<-c(1,1,1,0,0) y3<-cbind(y1,y2) # Vector Cluster contains a indicator variable of cluster membership Cluster <- c("C1", "C2", "C1", "C2", "C1") Cluster # Draws a stratified simple random sample without replacement of size n=3 T.SIC(y1,Cluster) T.SIC(y2,Cluster) T.SIC(y3,Cluster) ######################################################## ## Example 2 Sampling and estimation in Cluster smapling ######################################################## # Uses Lucy data to draw a clusters sample according to a SI design # Zone is the clustering variable data(Lucy) attach(Lucy) summary(Zone) # The population of clusters UI<-c("A","B","C","D","E") NI=length(UI) # The sample size nI=2 # Draws a simple random sample of two clusters samI<-S.SI(NI,nI) dataI<-UI[samI] dataI # The information about each unit in the cluster is saved in Lucy1 and Lucy2 data(Lucy) Lucy1<-Lucy[which(Zone==dataI),] Lucy2<-Lucy[which(Zone==dataI),] LucyI<-rbind(Lucy1,Lucy2) attach(LucyI) # The clustering variable is Zone Cluster <- as.factor(as.integer(Zone)) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) Ty<-T.SIC(estima,Cluster) # Estimation of the Population total E.SI(NI,nI,Ty) ```