R Code for Simple Random Sampling with Replacement

Installing Packages

#install.packages("survey")
#install.packages("sampling")
#install.packages("writexl")

Loading Packages

library(readxl)

## Warning: package 'readxl' was built under R version 4.5.3

library(survey)

## Warning: package 'survey' was built under R version 4.5.3

## Loading required package: grid

## Loading required package: Matrix

## Loading required package: survival

## 
## Attaching package: 'survey'

## The following object is masked from 'package:graphics':
## 
##     dotchart

library(sampling)

## Warning: package 'sampling' was built under R version 4.5.3

## 
## Attaching package: 'sampling'

## The following objects are masked from 'package:survival':
## 
##     cluster, strata

Reading Data

base<-readRDS(file = "Marco.rds")

Creating the Bogotá Dataset

base_bogota<-subset(base,base$COLE_COD_MCPIO_UBICACION==11001)

Creating the Academic School Variable

base_bogota$academico=ifelse(base_bogota$COLE_CARACTER=="ACADÉMICO",1,0)

Sample Size Calculation

tipo="p"
N=nrow(base_bogota)
alpha=0.05
p=0.5
e=0.05
deff=2

n.mas=function(tipo,N,s,e,p,alpha){
  if(tipo=="t"){n=round((qnorm(1-alpha/2)^2*N^2*s^2)/(e^2+qnorm(1-alpha/2)^2*N*s^2),0)}
  if(tipo=="t"){return(n)}
  if(tipo=="m"){n=round((qnorm(1-alpha/2)^2*s^2)/(e^2+(qnorm(1-alpha/2)^2*s^2/N)),0)}
  if(tipo=="m"){return(n)}
  if(tipo=="p"){n=round((qnorm(1-alpha/2)^2*(N/(N-1))*p*(1-p))/(e^2+(qnorm(1-alpha/2)^2*(N/(N-1))*p*(1-p)*(1/N))),0)
  if(tipo=="p"){return(n)}
  }}
  
  
r<-n.mas(tipo,N,s,e,p,alpha)*deff

Sample Selection

s.masr=function(base,r,seed){
  N=nrow(base)
  set.seed(seed)
  base=base[sample(c(1:nrow(base_bogota)),r,replace = T),]
  base$pik=1-(1-1/N)^r
  return(base)
}

r=764
seed=123
N=nrow(base_bogota)
muestra.r=s.masr(base_bogota,r,seed)

Creating the “dsgn” Objec

 muestra.r$Fexp=1/muestra.r$pik
 
dsgn=svydesign(id=~1,data=muestra.r,weights=~Fexp)

Estimation of the total number of academic schools in Bogotá

salida=function(est,alpha){
    est=as.data.frame(est)
    names(est)[2]="se"
    est$cv=100*(est$se/est[,1])
    est$ic_low=est[,1]-qnorm(1-alpha/2)*est$se 
    est$ic_upp=est[,1]+qnorm(1-alpha/2)*est$se
    return(round(est,2))
  }
   
   (est.r=svytotal(~academico,dsgn,deff=T)) 

##             total      SE   DEff
## academico 69381.4  1121.5 1.0093

  alpha=0.05
  (tabla=salida(est.r,alpha)) 

##              total      se deff   cv   ic_low   ic_upp
## academico 69381.38 1121.53 1.01 1.62 67183.21 71579.55

Global Average Score Estimation

(est1.r=svymean(~PUNT_GLOBAL,dsgn,deff=T))

##                 mean       SE   DEff
## PUNT_GLOBAL 265.4411   1.6835 1.0093

 (tabla=salida(est1.r,alpha))

##               mean   se deff   cv ic_low ic_upp
## PUNT_GLOBAL 265.44 1.68 1.01 0.63 262.14 268.74

Estimation of the Proportion

(est2.r=svymean(~DESEMP_INGLES,dsgn,deff=T))

##                      mean        SE   DEff
## DESEMP_INGLESA- 0.3062827 0.0166875 1.0093
## DESEMP_INGLESA1 0.3311518 0.0170379 1.0093
## DESEMP_INGLESA2 0.2290576 0.0152132 1.0093
## DESEMP_INGLESB+ 0.0261780 0.0057802 1.0093
## DESEMP_INGLESB1 0.1073298 0.0112058 1.0093

   (tabla=salida(est2.r,alpha))

##                 mean   se deff    cv ic_low ic_upp
## DESEMP_INGLESA- 0.31 0.02 1.01  5.45   0.27   0.34
## DESEMP_INGLESA1 0.33 0.02 1.01  5.15   0.30   0.36
## DESEMP_INGLESA2 0.23 0.02 1.01  6.64   0.20   0.26
## DESEMP_INGLESB+ 0.03 0.01 1.01 22.08   0.01   0.04
## DESEMP_INGLESB1 0.11 0.01 1.01 10.44   0.09   0.13

Parameter Estimation for Multiple Variables

(est3.r=svymean(~PUNT_GLOBAL+PUNT_LECTURA_CRITICA+PUNT_MATEMATICAS+PUNT_C_NATURALES+
                    PUNT_SOCIALES_CIUDADANAS+PUNT_INGLES,dsgn))

##                             mean     SE
## PUNT_GLOBAL              265.441 1.6835
## PUNT_LECTURA_CRITICA      55.577 0.3389
## PUNT_MATEMATICAS          54.719 0.3861
## PUNT_C_NATURALES          51.563 0.3586
## PUNT_SOCIALES_CIUDADANAS  50.157 0.4217
## PUNT_INGLES               54.051 0.4346

  (tabla=salida(est3.r,alpha))

##                            mean   se   cv ic_low ic_upp
## PUNT_GLOBAL              265.44 1.68 0.63 262.14 268.74
## PUNT_LECTURA_CRITICA      55.58 0.34 0.61  54.91  56.24
## PUNT_MATEMATICAS          54.72 0.39 0.71  53.96  55.48
## PUNT_C_NATURALES          51.56 0.36 0.70  50.86  52.27
## PUNT_SOCIALES_CIUDADANAS  50.16 0.42 0.84  49.33  50.98
## PUNT_INGLES               54.05 0.43 0.80  53.20  54.90