Ratio Estimators -2148142

    Ratio estimation  

2148142-Rakshana V

In a survey , if there is a correlation between a auxiliary variable and the variable under study in a bivariate data , the method of ratio estimation and regression estimation is used to estimate the values of mean of the variable under study. 

Let Y be the variable under study and X be an auxiliary variable which is correlated with Y . The

observations  on X and  on Y are obtained for each sampling unit.

The population mean of both the variables X and Y must be known given by  and . 

R = Y/X =  the ratio of the population totals or means of character y and x .

 

The variance of the estimate is given by

In the other methods of estimation ,we ensure that the estimators used are unbiased but in case of ratio estimator it is used even though it is a biased method as it is more efficient

The bias of the ratio is given by

                  

The confident limits of R is obtained using

 Merits and demerits of ratio estimators

Merits

1. It is simple and convenient to use.

2.It is more efficient than simple random sampling method of estimation.

3.the aggregate value can be used, which is not possible in case of stratified random sampling and regression method of estimation

Demerits

1.It is a biased estimator.

2.It is less efficient method compared to regression estimator

3. It is applicable only when data is correlated

R analysis

The data considered here for analysis is data consisting of 2 variables perfememployee and perFemEmployer which is explained as

PerFemEmployee
Employment to population ratio (%) of women who are of age 15 or older. Employment to population ratio is the proportion of a country's population that is employed. Employment is defined as persons of working age who, during a short reference period, were engaged in any activity to produce goods or provide services for pay or profit, whether at work during the reference period (i.e. who worked in a job for at least one hour) or not at work due to temporary absence from a job, or to working-time arrangements. Ages 15 and older are generally considered the working-age population.

PerFemEmployers
Employers, female (% of female employment). Employers are those workers who, working on their own account or with one or a few partners, hold the type of jobs defined as a "self-employment jobs" i.e. jobs where the remuneration is directly dependent upon the profits derived from the goods and services produced), and, in this capacity, have engaged, on a continuous basis, one or more persons to work for them as employee(s).

library(readxl)
Female_employment_data <- read_excel("A:/Female employment data.xlsx")
data <- Female_employment_data
attach(data)
str(data)

## tibble [25 x 2] (S3: tbl_df/tbl/data.frame)
##  $ PerFemEmploy   : num [1:25] 24.3 24.6 24.8 25.1 25.4 ...
##  $ PerFemEmployers: num [1:25] 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.11 0.11 0.11 ...

plot(PerFemEmploy,PerFemEmployers)

cor(PerFemEmploy,PerFemEmployers)

## [1] 0.8865423

library(survey)

## 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(SDaA)
l=svydesign(ids = ~1,weights = ~1,data=data)

RATIO ESTIMATOR

svyratio(~PerFemEmploy,~PerFemEmployers,design = l)

## Ratio estimator: svyratio.survey.design2(~PerFemEmploy, ~PerFemEmployers, design = l)
## Ratios=
##              PerFemEmployers
## PerFemEmploy        140.9409
## SEs=
##              PerFemEmployers
## PerFemEmploy        23.20984

X_bar = sum(PerFemEmployers)/25
X_bar

## [1] 0.1964

Y_bar_est = X_bar*140.9409
Y_bar_est

## [1] 27.68079

SE_ratio=23.20984
SE_Ybar=SE_ratio*X_bar
SE_Ybar

## [1]

t=qt(0.975,21-1)
t

## [1] 2.085963

LL=Y_bar_est-t*SE_Ybar
LL ## Lower Limit

## [1] 18.17211

UL=Y_bar_est+t*SE_Ybar
UL ## Upper Limit

## [1] 37.18947

 The data considered for analysis  is  highly correlated .

The ratio estimate as 140.9409 with a standard error of  23.20984 . The estimate of the mean of perfememployee data is 27.68079   with the standard error estimate of  4.558413 . The 95% confidence interval is [18.17211,37.18947].