Stratified Random Sampling -Optimum Allocation

 


                 STRATIFIED RANDOM SAMPLING 

                           Optimum Allocation

November 30,2020

Varsha Joshy

2048141

 

Definition of stratified random sampling

 Stratified random sampling  is a method of sampling that involves dividing a population into smaller groups–called strata. The groups or strata are organized based on the shared characteristics or attributes of the members in the group. The process of classifying the population into groups is called stratification. Stratified random sampling is also known as quota random sampling and proportional random sampling.  

 Optimal Allocation

Optimal allocation is a procedure for dividing the sample among the strata in a stratified sample survey. The allocation procedure is called "optimal" because in a particular survey sampling design (stratified simple random sampling) it produces the smallest variance for estimating a population mean and total (using the standard stratified estimator) given a fixed budget or sample size.

 

The number of samples selected from each stratum is proportional to the size, variation, as well as the cost (ci ) of sampling in each stratum. More sampling effort is allocated to larger and more variable strata, and less to strata that are more costly to sample



where k indexes the L strata.

If Ci’s are the same from stratum to stratum , the aboue equation leads to Neyman allocation. Similarly if Ci’s and Si’s do not vary from stratum to stratum it will lead to proportional allocation.


Advantages

 

1.     If measurements within strata have lower standard deviation, stratification gives smaller error in estimation.

2.     For many applications, measurements become more manageable and/or cheaper when the population is grouped into strata.

3.     It is often desirable to have estimates of population parameters for groups within the population.

Disadvantages

Stratified sampling is not useful when the population cannot be exhaustively partitioned into disjoint subgroups. It would be a misapplication of the technique to make subgroups' sample sizes proportional to the amount of data available from the subgroups, rather than scaling sample sizes to subgroup sizes. The knowledge of ( 1,2,..., ) i Si k = is needed to know i n . If there are more than one characteristics, then they may lead to conflicting allocation.

 R code

 

This Dataset Describes the agriculture Crops Cultivation/Production in India.  This Dataset can solves the problems of various crops Cultivation/production in india.

 

library(samplingbook)

data4 <- read.csv("~/data4.csv", header=FALSE)
data4

stratum1=data4[data4$V1=="COTTON",]
stratum2=data4[data4$V1=="MAIZE",]

N1=sum(data4$V1=="COTTON")

S1=sqrt(var(stratum1$V6))

N2=sum(data4$V1=="MAIZE")
S2=sqrt(var(stratum2$V6))

#determination of sample size using optimum allocation
stratasize(e=.1, Nh=c(N1,N2), Sh=c(S1,S2), type = "opt" )

##
## stratamean object: Stratified sample size determination
##
## type of sample: opt
##
## total sample size determinated: 9

The total sample size determined is 9

A real-world example of using stratified sampling would be for a political survey. If the respondents needed to reflect the diversity of the population, the researcher would specifically seek to include participants of various minority groups such as race or religion, based on their proportionality to the total population as mentioned above. A stratified survey could thus claim to be more representative of the population than a survey of simple random sampling or systematic sampling.

 


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