Circular Systematic Sampling

                                Circular Systematic sampling

                                                                              C.Sruti

Systematic sampling is selecting samples in a systematic order. It is the implementation of  probability sampling where a value is selected at regular interval to make a sample. 

types of systematic sampling are

-systematic random sampling

-linear systematic sampling

-circular systematic sampling

Circular Systematic Sampling

In the circular systematic sampling, for the population size N  and sample size n, the interval is taken as k which is obtained by dividing the population size by sample size [N/n =k]. Here from a random starting point for every k interval period a value is selected. The process is continued till selecting all the values of the sample.

Example:

let the sample size be 4, the total population size is 15

now, the k value is 15/4= 3.75, we take k as 3

As starting randomly the sample is 3, 6, 9, 12. 

 

• Steps to select sample using circular systematic sampling method:

• Step 1: The population N units should be arranged as U1, U2, …, UN around a circle.

• Step 2: A random number k should be selected such that 1<=k<=N.

• Step 3: For selecting a circular systematic sample of size n, select every ith element from the random start k in the circle until n elements are accumulated.

Let the selected units Ui, Uk + i, Uk + 2i, …, Uk+ (n − 1)i be the circular systematic sample of size n for the random start r. If k + ji > N, then select an item corresponding to  If  then unit N is selected.

The variance of the circular systematic sample mean is obtained as given below:

Difference between linear systematic and circular systematic sampling 

 

Linear systematic sampling	Circular systematic sampling
Create samples with sampling interval.	Create samples with total population.
Start and end points are distinct.	It is randomly started and there is no particular end point.
All units of population are arranged in linear format for selection.	All units of population are arranged in circular format for selection.

 

Circular systematic sampling in R

```{r}

# defines the inclusion probabilities for the population

pik=c(0.2,0.7,0.8,0.5,0.4,0.4)

# X is the population data frame

X=cbind.data.frame(pik,c("A","B","A","A","C","B"))

names(X)=c("Prob","town")

# selects a sample using circular systematic sampling

#42 rhg_strata

s=UPsystematic(pik)

# Xs is the sample data frame

Xs=getdata(X,s)

Xs

```

In the above example we have taken prob and town and we have drawn a  sample of size 3, using circular systematic sample in R studio. From the analysis we can understand that circular systematic sampling can be used in many conditions for example in real life for getting the values in a trend, for analysis of price of a commodity etc.