# Systematic Random Sampling in R with Example

Systematic Random Sampling, researchers frequently gather samples from a population and use the findings to derive conclusions about the entire population.

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## Systematic Random Sampling

Systematic sampling is a widely used sampling approach that involves a simple two-step procedure.

1. Sort the members of a population into some sort of order.

2. Select every nth member to be included in the sample from a random beginning point.

This article will show you how to use R to perform systematic sampling.

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### Approach: Systematic Sampling in R

Assume a CEO wishes to gather a sample of 100 employees from a company with a total workforce of 800.

He opts for systematic sampling, in which he arranges each employee alphabetically by the last name, selects a random beginning point, and selects every eighth employee to be included in the sample.

The following code demonstrates how to generate a fictitious data frame in R.

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Let’s make this a repeatable example.

set.seed(123)

We can now make a basic function that generates random last names.

rnames <- function(n = 5000) {do.call(paste0, replicate(5, sample(LETTERS, n, TRUE), FALSE))}

Now we can create a data frame

data<-data.frame(lastname = rnames(800),score = rnorm(800, mean=68, sd=2.4))

Let’s view the first six rows of the data frame.

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head(data)

lastname score 1 OKGCZ 68.54907 2 SXKBR 68.19697 3 NKUCC 69.64463 4 CDAAI 65.27310 5 JGSHK 68.92277 6 RXHZT 69.18259

The following code demonstrates how to use systematic sampling to obtain a sample of 100 students:

To obtain a systematic sample, define a function.

getsys = function(N,n){ k = ceiling(N/n) r = sample(1:k, 1) seq(r, r + k*(n-1), k) }

To obtain a systematic sample

systsample<- data[getsys(nrow(data), 100), ]

Now we can view the first six rows of the data frame.

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head(systsample)

lastname score 7 VRQCQ 66.57763 15 EJXCD 70.10791 23 GMVDS 66.85846 31 GMXRE 64.73415 39 ILJZI 72.58693 47 BQNTY 63.32294

Okey, view dimensions of the data frame.

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dim(systsample) [1] 100 2

## Conclusion

It’s worth noting that the sample’s first member was in row 7 of the original data frame. The next member of the sample is 8 rows after the previous one.

We can observe that the systematic sample we got is a data frame with 100 rows and 2 columns by using dim().