# Systematic Sampling in R (With Examples)

Researchers often take samples from a population and use the data from the sample to draw conclusions about the population as a whole.

One commonly used sampling method is systematic sampling, which is implemented with a simple two step process:

1. Place each member of a population in some order.

2. Choose a random starting point and select every nth member to be in the sample.

This tutorial explains how to perform systematic sampling in R.

## Example: Systematic Sampling in R

Suppose a superintendent wants to obtain a sample of 100 students from a school that has 500 total students. She chooses to use systematic sampling in which she places each student in alphabetical order according to their last name, randomly chooses a starting point, and picks every 5th student to be in the sample.

The following code shows how to create a fake data frame to work with in R:

#make this example reproducible
set.seed(1)

#create simple function to generate random last names
randomNames <- function(n = 5000) {
do.call(paste0, replicate(5, sample(LETTERS, n, TRUE), FALSE))
}

#create data frame
df <- data.frame(last_name = randomNames(500),
gpa = rnorm(500, mean=82, sd=3))

#view first six rows of data frame

last_name      gpa
1     GONBW 82.19580
2     JRRWZ 85.10598
3     ORJFW 88.78065
4     XRYNL 85.94409
5     FMDCE 79.38993
6     XZBJC 80.49061

And the following code shows how to obtain a sample of 100 students through systematic sampling:

#define function to obtain systematic sample
obtain_sys = function(N,n){
k = ceiling(N/n)
r = sample(1:k, 1)
seq(r, r + k*(n-1), k)
}

#obtain systematic sample
sys_sample_df = df[obtain_sys(nrow(df), 100), ]

#view first six rows of data frame

last_name      gpa
3      ORJFW 88.78065
8      RWPSB 81.96988
13     RACZU 79.21433
18     ZOHKA 80.47246
23     QJETK 87.09991
28     JTHWB 83.87300

#view dimensions of data frame
dim(sys_sample_df)

[1] 100   2

Notice that the first member included in the sample was in row 3 of the original data frame. Each subsequent member in the sample is located 5 rows after the previous member.

And from using dim() we can see that the systematic sample we obtained is a data frame with 100 rows and 2 columns.

## One Reply to “Systematic Sampling in R (With Examples)”

1. Louise Hoskin says:

Hi Zach, does this only work if your sample is a divisor of your data frame? i.e. I tried to use your code to take a sample of 49 students out of 500:

sys_sample_df = df[obtain_sys(nrow(df), 49), ]

And my last four rows were NA. I assume this is because there is a remainder in N/n, so in this case it selects every 11 students, but once it reaches the end of the dataframe it has only selected 45 students but needs more. It also would struggle if your sample was more than n/2 of your total size. I’ve written a rough while loop which basically continually samples until you hit your desired sample size, but I’m sure there could be a much neater way:

set.seed(1)

#create simple function to generate random last names
randomNames <- function(n = 5000) {
do.call(paste0, replicate(5, sample(LETTERS, n, TRUE), FALSE))
}

#create data frame
df <- data.frame(last_name = randomNames(500),
gpa = rnorm(500, mean=82, sd=3))

#view first six rows of data frame

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

#Total sample size
N_tot = 500
#Desired sample
n_samp = 49
#Run initial sample
sys_sample_df <- df[obtain_sys(N_tot, n_samp), ]
#Remove any duplicates and NAs
sys_sample_df <- sys_sample_df[!duplicated(sys_sample_df\$last_name),]
sys_sample_df <- sys_sample_df[!is.na(sys_sample_df\$last_name),]

while(length(unique(sys_sample_df\$last_name))<n_samp){
df2 <- df[which(!df\$last_name %in% sys_sample_df\$last_name), ]
#redefine samples and total
N_tot2 <- N_tot – length(unique(sys_sample_df\$last_name))
n_samp2 <- n_samp – length(unique(sys_sample_df\$last_name))

#Run sample again
sys_sample_df2 = df2[obtain_sys(N_tot2, n_samp2), ]

#Remove any duplicates and NAs
sys_sample_df2 <- sys_sample_df2[!duplicated(sys_sample_df2\$last_name),]
sys_sample_df2 <- sys_sample_df2[!is.na(sys_sample_df2\$last_name),]

#Join together samples
sys_sample_df <- rbind(sys_sample_df, sys_sample_df2)
}