Sample from a Population Using R

Sampling from a population is a critical technique in statistics and data analysis. It allows you to draw conclusions about a large group (the population) by examining a smaller, representative subset (the sample). In R, you can easily perform random sampling to obtain a sample from a population, which is useful for various applications such as hypothesis testing, data visualization, and model building.

Key Functions for Sampling in R:

• sample(): The sample() function is the most commonly used function for random sampling in R. It can be used to sample from vectors, data frames, and lists.

• replicate(): The replicate() allows you to repeat a sampling process a specified number of times and store the results in a list.

Concepts Related to the sampling from a population:

• Population: The whole gathering of interest that you need to study or examine.

• Sample: A subset of the population that is chosen for investigation.

• Random Sampling: A course of choosing people or things from a population so that every individual from the population has an equivalent possibility of being remembered for the sample.

• Sample Size: The quantity of components in the sample.

• With Replacement vs. Without Replacement: In sampling, you can decide to either permit chosen things to be returned to the population (with replacement) or not (without replacement).

Steps Needed:

To create an R program for random sampling, follow these steps:

• Load the necessary R libraries (e.g., dplyr or base).
• Define the population, either as a vector or a data frame.
• Specify the sample size.
• Use a random sampling function (e.g., sample()) to draw a sample from the population.
• Analyze or visualize the sample as needed.

Sampling with Replacement:

When you sample with replacement, each selected item is returned to the population before the next item is drawn. In R, you can specify this behavior using the replace argument in the sample() function.

1. Sampling from a Vector:

R

#Create a vector of data
population_vector <- c(10, 20, 30, 40, 50)

#Sample 3 values with replacement
sampled_vector <- sample (population_vector, size = 3, replace = TRUE)
print (sampled_vector)

Output

[1] 50 20 50

In this example, we sample three values with replacement from the population_vector, which contains numbers from 10 to 50. In the output, the code randomly selected the values 50, 20, and 50 from the population_vector, and it’s possible to see that the value 50 appears twice because replacement is allowed (replace = TRUE). This demonstrates that in sampling with replacement, the same value can be selected multiple times in the sample. In summary, the code showcases how to perform random sampling with replacement from a vector in R, which can be useful in various statistical and simulation scenarios.

2. Sampling from a Data Frame:

R

# Create a data frame
population_df <- data.frame(
  Name = c("Alice", "Bob", "Charlie", "David", "Eve"),
  Age = c(25, 30, 35, 40, 45)
)

# Sample 2 rows with replacement
sampled_df <- population_df[sample(nrow(population_df), size = 2, replace = TRUE), ]
print(sampled_df)

Output

     Name Age
1   Alice  25
1.1 Alice  25

In this example, we sample two rows with replacement from the population_df, a data frame containing names and ages. In the output, the code randomly selected the row with “Alice” and an age of 25 twice because replacement is allowed (replace = TRUE). This demonstrates that in sampling with replacement, the same row can be selected multiple times in the sample. In summary, the code illustrates how to perform random sampling with replacement from a data frame in R, which can be useful when you want to generate a random subset of rows from a dataset for analysis or simulation purposes.

3. Sampling from a List:

R

# Create a list
population_list <- list(
  fruits = c("Apple", "Banana", "Cherry", "Date"),
  colors = c("Red", "Yellow", "Red", "Brown")
)

# Sample 4 elements from the 'fruits' list with replacement
sampled_list <- sample(population_list$fruits, size = 4, replace = TRUE)
print(sampled_list)

Output

[1] "Apple"  "Cherry" "Apple"  "Date" 

Here, we sample four elements with replacement from the ‘fruits’ list within the population_list. In this example, the code randomly selected “Apple” , “Cherry”, “Apple” and “Date” from the ‘fruits’ list. Since replacement is allowed (replace = TRUE), “Apple” appears twice in the output, demonstrating that the same element can be selected multiple times in a sample. In summary, the code illustrates how to sample elements from a specific list in R within a larger list, considering whether or not replacement is allowed during the sampling process.

4. Replicating Sampling:

R

# Define a population vector
population_vector <- c(10, 20, 30, 40, 50, 60, 70, 80, 90, 100)

# Replicate sampling 5 times without replacement
replicated_samples <- replicate(5, sample(population_vector, size = 3, replace = FALSE))

# Print the replicated samples
print(replicated_samples)

Output

   [,1] [,2] [,3] [,4] [,5]
[1,]   60   80   50   90   10
[2,]   80   20  100   70  100
[3,]   10   10   60   60   20

In this example We define a population vector population_vector containing ten numbers. We use replicate(5, …) to replicate the sampling process five times. Inside the replicate() function, we use sample() to randomly select 3 items from the population_vector without replacement for each replication. The replicated_samples matrix will contain five columns, each representing a separate replication of sampling. Each row within a column will contain three unique numbers randomly selected from the population vector.

Sampling without replacement

1. Sampling from a vector without replacement

R

# Sampling from a vector without replacement
items <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
sample_size <- 5
sample <- sample(items, size = sample_size, replace = FALSE)
print(sample)

Output

[1] 3 5 6 9 8

In this example, we have a vector items containing numbers from 1 to 10. We want to randomly select 5 unique numbers from this vector without allowing any number to be repeated within the sample. The sample() function is used with replace = FALSE to achieve this. The output will be a list of 5 unique numbers, representing a random sample drawn from the items vector. This output demonstrates the concept of selecting a subset of items from a population without replacement.

2. Shuffling a deck of cards (52 cards) without replacement

R

deck <- 1:52
shuffled_deck <- sample(deck, size = length(deck), replace = FALSE)
hand_size <- 5
hand <- shuffled_deck[1:hand_size]
print(hand)

Output

[1]  9 34 41 43 11

In this example, we simulate shuffling a standard deck of 52 playing cards. The deck is represented as numbers from 1 to 52, with each number corresponding to a unique card. We use the sample() function with replace = FALSE to shuffle the deck randomly, ensuring that no card is duplicated in the process. After shuffling, we take the first 5 cards to simulate drawing a random hand. The output will be a list of 5 unique numbers, representing the randomly selected cards in your hand. This example illustrates the concept of shuffling a deck of cards and drawing a random hand without replacement.

Random sampling using the dplyr package

The dplyr package is a well known R package for data manipulation and transformation. It gives a bunch of functions that make it simpler to work with data casings and data tables in R. One common undertaking in data analysis is random sampling, which can be accomplished using the sample_n() and sample_frac() functions in dplyr.

1: Randomly Sampling Rows from a Data Frame

In this code, we’ll randomly sample a specified number of rows from a data frame.

R

# Load the dplyr package
library(dplyr)

# Create a sample data frame
# Set seed for reproducibility
set.seed(123)
data <- data.frame(
  ID = 1:100,
  Value = rnorm(100)
)

# Randomly sample 10 rows from the data frame
sampled_data <- data %>%
  sample_n(10)

# View the sampled data
print(sampled_data)

Output

   ID      Value
1   7  0.56047565
2   9 -0.23017749
3  15  1.55870831
4  16  0.07050839
5  20  1.71506598
6  23 -0.68685285
7  42  1.78691314
8  46  1.06782371
9  50  0.49850701
10 68 -0.29472045

In this code, we first load the dplyr package and create a sample data frame called data. We then use the sample_n() function to randomly sample 10 rows from the data frame and store the result in the sampled_data variable.

2: Random Sampling a Fraction of Rows from a Data Frame

In this code, we’ll randomly sample a specified fraction of rows from a data frame.

R

# Load the dplyr package
library(dplyr)

# Create a sample data frame
# Set seed for reproducibility
set.seed(456)
data <- data.frame(
  ID = 1:200,
  Value = rnorm(200)
)

# Randomly sample 20% of the rows from the data frame
sampled_data <- data %>%
  sample_frac(0.20)

# View the sampled data
print(sampled_data)

Output

      ID        Value
1  151  1.200410172
2  140 -0.181812198
3   88  0.920529800
4   68 -1.431378346
5  191 -0.697237001
6   27 -0.462854969
7   75 -0.020014663
8   90 -0.236867797
9   46  0.120851803
10  71 -0.169987994
11 163 -1.035274763
12  62 -0.982060062
13 175 -1.549384356
14  85  0.708817307
15 174  0.309910662
16 119 -1.433778349
17  49 -1.175402402
18 126 -1.126327533
19  69 -0.544594202
20 130  0.355610384
21 193  1.232308978
22  36  1.815652319
23  60  0.577150467
24 132  1.149194486
25 118  1.207347447
26  42  0.393037377
27 131  0.004052138
28 167  1.772544877
29 181 -1.388188492
30  45  2.078874614
31  17  1.736936177
32  77 -0.112933852
33  26  1.134284565
34 124  0.313843454
35 133 -0.496614335
36  83  2.020634788
37  35  0.170625252
38 197 -0.196112610
39 116  0.982940735
40 149  1.210757937

In this code, we again load the dplyr package and create a sample data frame called data. We use the sample_frac() function to randomly sample 20% of the rows from the data frame and store the result in the sampled_data variable.

Conclusion

Sampling from a population is a fundamental task in statistics and data analysis, and R provides powerful tools to make this process easy and efficient. In this article, we explored how to use R to sample from a population, whether it’s a simple vector of data or a more complex scenario like shuffling a deck of cards or simulating lottery draws. We discussed the importance of specifying whether sampling should be done with or without replacement, as it can significantly impact the results.

Sampling allows us to draw representative subsets of data, perform simulations, and make informed decisions based on a sample’s characteristics. Whether you’re conducting statistical analysis, running simulations, or simply selecting random elements, R’s built-in functions like sample() and replicate() provide the flexibility and precision needed to carry out these tasks efficiently.