R Program to Sample from a Population

R is a powerful and widely used programming language for statistical computing and data analysis. It provides a user-friendly ecosystem of R packages for various analytical tasks and is known for its flexibility and visualization capabilities. In R Programming Language It’s like a super-smart assistant for handling numbers and information what makes R really special is its knack for creating neat charts and graphs.

Sampling from a population is a fundamental technique in data science, allowing us to learn about large populations by studying smaller, more manageable samples. It’s very important in the era of big data, where it’s often impossible to collect and analyze data from every single individual or item in a population.

Population

In R language, “population” means you want all the data or individual items for a study. It means the whole group you want to learn about. For instance, if you’re studying the heights of all adult females in a city, that’s your population.

So, let’s focus on some basic key points that define the population more clearly.

• Includes Everyone: The population covers all the relevant people or things for the study. No one or nothing is left out. Understanding the population helps us set up rules, figure out sample size, and do statistical tests.
• Using Data Structures: Defining the population is important because it sets the boundaries for what your study will look at. In R, we represent the population using tools like lists, vectors, or data frames. This makes it easier to work with and analyze.
• Applied in Real World: Whether it’s studying animals, looking at economics, or anything else, defining the population is where it all begins.

In statistics, it’s often not feasible to collect data from an entire population, so you usually work with a sample, which is a subset of the population.

In R, there are various functions and packages that can help you work with populations and samples, depending on what specific analyses you’re interested in performing. Some common functions and packages for working with populations and samples in R include:

• sample(): This is a base R function used to generate random samples from a dataset.
• dplyr package: This package provides a suite of functions for data manipulation. Functions like filter(), select(), and group_by() can be used to work with specific subsets of your data.
• survey package: This package is used for analyzing complex survey data. It provides functions for working with populations that are sampled in a structured way.
• sampling package: This package provides functions for sampling from populations, and for calculating sample sizes and margins of error.

Sample

In R, a “sample” refers to a subset of data drawn from a larger dataset or population. This subset is selected randomly or according to specific criteria, and it is used for various purposes such as statistical analysis, modeling, and hypothesis testing.

• For example It’s like to get a sense of the average height without measuring every single females in the city , you might randomly select 200 adult females from various parts of the city. This smaller group represents the sample. The sample helps us build a conclusions about the whole population without having to study every single item.
• It’s important to note that a well-chosen sample should accurately represent the characteristics of the larger population.
• The primary function used for generating random samples in R is sample(). Here is the basic syntax of the sample() function.

sample(x, size, replace = FALSE, prob = NULL)

• x: The data from which to take the sample. This can be a vector or a set of elements.
• size: The number of samples you want to draw from x.
• replace: A logical value indicating whether sampling should be done with replacement. If set to TRUE, elements can be selected multiple times; if set to FALSE, each element can be selected at most once.
• prob: An optional vector of probabilities for each element in x. If provided, it determines the probability of each element being selected.

Simple Random Sampling

Simple Random Sampling is a fundamental technique in statistics for selecting a subset of individuals or items from a larger population.

In simple random sampling:

1. 1. Each individual or item in the population has an equal chance of being selected.
2. 2. The selection of each item is independently.

Perform Simple Random Sampling

• In simple random sampling, you usually don’t choose the same item more than once (no replacement).
• For example, in R, you might use the sample() function.

Example 1: Sampling data from a Vector

Let’s say you have a vector of ages of people in a community and you want to randomly select 5 ages for a survey.

R

# Create a vector of ages
ages <- c(25, 30, 35, 40, 45, 50, 55, 60, 65, 70)

# Perform simple random sampling of 5 ages
sampled_ages <- sample(ages, size = 5, replace = FALSE)

# Print the sampled ages
print(sampled_ages)

Output:

[1] 35 30 60 65 70

This code will randomly select 5 ages from the vector ages.

Example 2: Sampling data from a Lists

R

# Create a list of favorite colors
favorite_colors <- list("Red", "Blue", "Green", "Yellow", "Purple", "Orange")

# Convert the list into a vector
colors_vector <- unlist(favorite_colors)

# Perform simple random sampling of 2 colors
sampled_colors <- sample(colors_vector, size = 2, replace = FALSE)

# Print the sampled colors
print(sampled_colors)

Output:

[1] "Yellow" "Blue"  

We start with a list called favorite_colors containing various color names.

• We use the unlist() function to convert the list into a vector called colors_vector.
• Then, we perform simple random sampling on the vector to select 2 colors.
• Finally, we print the sampled colors.

Example 3: Sampling Using Data Frames (as a column)

R

# Create a sample data frame
employees <- data.frame(
  Name = c("John", "Jane", "Jim", "Jill", "Joe", "Janet"),
  Age = c(30, 35, 25, 40, 45, 28),
  Salary = c(50000, 60000, 45000, 70000, 80000, 55000)
)

# Perform simple random sampling of 2 employees
sampled_employees <- employees[sample(nrow(employees), size = 2,
                                      replace = FALSE), ]

# Print the sampled employees
print(sampled_employees)

Output:

   Name Age Salary
6 Janet  28  55000
5   Joe  45  80000