Simple random sampling is fundamental to collecting unbiased population data in research and statistical analysis. This method entails selecting individuals or items from a larger population in a random manner. To ensure choosing every item has an equal chance.

In this blog, we will understand the definition, formula, examples, and types of simple random sampling and explore why it is a valuable tool in research.

## What is Simple Random Sampling?

Simple random sampling is a statistical technique that selects a sample from a larger population with an equal chance of selection. In simple random sampling, we assign a unique number to every individual or item in the population. We randomly select a subset of these values to create the sample from the assigned numbers.

Scientific investigations use this sampling technique since it guarantees accuracy in its representation. The equal odds of selection for every population member also help reduce bias in the recruitment process.

## What is the Simple Random Sampling Formula?

The formula for simple random sampling is simple and straightforward. You can calculate the probability of selecting a sample of n items by using the following formula:

**Simple Random Sampling Formula –**

*P = 1 – (N-1/N)/(N-2/N-1)…(N-n/N-(n-1))*

P = the probability of selecting a sample of ‘y’ items

n = the sample size

N = the population size

You divide the population by the sample size and select items based on the resulting fraction. For example, you may divide 50 by 1000 and choose every 20th entity if you want to choose 50 participants from a population of 1000.

## Types of Simple Random Sampling

Simple random sampling can be broken down into two categories:

- sampling with replacement and

- sampling without replacement.

The research question and the population’s characteristics influence the selection of the sampling technique.

**Sampling with Replacement **

Sampling with replacement means that each selected item returns to the population. This should occur before selecting the following item again. As a result, in each round, the selection of items is equally likely.

Simple random sampling with replacement is practical when the population size is small. This sample size is significant as compared to the population size. It is useful when the population changes over time, and the researcher wants to ensure the ability to select the same item more than once.

Sampling without replacement means that the researcher returns each selected item to the population after selecting the following item. So, the probability of choosing an item decreases with each round.

**Sampling without Replacement**

On the other hand, in sampling without replacement, you select items from a population without returning them before choosing the next item. So, the probability of selecting an item decreases with each round.

Sampling without replacement is useful when the population is large, and the sample is small. Using this can ensure the selection of each item happens only once to avoid duplicate data.

## Why Do We Use Simple Random Sampling?

You can use simple random sampling for several reasons, including:

**Representative Sampling**- Simple random sampling assures everyone an equal opportunity to be chosen for the sample, rendering it representative. It indicates that the sample fairly depicts the traits of the overall population.

**Unbiased Sampling**- Simple random sampling reduces selection bias, the tendency to select items based on personal bias or convenience. By ensuring that every item in the population has an equal opportunity for selection, simple random sampling eliminates the possibility of bias.

**Statistical Conjecture**- Simple random sampling is used in statistical conjecture, a process of extrapolating generalizations about a population from a sample. Researchers can accurately predict the attributes of the complete population using simple random sampling.

**Efficiency**- Simple random sampling is a straightforward method that can be applied to any population, making it an efficient sample selection. Also, it is appropriate for the exploratory study because it doesn’t require any prior demographic knowledge.

## Limitations of Random Sampling

While simple random sampling is a powerful tool, it does have limitations. The following are a few limitations of simple random sampling –

**Population Size:**It can be time-consuming and inefficient for large populations. After all, it requires a complete list of all members of the population.

**Cost:**It can be costly, particularly if the population is geographically dispersed or inaccessible.

**Sample Size:**With simple random sampling, a sizable sample size is required to acquire a representative sample, which can be laborious and costly.

**Underrepresentation:**The sampling may result in underrepresenting specific subgroups if they are underrepresented in the sample.

### Summary

In conclusion, simple random sampling is a powerful tool for collecting unbiased data from a population. It ensures that every item/person in the population has an equal opportunity for selection.

Researchers should know the drawbacks of the technique and choose the appropriate sampling method based on the research question. Using the simple random sampling formula, researchers can calculate the probability of selecting a specific number with a particular characteristic. Further enhancing the reliability and accuracy of research findings.

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