Simple Random Sample

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Blog Author :

Aswathi Jayachandran

Edited by :

Alfina L.

Reviewed by :

Dheeraj Vaidya, CFA, FRM

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Simple Random Sample Definition

A simple random sample is a sample chosen to ensure that every possible sample of a given size has an equal chance of being chosen. There are two methods for drawing samples. They are simple random sampling without replacement (SRSWOR) and simple random sampling with replacement (SRSWR).

Simple Random Sample

This method randomly collects units of a larger group, and each unit has the same probability of being chosen. Often, this chosen sample is free from bias and fairly represents its larger group. It helps in obtaining, analyzing, examining, and interpreting data from a group.

Table of contents
  • A simple random sample is a type of probability calculation where the probabilities regarding various possible samples are equal. It is calculated with or without replacing the units after being drawn.
  • SRS is a method of random sampling. Random sampling is used to choose a sample of data from the population to make inferences about a population.
  • One of the biggest advantages of SRS, apart from being easy to use, is that it provides results that are free from bias. Hence the results have fewer chances of being skewed.

Simple Random Sample Explained

The simple random sample method (SRS) is a type of probability calculation where the probabilities regarding various possible samples are equal. In this sampling type, individual units of a sample all have an equal probability of being chosen in each draw. There are a few basic concepts related to SRS, such as units, population, and sample. In data collection, units are single members of a population, and the population is the complete set of units intended to study.

In other words, an aggregate of individuals about whom data is required is referred to as a population. A sample is the smaller part, a set of units or a subset of the population collected for study. A Simple Random Sample calculator uses two methods - SRSWOR and SRSWR.

Simple random sample without replacement (SRSWOR):

In this scenario, the sample's "n units" are drawn from the population one at a time. It is drawn as 1/N for the first draw, 1/ (N-1) for the second, 1/ (N-r+1) for the third, and so on. Therefore, the probability of drawing "n" units from a sample and its selection in the rth draw is n/N.

Simple random sample with replacement (SRSWR):

In this scenario, n units of the sample are drawn one at a time from the population. The units collected at each draw are replaced in the population so that the probability of obtaining any unit in any draw is 1/N. 

Formula

The formula for Simple random sampling without replacement (SRSWOR) is given as follows:

Simple Random Sampling - Pn

The probability of selecting a specified unit at the rth draw is:

Simple Random Sampling - rth row

A defined unit's inclusion in the sample has a probability of 

Simple Random Sampling - probability

The formula for Simple random sampling with replacement (SRSWR) is given:

The probability of selecting a sample of n units is:

Simple Random Sampling - probability

The given unit has a 1/N probability of being chosen at any draw and an n/N probability of being in the sample.

Examples

Check out these examples to get a better idea of a simple random sample generator:

Example #1

There is a group of 6 people, and two will be chosen as leaders. First, let us look at the probability through SRS. Assuming that sampling is done here without replacement.

Simple Random Sample - Example 1

Therefore the chances of one of the pairs being selected out of 15 possibilities are 0.06

Example #2

On its twelfth anniversary, a private library in a locality decided to give away free books to 12 kids in that locality. In addition, the library decided to give away two bookmarks to two kids in the area. The two chosen kids are randomly from a bowl where all the names of the children are written. The bowl is shaken several times to ensure the names are mixed and the pair of children's names are equally picked. To determine which pair of kids will be chosen, it is important to determine the number of distinct pairs. From among these 12 kids, here in the bowl, there is a possibility of

Simple Random Sample - Example 2

Hence, the chance of selecting one of these 66 pairs is 1/66 = 0.015.

Advantages & Disadvantages

Here are some of the advantages and disadvantages of the SRS method:

Advantages

  • Since the collection process is unbiased and free from influence, there is a fair and equal chance of being selected for all elements.
  • This method produces random outcomes from a larger pool. Because the smaller groups in the sample represent the entire population, no further segmentation is required to filter them.

Disadvantages

  • The method is not completely exempted from sampling or calculation errors, which may negatively influence the final results.

Simple Random Sample vs Random Sample

Random sampling is a technique for selecting a sample of observations from a population to conclude the population. It is also known as probability sampling. This method is known as the "Method of Chance Selection" since it depends on the possibility. Furthermore, it uses a large sample size and a random selection of items. 

A simple random sampling is a method of random sampling. In a simple random sample, a unit in the population has an equal and likely chance of being chosen for the sample. There is no randomization of selection as the elements are not chosen at random like in random sampling.

Frequently Asked Questions (FAQs)

1. What is a simple random sample, and why is it important?

An SRS provides units to be chosen fairly and equally. It enables an equal chance of selection for every unit in the population, thereby preventing the samples from having skewed results. It is important as the chosen sample is free from bias.

2. How is a simple random sample obtained?

A simple random sample calculator chooses a unit of population and picks a random number whose serial number matches the randomly selected number. SRSWR accepts all random numbers regardless of how many times they are repeated. In the case of SRSWOR, repeated random numbers are disregarded in favor of drawing more numbers.

3. When is using a simple random sample appropriate?

An SRS is the most suitable method when the entire population from which the sample is drawn is homogeneous. It's one of the techniques researchers employ to select a sample from a larger population to conclude that population.