What is this sampling method where every nth element of the population is selected?

Simple random sampling selects a smaller group (the sample) from a larger group of the total number of participants (the population). It’s one of the simplest systematic sampling methods used to gain a random sample.

The technique relies on using a selection method that provides each participant with an equal chance of being selected, giving each participant the same probability of being selected.

Since the selection process is based on probability and random selection, the end smaller sample is more likely to be representative of the total population and free from researcher bias. This method is also called a method of chances.

Simple random sampling is one of the four probability sampling techniques: Simple random sampling, systematic sampling, stratified sampling, and cluster sampling.

The process of simple random sampling

1. Define the population size you’re working with. This could be based on the population of a city. For this exercise, we will assume a population size of 1000.
2. Assign a random sequential number to each participant in the population, which acts as an ID number – e.g. 1, 2, 3, 4, 5, and so on to 1000.
3. Decide the sample size number needed. Not sure about what the right sample size should be? Try our Sample Size Calculator. For this exercise, let’s use 100 as the sample size.
4. Select your sample by running a random number generator to provide 100 randomly generated numbers from between 1 and 1000.

Why do we use simple random sampling?

Simple random sampling is normally used where there is little known about the population of participants. Researchers also need to make sure they have a method for getting in touch with each participant to enable a true population size to work from. This leads to a number of advantages and disadvantages to consider.

Advantages of simple random sampling

This sampling technique can provide some great benefits.

• Participants have an equal and fair chance of being selected. As the selection method used gives every participant a fair chance, the resulting sample is unbiased and unaffected by the research team. It is perfect for blind experiments.
• This technique also provides randomised results from a larger pool. The resulting smaller sample should be representative of the entire population of participants, meaning no further segmenting is needed to refine groups down.
• Lastly, this method is cheap, quick, and easy to carry out – great when you want to get your research project started quickly.

Disadvantages of simple random sampling

• There may be cases where the random selection does not result in a truly random sample. Sampling errors may result in similar participants being selected, where the end sample does not reflect the total population.
• This provides no control for the researcher to influence the results without adding bias. In these cases, repeating the selection process is the fairest way to resolve the issue.

What selection methods can you use?

A lottery is a good example of simple random sampling at work. You select your set of numbers, buy a ticket, and hope your numbers match the randomly selected lotto balls. The players with matching numbers are the winners, who represent a small proportion of winning participants from the total number of players.

Other selection methods used include anonymising the population – e.g. by assigning each item or person in the population a number – and then picking numbers at random.

Researchers can use a simpler version of this by placing all the participants’ names in a hat and selecting names to form the smaller sample.

Comparing simple random sampling with the three other probability sampling methods

The three other types of probability sampling techniques have some clear similarities and differences to simple random sampling:

Systematic sampling

Systematic sampling, or systematic clustering, is a sampling method based on interval sampling – selecting participants at fixed intervals.

All participants are assigned a number. A random starting point is decided to choose the first participant. A defined interval number is chosen based on the total sample size needed from the population, which is applied to every nth participant after the first participant.

For example, the researcher randomly selects the 5th person in the population. An interval number of 3 is chosen, so the sample is populated with the 8th, 11th, 14th, 17th, 20th, (and so on) participants after the first selection.

Since the starting point of the first participant is random, the selection of the rest of the sample is considered to be random.

Simple random sampling differs from systematic sampling as there is no defined starting point. This means that selections could be from anywhere across the population and possible clusters may arise.

Stratified sampling

Stratified sampling splits a population into predefined groups, or strata, based on differences between shared characteristics – e.g. race, gender, nationality. Random sampling occurs within each of these groups.

This sampling technique is often used when researchers are aware of subdivisions within a population that need to be accounted for in the research – e.g. research on gender split in wages requires a distinction between female and male participants in the samples.

Simple random sampling differs from stratified sampling as the selection occurs from the total population, regardless of shared characteristics. Where researchers apply their own reasoning for stratifying the population, leading to potential bias, there is no input from researchers in simple random sampling.

Cluster sampling

There are two forms of cluster sampling: one-stage and two-stage.

One-stage cluster sampling first creates groups, or clusters, from the population of participants that represent the total population. These groups are based on comparable groupings that exist  – e.g. zip codes, schools, or cities.

The clusters are randomly selected, and then sampling occurs within these selected clusters. There can be many clusters and these are mutually exclusive, so participants don’t overlap between the groups.

Two-stage cluster sampling first randomly selects the cluster, then the participants are randomly selected from within that cluster.

Simple random sampling differs from both cluster sampling types as the selection of the sample occurs from the total population, not the randomly selected cluster that represents the total population.

In this way, simple random sampling can provide a wider representation of the population, while cluster sampling can only provide a snapshot of the population from within a cluster.

Frequently asked questions (FAQs) about simple random sampling

What if I’m working with a large population?

Where sample sizes and the participant population are large, manual methods for selection aren’t feasible with the available time and resources.

This is where computer-aided methods are needed to help to carry out a random selection process – e.g. using a spreadsheet’s random number function, using random number tables, or a random number generator.

What is the probability formula for being selected in the sample?

Let’s take an example in practice. A company wants to sell its bread brand in a new market area. They know little about the population. The population is made up of 15,000 people and a sample size of 10% (1,500) is required. Using this example, here is how this looks as a formula:

Sample size (S) = 1,500

The total population (P) = 15,000

The probability of being included in the sample is: (S ÷ P) x 100%

E.g. = (1,500 ÷ 15,000) x 100% = 10%

What are random number tables?

One way of randomly selecting numbers is to use a random number table (visual below). This places the total population’s sequential numbers from left to right in a table of N number of rows and columns.

To randomly select numbers, researchers will select certain rows or columns for the sample group.

How do I generate random numbers in an Excel spreadsheet?

Microsoft Office’s Excel spreadsheet application has a formula that can help you generate a random number. This is:

=RAND()

It provides a random number between 1 and 0.

For random numbers from the total population (for example, a population of 1000 participants), the formula is updated to:

=INT(1000*RAND())+1

Simply copy and paste the formula into cells until you get to the desired sample size – if you need a sample size of 25, you must paste this formula into 25 cells. The returned numbers between 1 and 1000 will indicate the participant’s ID numbers that make up the sample.

Conclusion: Where to go next to learn more?

What sample size should you go for? Try our online calculator to see how many people you should be selecting: Calculate the perfect sample size

Systematic sampling is a statistical method that researchers use to zero down on the desired population they want to research. Researchers calculate the sampling interval by dividing the entire population size by the desired sample size. Systematic sampling is an extended implementation of probability sampling in which each member of the group is selected at regular periods to form a sample.

Systematic sampling definition

Systematic sampling is defined as a probability sampling method where the researcher chooses elements from a target population by selecting a random starting point and selects sample members after a fixed ‘sampling interval.’

Select your respondents

For example, in school, while selecting the captain of a sports team, most of our coaches asked us to call out numbers such as 1-5 (1-n) and the students with a random number decided by the coach. For instance, three would be called out to be the captains of different teams. It is a non-stressful selection process for both the coach and the players. There’s an equal opportunity for every member of a population to be selected using this sampling technique.

What are the steps to form a sample using the systematic sampling technique?

Here are the steps to form a systematic sample:

Step one: Develop a defined structural audience to start working on the sampling aspect.

Step two: As a researcher, figure out the ideal size of the sample, i.e., how many people from the entire population to choose to be a part of the sample.

Step three: Once you decide the sample size, assign a number to every member of the sample.

Step four: Define the interval of this sample. This will be the standard distance between the elements.

For example, the sample interval should be 10, which is the result of the division of 5000 (N= size of the population) and 500 (n=size of the sample).

Step five: Select the members who fit the criteria which in this case will be 1 in 10 individuals.

Step six: Randomly choose the starting member (r) of the sample and add the interval to the random number to keep adding members in the sample. r, r+i, r+2i, etc. will be the elements of the sample.

How systematic sampling works

When you are sampling, ensure you represent the population fairly. Systematic sampling is a symmetrical process where the researcher chooses the samples after a specifically defined interval. Sampling like this leaves the researcher no room for bias regarding choosing the sample. To understand how systematic sampling exactly works, take the example of the gym class where the instructor asks the students to line up and asks every third person to step out of the line. Here, the instructor has no influence over choosing the samples and can accurately represent the class.

Systematic sampling example

For instance, if a local NGO is seeking to form a systematic sample of 500 volunteers from a population of 5000, they can select every 10th person in the population to build a sample systematically.

What are the types of systematic sampling?

Here are the types of systematic sampling:

1. Systematic random sampling
2. Linear systematic sampling
3. Circular systematic sampling

Let’s take a closer look at these sampling techniques.

Systematic random sampling:

Systematic random sampling is a method to select samples at a particular preset interval. As a researcher, select a random starting point between 1 and the sampling interval. Below are the example steps to set up a systematic random sample:

1. First, calculate and fix the sampling interval. (The number of elements in the population divided by the number of elements needed for the sample.)
2. Choose a random starting point between 1 and the sampling interval.
3. Lastly, repeat the sampling interval to choose subsequent elements.

Linear systematic sampling:

Linear systematic sampling is a systematic sampling method where samples aren’t repeated at the end and ‘n’ units are selected to be a part of a sample having ‘N’ population units. Rather than selecting these ‘n’ units of a sample randomly, a researcher can apply a skip logic to select these. It follows a linear path and then stops at the end of a particular population.

This sampling or skip interval (k) = N (total population units)/n (sample size)

How is a Linear systematic sample selected?

• Arrange the entire population in a classified sequence.
• Select the sample size (n)
• Calculate sampling interval (k) = N/n
• Select a random number between 1 to k (including k)
• Add the sampling interval (k) to the chosen random number to add the next member to a sample and repeat this procedure to add remaining members of the sample.
• In case k isn’t an integer, you can select the closest integer to N/n.

Circular systematic sampling:

In circular systematic sampling, a sample starts again from the same point once again after ending; thus, the name. For example, if N = 7 and n = 2, k=3.5. There are two probable ways to form sample:

1. If we consider k=3, the samples will be – ad, be, ca, db and ec.
2. If we consider k=4, the samples will be – ae, ba, cb, dc and ed.

How is a circular systematic sample selected?

• Calculate sampling interval (k) = N/n. (If N = 11 and n = 2, then k is taken as 5 and not 6)
• Start randomly between 1 to N
• Create samples by skipping through k units every time until you select members of the entire population.
• In the case of this method, there will be N number of samples, unlike k samples in the linear systematic sampling method.

Difference between linear systematic sampling and circular systematic sampling:

Here is the difference between linear systematic sampling and circular systematic sampling.

What are the advantages of systematic sampling?

Here are the advantages of systematic sampling.

• It’s extremely simple and convenient for the researchers to create, conduct, analyze samples.
• As there’s no need to number each member of a sample, it is better for representing a population in a faster and simpler manner.
• The samples created are based on precision in member selection and free from favoritism.
• In the other methods of probability sampling methods such as cluster sampling and stratified sampling or non-probability methods such as convenience sampling, there are chances of the clusters created to be highly biased which is avoided in systematic sampling as the members are at a fixed distance from one another.
• The factor of risk involved in this sampling method is extremely minimal.
• In case there are diverse members of a population, this sampling technique can be beneficial because of the even distribution of members to form a sample.

Other probability sampling techniques like cluster sampling and stratified random sampling can be very unorganized and challenging due to which researchers and statisticians have turned to methods like systematic sampling or simple random sampling for better sampling results. It consumes the least time as it requires a selection of sample size and identification of the starting point for this sample, which needs to be continued at regular intervals to form a sample.

Select your respondents

When to use systematic sampling?

Let’s take an example where you want to form a sample of 500 individuals out of a population of 5000; you’d have to number every person in the population.

Once the numbering is done, the researcher can select a number randomly, for instance, 5. The 5th individual will be the first to be a part of the systematic sample. After that, the 10th member will be added into the sample, so on and so forth (15th, 25th, 35, 45th, and members till 4995).

Here are 4 other situations of when to use Systematic Sampling:   

1. Budget restrictions: In comparison to other sampling methods like simple random sampling, this sampling technique is more suitable for conditions where there are budget restrictions and also the extremely uncomplicated accomplishment of the study.
2. Uncomplicated implementation: As systematic sampling depends on the defined sampling intervals to decide the sample, it becomes simple for the researchers and statisticians to manage samples with more respondents. This is because the time invested in creating samples is minimal, and the cost spent is also restricted due to the periodic nature of systematic sampling.
3. Absence of data pattern: There are specific data that don’t have an arrangement in place. This data can be analyzed in an unbiased manner, using systematic sampling.
4. Low risk of data manipulation in research: It is highly productive while researching a broad subject, especially when there’s a negligible risk of data manipulation.

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