In which method of sampling every nth term is chosen as sample?

Systematic sampling is a method of population sampling for statistical inference. It is a form of random sampling. To perform systematic sampling, a sample size from a population must be determined. Then the nth value can be calculated. For example, if the population size is 10,000 and the target sample size is 100, then every 10,000/100 = 100 participants should be chosen. 100 is the nth value. This means every 100 people within the population should be sampled.

One drawback of systematic sampling is skew. If the population is categorized or grouped, skew can occur in the samples. An example of this is a company with departments of 100 people. If each first person in every 100 samples is a manager of the department, then the sampling will be overweight towards managers.

When performing systematic sampling, the starting point should be chosen at random. From there, the constant interval (i.e., nth value) is used consistently throughout the sampling to choose participants. The main benefit of using systematic sampling is that statisticians don’t have to sample every individual within a population — often an impractical task. Systematic sampling is popular with researchers because it is fast and easy. While only a few participants from the population are selected, systematic sampling provides an accurate representation of the total population.

The starting point of a systematic sampling must be random. Using the example from above, a number between 1-100 can be chosen as the starting point. If 25 is the random number that comes up, then the 25th person in the first 100 block of participants is chosen first. In the next round, the 125th person is chosen since 100 is the nth value. Additionally, a time element can be injected into the process. Perhaps a participant is chosen each 12 hours until all participants have been chosen.

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.

In which method of sampling every nth term is chosen as sample?

As sourced from Statistical Aid

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

What type of probability sampling is nth person?

One popular method of probability sampling is the systematic sampling method, which involves ordering the population and then choosing every nth person.

What is Nth in systematic sampling?

Systematic sampling is when a researcher selects every nth person on the sampling frame to be part of the sample. The nth number is selected by dividing the target population size (the number in the sampling frame) by the desired sample size.

What type of sampling method uses samples that are chosen for every KTH member of the population?

A method of sampling from a list of the population so that the sample is made up of every kth member on the list, after randomly selecting a starting point from 1 to k.

Which type of sampling requires the researcher to select every nth subject from a list?

Example of Systematic Sampling For example, you could choose every 5th participant or every 20th participant but you must choose the same one in every population. The process of selecting this nth number is systematic sampling.