What is N in simple random sampling?

Simple random sampling is a type of probability sampling technique [see our article, Probability sampling, if you do not know what probability sampling is]. With the simple random sample, there is an equal chance (probability) of selecting each unit from the population being studied when creating your sample [see our article, Sampling: The basics, if you are unsure about the terms unit, sample and population]. This article (a) explains what simple random sampling is, (b) how to create a simple random sample, and (c) the advantages and disadvantages of simple random sampling.

Simple random sampling explained

Imagine that a researcher wants to understand more about the career goals of students at a single university. Let's say that the university has roughly 10,000 students. These 10,000 students are our population (N). Each of the 10,000 students is known as a unit (although sometimes other terms are used to describe a unit; see Sampling: The basics). In order to select a sample (n) of students from this population of 10,000 students, we could choose to use a simple random sample.

With simple random sampling, there would an equal chance (probability) that each of the 10,000 students could be selected for inclusion in our sample. If our desired sample size was around 200 students, each of these students would subsequently be sent a questionnaire to complete (imagining we choose to collect our data using a questionnaire).

Creating a simple random sample

To create a simple random sample, there are six steps: (a) defining the population; (b) choosing your sample size; (c) listing the population; (d) assigning numbers to the units; (e) finding random numbers; and (f) selecting your sample.

Define the population

In our example, the population is the 10,000 students at the single university. The population is expressed as N. Since we are interested in all of these university students, we can say that our sampling frame is all 10,000 students. If we were only interested in female university students, for example, we would exclude all males in creating our sampling frame, which would be much less than 10,000 students.

Choose your sample size

Let's imagine that we choose a sample size of 200 students. The sample is expressed as n. This number was chosen because it reflects the limit of our budget and the time we have to distribute our questionnaire to students. However, we could have also determined the sample size we needed using a sample size calculation, which is a particularly useful statistical tool. This may have suggested that we needed a larger sample size; perhaps as many as 400 students.

List the population

To select a sample of 200 students, we need to identify all 10,000 students at the university. If you were actually carrying out this research, you would most likely have had to receive permission from Student Records (or another department in the university) to view a list of all students studying at the university. You can read about this later in the article under Disadvantages of simple random sampling.

Assign numbers to the units

We now need to assign a consecutive number from 1 to N, next to each of the students. In our case, this would mean assigning a consecutive number from 1 to 10,000 (i.e., N = 10,000; the population of students at the university).

Find random numbers

Next, we need a list of random numbers before we can select the sample of 200 students from the total list of 10,000 students. These random numbers can either be found using random number tables or a computer program that generates these numbers for you.

Select your sample

Finally, we select which of the 10,000 students will be invited to take part in the research. In this case, this would mean selecting 200 random numbers from the random number table. Imagine the first three numbers from the random number table were:

0011(the 11th student from the numbered list of 10,000 students)9292(the 9,292nd student from the list)2001(the 2,001st student from the list)

We would select the 11th, 9,292nd and 2,001st students from our list to be part of the sample. We keep doing this until we have all 200 students that we want in our sample.

Advantages and disadvantages of simple random sampling

The advantages and disadvantages of simple random sampling are explained below. Many of these are similar to other types of probability sampling technique, but with some exceptions. Whilst simple random sampling is one of the 'gold standards' of sampling techniques, it presents many challenges for students conducting dissertation research at the undergraduate and master's level.

  • Advantages of simple random sampling

    The aim of the simple random sample is to reduce the potential for human bias in the selection of cases to be included in the sample. As a result, the simple random sample provides us with a sample that is highly representative of the population being studied, assuming that there is limited missing data.

    Since the units selected for inclusion in the sample are chosen using probabilistic methods, simple random sampling allows us to make generalisations (i.e., statistical inferences) from the sample to the population. This is a major advantage because such generalisations are more likely to be considered to have external validity.

  • Disadvantages of simple random sampling

    A simple random sample can only be carried out if the list of the population is available and complete.

    Attaining a complete list of the population can be difficult for a number of reasons:

    • Even if a list is readily available, it may be challenging to gain access to that list. The list may be protected by privacy policies or require a lengthy process to attain permissions.

    • There may be no single list detailing the population you are interested in. As a result, it may be difficult and time consuming to bring together numerous sub-lists to create a final list from which you want to select your sample. As an undergraduate and master?s level dissertation student, you may simply not have sufficient time to do this.

    • Many lists will not be in the public domain and their purchase may be expensive; at least in terms of the research funds of a typical undergraduate or master's level dissertation student.

    • In terms of human populations (as opposed to other types of populations; see the article: Sampling: The basics), some of these populations will be expensive and time consuming to contact, even where a list is available. Assuming that your list has all the contact details of potential participants in the first instance, managing the different ways (e.g., postal, telephone, email) that may be required to contact your sample may be challenging, not forgetting the fact that your sample may also be geographical scattered.

    In the case of human populations, to avoid potential bias in your sample, you will also need to try and ensure that an adequate proportion of your sample takes part in the research. This may require re-contacting non-respondents, can be very time consuming, or reaching out to new respondents.

If you are an undergraduate or master's level dissertation student considering using simple random sampling, you may also want to read more about how to put together your sampling strategy [see the section: Sampling Strategy].