What constitutes an appropriate sample depends upon the research question(s), the research objectives, the researchers understanding of the phenomenon under study (developed through the literature review), and practical constraints (Palys & Atchison, 2014).  These considerations will influence whether the researcher chooses to employ probabilistic or non-probabilistic sampling techniques. Probabilistic sampling techniques are employed to generate a formal or statistically representative sample.  This technique is utilized when the researcher has a well-defined population to draw a sample from, as is often the case in quantitative research.  This fact enables the researcher to generalize back to the broader population (Palys & Atchison, 2014). On the other hand, a non-probabilistic sampling technique is the method of choice when the population is not created equal and some participants are more desirable in advancing the research project´s objectives.  Non-probability sampling techniques are the best approach for qualitative research. Because the researcher seeks a strategically chosen sample, generalizability is more of a theoretical or conceptual issue, and it is not possible to generalize back to the population (Palys & Atchison, 2014).  In the following sections we will look at the types of sampling methods utilized with non-probabilistic and probabilistic samples.

Probabilistic sampling techniques

As previously mentioned, probability sampling refers to sampling techniques for which a person’s (or event’s) likelihood of being selected for membership in the sample is known. You might ask yourself why we should care about a study element’s likelihood of being selected for membership in a researcher’s sample. The reason is that, in most cases, researchers who use probability sampling techniques are aiming to identify a representative sample from which to collect data. A representative sample is one that resembles the population from which it was drawn in all the ways that are important for the research being conducted. If, for example, you wish to be able to say something about differences between men and women at the end of your study, you better make sure that your sample doesn’t contain only women. That is a bit of an oversimplification, but the point with representativeness is that if your population varies in some way that is important to your study, your sample should contain the same sorts of variation.

Obtaining a representative sample is important in probability sampling because a key goal of studies that rely on probability samples is generalizability. In fact, generalizability is perhaps the key feature that distinguishes probability samples from nonprobability samples. Generalizability refers to the idea that a study’s results will tell us something about a group larger than the sample from which the findings were generated. In order to achieve generalizability, a core principle of probability sampling is that all elements in the researcher’s target population have an equal chance of being selected for inclusion in the study. In research, this is the principle of random selection. Random selection is a mathematical process that must meet two criteria.  The first criterium is that chance governs the section process.  The second is that every sampling element has an equal probability of being selected (Palys & Atchison, 2014). The core principal of probability sampling is random selection. If a researcher uses random selection techniques to draw a sample, he or she will be able to estimate how closely the sample represents the larger population from which it was drawn by estimating the sampling error.

Sampling error is the degree to which your sample deviates from the population’s characteristics.  It is a statistical calculation of the difference between results from a sample and the actual parameters of a population. It is important to ensure that there is a minimum of sampling error (your sample needs to match the diversity of the population as closely as possible.)  Sampling error comes from two main sources – systemic error and random error. Random error is due to chance, while systemic error means that there is some bias in the selection of the sample that makes particular individuals more likely to be selected than others. Here is an example to more fully explain the difference between a random and systemic error.

Why is all of this error talk important?  The use of the right techniques for sampling gives researchers the best chances at minimizing sampling error and thus the strongest ability to say their results are reflective of the population. Research is done to benefit society, in some way, so this is important that research results be reflective of what we might expect to see in society. Sample size also impacts sampling error. Generally, the bigger the sample is, the smaller the error. However, there is a point of diminishing returns where only small reductions in error are given for increases in size. Cost and resources usually also prohibit very large samples, so ultimately the sample size is dependent upon a variety of factors of which sampling error is only one.

Probability sampling techniques

There are a variety of probability samples that researchers may use. For our purposes we will focus on four: simple random samples, systematic samples, stratified samples, and cluster samples (see Table 6.1 for a summary of these four techniques). Simple random samples are the most basic type of probability sample, but their use is not particularly common. Part of the reason for this may be the work involved in generating a simple random sample. To draw a simple random sample, a researcher starts with a list of every single member, or element, of his or her population of interest. This list is sometimes referred to as a sampling frame. Once that list has been created, the researcher numbers each element sequentially and then randomly selects the elements from which he or she will collect data. To randomly select elements, researchers use a table of numbers that have been generated randomly. There are several possible sources for obtaining a random number table. Some statistics and research methods textbooks offer such tables as appendices to the text. Perhaps a more accessible source is one of the many free random number generators available on the Internet. A good online source is the website Stat Trek, which contains a random number generator that you can use to create a random number table of whatever size you might need.

As you might have guessed, drawing a simple random sample can be quite tedious. Systematic sampling techniques are somewhat less tedious but offer the benefits of a random sample. As with simple random samples, you must be able to produce a list of every one of your population elements. Once you have done that, to draw a systematic sample you would simply select every kth element on your list. But what is k, and where on the list of population elements does one begin the selection process? k is your selection interval or the distance between the elements you select for inclusion in your study. To begin the selection process, you would need to figure out how many elements you wish to include in your sample.

Let us say you want to interview 25 students from the law program at your college or university.  You do some research and discover that there are 150 students currently registered in the program. In this case, your selection interval, or k, is 6. To arrive at 6, simply divide the total number of population elements by your desired sample size.  To determine where on your list of population elements to begin selecting the names of the 25 students you will interview, select a random number between 1 and k, and begin there. If we randomly select 3 as our starting point, we would begin by selecting the third student on the list and then select every fourth student from there.

There is one clear instance in which systematic sampling should not be employed. If your sampling frame has any pattern to it, you could inadvertently introduce bias into your sample by using a systemic sampling strategy. This is sometimes referred to as the problem of periodicity. Periodicity refers to the tendency for a pattern to occur at regular intervals.  For example, suppose you wanted to observe how people use the outdoor public spaces in your city or town and you need to have your observations completed within 28 days.  During this time, you wish to conduct four observations on randomly chosen days. To determine which days you will conduct your observations, you will need to determine a selection interval. As you will recall from the preceding paragraphs, to do so you must divide your population size – in this case 28 days – by your desired sample size, in this case 4 days. This formula leads you to a selection interval of 7. If you randomly select 2 as your starting point and select every seventh day after that, you will wind up with a total of 4 days on which to conduct your observations. But what happens is that you are now observing on the second day of the week, being Tuesdays.  As you have probably figured out, that is not such a good plan if you really wish to understand how public spaces in your city or town are used. Weekend use probably differs from weekday use, and that use may even vary during the week.

In cases such as this, where the sampling frame is cyclical, it would be better to use a stratified sampling technique. In stratified sampling, a researcher will divide the study population into relevant subgroups and then draw a sample from each subgroup. In this example, you might wish to first divide your sampling frame into two lists: weekend days and weekdays. Once you have your two lists, you can then apply either simple random or systematic sampling techniques to each subgroup.

Stratified sampling is a good technique to use when, as in the example, a subgroup of interest makes up a relatively small proportion of the overall sample. In the example of a study of use of public space in your city or town, you want to be sure to include weekdays and weekends in your sample.  However, because weekends make up less than a third of an entire week, there is a chance that a simple random or systematic strategy would not yield sufficient weekend observation days. As you might imagine, stratified sampling is even more useful in cases where a subgroup makes up an even smaller proportion of the study population, say, for example, if you want to be sure to include both male and female perspectives in a study, but males make up only a small percentage of the population. There is a chance simple random or systematic sampling strategy might not yield any male participants, but by using stratified sampling, you could ensure that your sample contained the proportion of males that is reflective of the larger population.  Let us look at another example to help clarify things.

Up to this point in our discussion of probability samples, we have assumed that researchers will be able to access a list of population elements in order to create a sampling frame. This, as you might imagine, is not always the case. Let us say, for example, that you wish to conduct a study of bullying in high schools across Canada. Just imagine trying to create a list of every single high school student in the country. Basically, we are talking about a list of every high school student in the country. Even if you could find a way to generate such a list, attempting to do so might not be the most practical use of your time or resources. When this is the case, researchers turn to cluster sampling. Cluster sampling occurs when a researcher begins by sampling groups (or clusters) of population elements and then selects elements from within those groups.  Here is an example of when a cluster sampling technique would be suitable.