a) Simple random sampling

In simple random sampling, we use an unsystematic random selection process i.e. we identify every element in the sampling frame then choose them on some planned basis ensuring that every element has the same opportunity of being selected. What if the sample frame is too large? We can use a random number table. This is a table containing random numbers. In order to use the table, you will need to determine the size of your sample frame and the largest number in your sample frame has to be included into the table. Let us look at this table below with three columns and nine rows.

 24356   46724   25641   67514   98257   98165   35678   87192   98173   
 17625   78256   71522   98127   09161   01823   91728   56720   09765   
 28937   97628   09152   61723   91873   91723   87542   19782   25637   

Let us create some fictitious numbers of 45 students in a class and we want to get the average math score for seven students. How do we go about choosing the seven students using the random sample table above?  The first step is to decide how to move in the columns and rows: either up or down but this has to be systematic. Second, choose any starting point to select a sample of seven from the sampling frame of 45. Let us assume that we are using the first two digits of the number. Let us take column two row seven. The numbers are 9 and 1. We are already in a problem. 91 is too large than 45. Let us take column one row three. The number is 2 and 5. 25 is within the range of 45. This 

will be our first number to use from the sample frame of 45. We will then continue until we get to the seven students we needed.
 

b) Systematic random sampling

Systematic random sampling is done through some ordered criteria by choosing elements from a randomly arranged sampling frame. You can chose from every “nth” element in a sample frame i.e. 10th, 15th, 20th and so on. What are the procedures involved? You have to decide on your sample size. Let us say your sample size will be made up of 30 students from a sample frame of 400 students, you may want a proportion of 30/400 = 0.075, which is every 13th person. 

In both the simple random sampling and the systematic sampling you will be required to generate a list from the sampling frame. It also requires that the elements within the sampling frame be homogeneous.

c) Stratified random sampling

When dealing with a sample frame that is not homogeneous and contains subgroups such as freshmen, juniors, and so on in a listing of university students for instance, you will need to represent those subgroups in your sample. In order to achieve this, random selection from each subgroup in the sampling frame has to be considered using the same procedures. The subgroups within the sample frame will have to be treated as though they are separate sampling frames themselves. Does this sound like yet another tongue twister? Not after we have equipped ourselves with the sampling jargons identified earlier in this lesson. Just to refresh our minds on this, click here.

d) Cluster sampling

Have you ever imagined a situation whereby a sampling frame list is unavailable and as a researcher you have to continue with your work? For instance, how would you go about obtaining a sample frame list of all college students in Canada? Hard! Would you abandon carrying your research on this basis? If I were you I would say a big NO! Why? Through cluster sampling, we can randomly select hierarchical groups from the sampling frame by creating clusters that can be further sampled into finer gradations of clusters until we can obtain a list of elements. 

Let us create a scenerio that will illustrate how cluster sampling is achieved.  To select a random sample of 600 college students in Canada for instance, let us create a sample frame consisting of a list of colleges. Using the simple random sampling, we can select six colleges from the list. Then from the clusters, we can randomly select 100 students from the six colleges to obtain 600 students residing in Canada.
 
 
 

Non probability Sampling
Non probability sampling is any procedure in which elements will not have the equal opportunities of being included in a sample. In non-probability sampling, you set criteria for elements to be included in the sample i.e. on basis of region, appearance and so forth hence limiting the chances of representation in the sample. The simple question one would be obliged to ask is why bother with non-probability sampling when we already know that there exists bias in sample selection? Non probability sampling equally plays a major role in the field of explanatory research. However one major feature of non-probability sampling is that it does not use random sampling and therefore you cannot estimate sampling error. 

We will now look at some examples of non-probability sampling used in research.

a) Accidental sampling

This is selection based on availability or ease of inclusion. Assume that you were walking down the street and an interviewer chose to videotape you for the evening local news broadcast. Can this be termed accidental or random sampling? I would argue strongly for accidental sampling because this was a mere selection based on your availability and willingness to talk. Accidental sampling can lead to misinterpretation of results. Do you recall the outcome of the 1936 U.S presidential elections published in The literary Digest? Maybe you were not yet born by that time. Try to find this publication and see what results accidental sampling can produce.

b) Purposive sampling

In exploratory or pilot projects you may be purposely inclined to obtain data from specific individuals. Such data may give you internal validity of your project, but you may not be able to generalize it to other places and people.

c) Quota sampling 

In quota sampling, you select sampling elements on the basis of categories that are assumed to exist within a population. How is quota sampling different from stratified random sampling discussed earlier on? In the former, elements are randomly selected from stratified groups while in the latter a presumed subdivision is used as the bases of the selection procedure. Although in quota sampling the results may almost reflect similarities with the population, there is difficulty in determining the amount of sample error. Do you remember the famous 1948 photograph of Harry Truman holding a newspaper with the following infamous headline…DEWEY DEFEATS TRUMAN? (Dane, 1990). Find out more about this story and reflect on how quota sampling may lead to our inability to generalize to a population.