There are a variety of probability samples that researchers may use. These include simple random samples, systematic samples, stratified samples, and cluster samples.
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 (http://stattrek.com/Tables/Random.aspx). Randomizer.org also offers a useful random number generator (http://randomizer.org).
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’ve done that, to draw a systematic sample you’d 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? kis your selection interval or the distance between the elements you select for inclusion in your study. To begin the selection process, you’ll need to figure out how many elements you wish to include in your sample. Let’s say you want to interview 25 fraternity members on your campus, and there are 100 men on campus who are members of fraternities. In this case, your selection interval, or k, is 4. To arrive at 4, simply divide the total number of population elements by your desired sample size. This process is represented in “Figure 7.1”.
To determine where on your list of population elements to begin selecting the names of the 25 men you will interview, select a random number between 1 and k, and begin there. If we randomly select 3 as our starting point, we’d begin by selecting the third fraternity member on the list and then select every fourth member from there. This might be easier to understand if you can see it visually. “Table 7.2” lists the names of our hypothetical 100 fraternity members on campus. You’ll see that the third name on the list has been selected for inclusion in our hypothetical study, as has every fourth name after that. A total of 25 names have been selected.
Number 
Name 
Include in study? 
Number 
Name 
Include in study? 

1 
Jacob 
51 
Blake 
Yes 

2 
Ethan 
52 
Oliver 

3 
Michael 
Yes 
53 
Cole 

4 
Jayden 
54 
Carlos 

5 
William 
55 
Jaden 
Yes 

6 
Alexander 
56 
Jesus 

7 
Noah 
Yes 
57 
Alex 

8 
Daniel 
58 
Aiden 

9 
Aiden 
59 
Eric 
Yes 

10 
Anthony 
60 
Hayden 

11 
Joshua 
Yes 
61 
Brian 

12 
Mason 
62 
Max 

13 
Christopher 
63 
Jaxon 
Yes 

14 
Andrew 
64 
Brian 

15 
David 
Yes 
65 
Mathew 

16 
Logan 
66 
Elijah 

17 
James 
67 
Joseph 
Yes 

18 
Gabriel 
68 
Benjamin 

19 
Ryan 
Yes 
69 
Samuel 

20 
Jackson 
70 
John 

21 
Nathan 
71 
Jonathan 
Yes 

22 
Christian 
72 
Liam 

23 
Dylan 
Yes 
73 
Landon 

24 
Caleb 
74 
Tyler 

25 
Lucas 
75 
Evan 
Yes 

26 
Gavin 
76 
Nicholas 

27 
Isaac 
Yes 
77 
Braden 

28 
Luke 
78 
Angel 

29 
Brandon 
79 
Jack 
Yes 

30 
Isaiah 
80 
Jordan 

31 
Owen 
Yes 
81 
Carter 

32 
Conner 
82 
Justin 

33 
Jose 
83 
Jeremiah 
Yes 

34 
Julian 
84 
Robert 

35 
Aaron 
Yes 
85 
Adrian 

36 
Wyatt 
86 
Kevin 

37 
Hunter 
87 
Cameron 
Yes 

38 
Zachary 
88 
Thomas 

39 
Charles 
Yes 
89 
Austin 

40 
Eli 
90 
Chase 

41 
Henry 
91 
Sebastian 
Yes 

42 
Jason 
92 
Levi 

43 
Xavier 
Yes 
93 
Ian 

44 
Colton 
94 
Dominic 

45 
Juan 
95 
Cooper 
Yes 

46 
Josiah 
96 
Luis 

47 
Ayden 
Yes 
97 
Carson 

48 
Adam 
98 
Nathaniel 

49 
Brody 
99 
Tristan 
Yes 

50 
Diego 
100 
Parker 

Note: In case you’re wondering how I came up with 100 unique names for this table, I’ll let you in on a little secret: lists of popular baby names can be great resources for researchers. I used the list of top 100 names for boys based on Social Security Administration statistics for this table. I often use baby name lists to come up with pseudonyms for field research subjects and interview participants. See Family Education. (n.d.). Name lab. Retrieved from http://babynames.familyeducation.com/popularnames/boys. 
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. Let’s say, for example, that you wanted to observe how people use the outdoor public spaces on your campus. Perhaps you need to have your observations completed within 28 days and you wish to conduct four observations on randomly chosen days. “Table 7.3” shows a list of the population elements for this example. To determine which days we’ll conduct our observations, we’ll need to determine our selection interval. As you’ll recall from the preceding paragraphs, to do so we must divide our population size, in this case 28 days, by our desired sample size, in this case 4 days. This formula leads us to a selection interval of 7. If we randomly select 2 as our starting point and select every seventh day after that, we’ll wind up with a total of 4 days on which to conduct our observations. You’ll see how that works out in the following table.
Number 
Day 
Include in study? 
Number 
Day 
Include in study? 

1 
Monday 
15 
Monday 

2 
Tuesday 
Yes 
16 
Tuesday 
Yes 

3 
Wednesday 
17 
Wednesday 

4 
Thursday 
18 
Thursday 

5 
Friday 
19 
Friday 

6 
Saturday 
20 
Saturday 

7 
Sunday 
21 
Sunday 

8 
Monday 
22 
Monday 

9 
Tuesday 
Yes 
23 
Tuesday 
Yes 

10 
Wednesday 
24 
Wednesday 

11 
Thursday 
25 
Thursday 

12 
Friday 
26 
Friday 

13 
Saturday 
27 
Saturday 

14 
Sunday 
28 
Sunday 
Do you notice any problems with our selection of observation days? Apparently we’ll only be observing on Tuesdays. As you have probably figured out, that isn’t such a good plan if we really wish to understand how public spaces on campus are used. My guess is that weekend use probably differs from weekday use, and that use may even vary during the week, just as class schedules do. 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, we might wish to first divide our sampling frame into two lists: weekend days and weekdays. Once we have our two lists, we can then apply either simple random or systematic sampling techniques to each subgroup.
Stratified sampling is a good technique to use when, as in our example, a subgroup of interest makes up a relatively small proportion of the overall sample. In our example of a study of use of public space on campus, we want to be sure to include weekdays and weekends in our sample, but because weekends make up less than a third of an entire week, there’s 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 we want to be sure to include both men’s and women’s perspectives in a study, but men make up only a small percentage of the population. There’s a chance simple random or systematic sampling strategy might not yield any male participants, but by using stratified sampling, we could ensure that our sample contained the proportion of men that is reflective of the larger population.
Up to this point in our discussion of probability samples, we’ve 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’s say, for example, that you wish to conduct a study of hairstyle preferences across the United States. Just imagine trying to create a list of every single person with (and without) hair in the country. Basically, we’re talking about a list of every person 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.
Let’s take a look at a couple more examples. Perhaps you are interested in the workplace experiences of public librarians. Chances are good that obtaining a list of all librarians that work for public libraries would be rather difficult. But I’ll bet you could come up with a list of all public libraries without too much hassle. Thus you could draw a random sample of libraries (your cluster) and then draw another random sample of elements (in this case, librarians) from within the libraries you initially selected. Cluster sampling works in stages. In this example, we sampled in two stages. As you might have guessed, sampling in multiple stages does introduce the possibility of greater error (each stage is subject to its own sampling error), but it is nevertheless a highly efficient method.
Jessica Holt and Wayne Gillespie (2008) 1 used cluster sampling in their study of students’ experiences with violence in intimate relationships. Specifically, the researchers randomly selected 14 classes on their campus and then drew a random subsample of students from those classes. But you probably know from your experience with college classes that not all classes are the same size. So if Holt and Gillespie had simply randomly selected 14 classes and then selected the same number of students from each class to complete their survey, then students in the smaller of those classes would have had a greater chance of being selected for the study than students in the larger classes. Keep in mind with random sampling the goal is to make sure that each element has the same chance of being selected. When clusters are of different sizes, as in the example of sampling college classes, researchers often use a method called probability proportionate to size (PPS). This means that they take into account that their clusters are of different sizes. They do this by giving clusters different chances of being selected based on their size so that each element within those clusters winds up having an equal chance of being selected.
Sample type 
Description 
Simple random 
Researcher randomly selects elements from sampling frame. 
Systematic 
Researcher selects every kth element from sampling frame. 
Stratified 
Researcher creates subgroups then randomly selects elements from each subgroup. 
Cluster 
Researcher randomly selects clusters then randomly selects elements from selected clusters. 
KEY TAKEAWAYS
 In probability sampling, the aim is to identify a sample that resembles the population from which it was drawn.
 There are several types of probability samples including simple random samples, systematic samples, stratified samples, and cluster samples.
EXERCISES
 Imagine that you are about to conduct a study of people’s use of public parks. Explain how you could employ each of the probability sampling techniques described earlier to recruit a sample for your study.
 Of the four probability sample types described, which seems strongest to you? Which seems weakest? Explain.
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