A "Simple Random Sample", sometimes referred to as an SRS, is a sample drawn in such a way that every item in the population has an equal chance of being selected. This equality of likelihood of being selected must remain essentially true even after some items in the population have been selected. Another way to look at this is that if we are in the middle of the selection process, then knowing that a particular item has already been selected tells you nothing about the likelihood that any other item will be selected.

For example, in the fall term of 2013 let us say that there were 11,413 registered credit students at the community college. If we have a list of those students, one student per line, then we could use a random number table, or more likely, a random number generator on a computer, to select a sample of 60 students. We would just be selecting items from this long list of students. Each student has an equal chance of being selected for the first spot in our sample. After selecting that student, then the 11,412 remaining students have an equal chance of being selected for the second spot in the sample, and so on. Knowing that any one student has been selected does not help you make any better guess about whether or not some other student has been or will be selected.

You might have "raised an eyebrow" at the use of the term "essentially" above. We say "essentially" because the probability of being selected as the first student in the sample is 1/11413 whereas, once that student has been selected, the probability of being the second student to be selected is 1/11412, a slightly different number. Following that pattern, once the first 59 students have been selected for the sample, the probability of being selected to be the 60th student in the sample is just 1/(11413-59) or 1/11354. However, 1/11413≅0.00008762 and 1/11354≅0.00008807, two values that are "essentially" the same. If you examine some of the other sampling techniques you will see that those techniques do not even come close to the ideal of having the same chance of items being selected even in the middle of the selection process.

Before leaving this topic, we should note that even though some approach may "look like" it is a simple random sample, the details may force us to recognize that such is not the case. For example, it is quite easy to get the list of students at the community college by just getting the class lists for all credit classes. If we did this we might find that there 35,819 such entries. What if we selected our 60 student sample from that list of 35,819 items? This is an interesting case because it has two possible interpretations. First, if we are interested in getting a simple random sample of credit students at the college, then this methodology does not work. A student who is enrolled in four classes has four times the likelihood of being selected as does a student registered for just one class. Such an inequality of the likelihood of being selected indicates that this methodology does not give us a simple random sample.

on the other hand, if we are looking for a simple random sample of "registrations" then this is exactly what we want to do. (We might note that as a researcher we would have to tackle the unlikely but real possibility that the same students might be selected for two different registrations.) It is important to point out that if we want sample of registrations, then our earlier approach (get a list of the 11,413 different students and draw the sample from there) would be inappropriate.