Abstract and Tangible Populations
Every semester, the majority of my students have difficulty distinguishing between "abstract" and "tangible" populations. Anticipating that this little problem is likely to happen again, I'd like to try here to point out how these two kinds of populations differ.
Suppose I take the class roll, give each person an ID number (1, 2, 3, etc.), and then use a table of random numbers to identify the 5 students to be in my sample. If I ask each of those 5 students a question with the intent of extrapolating my results to the full class, then the full class is a tangible population. It is "tangible" in the sense that I have the ability, either before or after the sample is drawn, to think about or point to each of the "things" that make up the population. In my little example, of course, each of these "things" is a person enrolled this semester in our course.
Now, suppose I ask my question to everyone who's enrolled this semester. If my interest was focused on how you and your classmates answer my question, then the people listed on my class roll would once again constitute a tangible population. There would be no sample here, of course, because my data would be coming from each and every member of the population.
But suppose, after asking my question to everyone now enrolled in this course, I want to generalize my "findings" to other groups of students who will take this course next semester and in the academic terms that follow. If that's the case, then you and your peers no longer are the population; instead, you constitute the sample from which I make my inference. This population would be abstract (not tangible) in nature because I cannot list or point to the students who will be enrolled in this course in future semesters. At present, those "future" students exist only in my imagination. That's why they would constitute an "abstract" population.
To see whether I've been able to clarify the difference between abstract and tangible populations, consider now this fourth scenario. Suppose I take the class roll, give each person an ID number, and then use a table of random numbers to identify the 5 students to be in my sample. If, on the last day of the semester, I ask each of those 5 students a question with the intent of extrapolating my results those who will be enrolled next semester, do I have an abstract or a tangible population?
Copyright © 2012
Schuyler W. Huck