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Degrees of Freedom

Degrees of freedom is a statistical concept that gives researchers, including those studying communication, a sense of how strongly a sample reflects the population of interest. Although degrees of freedom assist in understanding sophisticated, inferential statistics, they can also have application to everyday life. The following example is inspired by Joseph G. Eisenhauer’s illustration of applying the concept of degrees of freedom in everyday life and could be considered a lived application of degrees of freedom:

Consider a student who has a single afternoon in which to accomplish multiple tasks. Assume that the student wants to allocate one hour to eat lunch; one hour to study for a late afternoon math class; one hour to work out; one hour to shower, dress, and take care of odds and ends before class; and one hour to commute to campus, find a parking spot, and walk to class. In total, there are five tasks to accomplish within the afternoon and each task will take one hour of time. Assuming the class starts at 5 p.m., the challenge is how to accomplish all five tasks within the time constraints allotted.

Although the student has some flexibility regarding the ordering of each task—for example, the student might choose to eat lunch first or choose to work out first, and then shower, dress and take care of odds and ends before eating lunch—once the student starts assigning time slots for each of the tasks, there is less flexibility available to assign the remaining tasks, until the time slot is assigned for the remaining task by default.

The concept of degrees of freedom can also be applied within the context of inferential statistics. Within the statistical arena, one needs to consider the notion that whereas the degrees of freedom vary depending on the specific statistical test, there are some commonly recognized aspects to keep in mind as they relate to the concept of degrees of freedom. First, degrees of freedom are related to the size of the sample. Second, degrees of freedom are associated with the number of comparison groups. Third, degrees of freedom are tied to the notion of inference. More specifically, there are inferences made to a population from a sample and from a statistic to a parameter.

The purpose of this entry is to identify and describe key considerations as they relate to the concept of degrees of freedom and to address degrees of freedom as they relate to some common, elementary statistical tests. Although only a sample of elementary tests and their attendant degrees of freedom formulas are addressed, the entry’s intention is to provide a better understanding of the conceptual meaning of degrees of freedom and to offer helpful illustrations.

Degrees of Freedom Overview

Within beginning inferential statistics classes, students learn that researchers use statistics to make inferences about parameters. Parameters are tied to populations of interest and are numeric qualities of the population. For example, the average (mean) and the variability (variance) of the population are parameters. Often, researchers cannot know the parameters of a given population because they cannot capture an entire population of interest for a variety of reasons.

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