t-Test, One Sample

The One-Sample t-Test

The ability to correctly use the one-sample t-test is an important tool in any communication researcher’s toolbox. As briefly noted, this test ought to be used when a researcher collects data on a single sample from a defined population when the population variance is unknown. Essentially, the researcher would be comparing one-sample mean to what is known about the larger population in order to determine whether the sample is significantly different from the population. Or, the researcher could compare the sample mean to another specified test value.

When to Use the One-Sample t-Test

Now that a basic definition of the one-sample t-test is understood, the next step is to determine when to use this test. An easy way to determine if the t-test in general—and here, the one-sample t-test—is the correct statistical procedure to use, ask a series of yes/no questions. First, to determine if a t-test is the appropriate test, ask: Am I comparing two means to determine if they are statistically different from each other? If the answer is “yes,” then it is time to figure out which of the three t-tests to use. Since the one-sample t-test is the focus here, start with that. If the answer to any of these questions is “yes,” proceed with the one-sample t-test. Am I trying to determine if a sample mean is statistically different from a population mean? Am I trying to determine if a sample mean is statistically different from the midpoint of my test variable? Am I trying to determine if a sample mean is statistically different from a chance level of performance on the test variable?

If a researcher is comparing two means, but answers “no” to all of the immediately preceding questions, it is likely that one of the other two types of t-tests will be appropriate to test the hypothesis or research question. For example, a scholar is interested in determining whether communication majors and mathematics majors have different mean extroversion scores. Since these are two independent groups, the independent samples t-test would be the best statistical test. Or, for example, a scholar is interested in voters’ likelihood to vote for a candidate before and after a television promotion. This “before and after” value for the same group of participants indicates that a paired samples t-test would be an appropriate test.

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