t Test, One Sample

Uses

The one-sample t test is appropriate whenever the researcher wants to determine whether the mean of some population differs from some test value. Note the one-sample t test closely resembles the one-sample z test. The difference is that the z test is used when the standard deviation of the population being studied is known, whereas the t test is used when the standard deviation of the population is not known.

An important characteristic of the one-sample t test (as well as of the one-sample z test) is that there is only one population that is being studied. This differentiates a one-sample test from other types of hypothesis tests (e.g., the independent samples t test) where there are two (or more) population parameters to be estimated. For example, a researcher interested in whether the average score of males differs from the average score of females would not use a one-sample t test, because there are two population parameters (the mean score of both males and females) to be estimated in that situation.

The one-sample t test can be used whenever the researcher is interested in determining whether the population mean differs from some specific value (the test value). This test value is generally determined in one of two ways. First, as in the previous example, the test value is chosen to reflect some value of theoretical interest, in that case, the “average” perceived ability. In the second situation, the test value reflects a known population value (or one estimated with a great deal of precision). For example, assume a medical researcher is interested in determining whether a medication affects the number of hours a night that a person sleeps. He finds information from the National Sleep Foundation saying that the average working American adult sleeps 6 hours and 40 minutes (400 minutes) on a work night. He then samples 100 working Americans who take the medication and records how long each of these people sleep on a work night. The mean number of hours slept from this sample could then be compared with 400 minutes via a one-sample t test. Note, however, these are [Page 1557]just example uses for the one-sample t test. In any situation where the researcher wants to test the mean of a sample against some particular value, a one-sample test is appropriate.

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