A t-test is one of the most frequently used procedures in statistics. But even people who frequently use t-tests often don’t know exactly what happens when their data are wheeled away and operated on behind the curtain using statistical software like Minitab.

It’s worth taking a quick peek behind that curtain, because if you know how a t-test works, you can understand what your results really mean. You can also better grasp why your study did (or didn’t) achieve “statistical significance.”

In fact, if you’ve ever tried to communicate with a distracted teenager, you already have experience with the basic principles behind a t-test.

Anatomy of a t-test

A t-test is commonly used to determine whether the mean of a population significantly differs from a specific value (called the “hypothesized mean”) or from the mean of another population.

For example, a one-sample t-test could test whether the mean waiting time for all patients in a medical clinic is greater than a target wait time of, say, 15 minutes, based on a random sample of patients.

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