The *t* distribution was introduced by a chemist working in quality control for the Guinness brewery in Ireland, William Sealy Gosset. Gosset described the *t* distribution in an article under the pseudonym Student; hence, the *t* distribution is sometimes called the Student’s *t* distribution and the *t*-test the Student’s *t*-test. There are three major types of *t*-test, all of which are concerned with testing the difference between means and involve comparing a test statistic to the *t* distribution to determine the probability of that statistic if the study’s null hypothesis is true. The one-way analysis of variance (ANOVA) procedure with two groups is mathematically equivalent to the *t*-test, but the *t*-test is used so commonly that it deserves its own chapter. In addition, understanding the logic of the *t-*test should make it easier to follow the logic of more complex ANOVA designs.

If you’re not familiar with inferential statistics, it might be wise to review Chapter 3 before continuing with this chapter. One basis for inferential statistics is the use of known probability distributions to make inferences about real data sets. In Chapter 3, we discussed the normal and binomial distributions; in this chapter, we discuss the *t* distribution. Like the normal distribution, the *t* distribution is continuous and symmetrical. Unlike the normal distribution, the shape of the *t* distribution depends on the degrees of freedom for a sample, meaning the number of values ...

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