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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