CHAPTER 24 Ten Distributions Worth Knowing 357

The Student t Distribution

This family of distributions is most often used when comparing means between

two groups, or between two paired measurements. Figure 24-8 shows the shape

of the Student t distribution for various degrees of freedom. (See Chapter 11 for

more info about t tests and degrees of freedom.)

In Figure 24-8, as the degrees of freedom increase, the shape of the Student t

distribution approaches that of the normal distribution.

Table 24-1 shows the critical t value for various degrees of freedom at α = 0.05.

Under α = 0.05, random fluctuations cause the t statistic to exceed the critical t

value only 5 percent of the time. This 5 percent includes exceeding t on either the

positive or negative side. From the table, if you determine your critical t is 2.01 at

50 df, and your test statistic is 2.45, it exceeds the critical t, and is statistically

significant at α = 0.05. But this would also be true if your test statistic was –2.45,

because the table only presents absolute values of critical t.

FIGURE 24-7:

The Weibull

distribution.

© John Wiley & Sons, Inc.

FIGURE 24-8:

The Student t

distribution.

© John Wiley & Sons, Inc.