© John Wiley & Sons, Inc.

FIGURE 24-7: The Weibull distribution.

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.)

© John Wiley & Sons, Inc.

FIGURE 24-8: The Student t distribution.

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.

TABLE 24-1 Critical Values of Student t for α = 0.05

Degrees of Freedom