358 PART 7 The Part of Tens

For other α and df values, the Microsoft Excel formula =T.INV.2T(α, df) gives the

critical Student t value.

The Chi-Square Distribution

This family of distributions is used most commonly for two purposes: testing

goodness-of-fit between observed and expected event counts, and for testing for

association between categorical variables. Figure  24-9 shows the shape of the

chi-square distribution for various degrees of freedom.

As you look across Figure 24-9, you may notice that as the degrees of freedom

increase, the shape of the chi-square distribution approaches that of the normal

distribution. Table 24-2 shows the critical chi-square value for various degrees of

freedom at α = 0.05.

Under α = 0.05, random fluctuations cause the chi-square statistic to exceed the

critical chi-square value only 5 percent of the time. If the chi-square value from

your test exceeds the critical value, the test is statistically significant at α = 0.05.

For other α and df values, the Microsoft Excel formula = CHIINV(α, df) gives the

critical

2 value.

TABLE 24-1

Critical Values of Student t for α = 0.05

Degrees of Freedom

tcrit

1

12.71

2

4.30

3

3.18

4

2.78

5

2.57

6

2.45

8

2.31

10

2.23

20

2.09

50

2.01

∞

1.96