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

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

value.