8.27. A study on educational aspirations of high school students2 measured aspirations using the scale

(some high school, high school graduate, some college, college graduate) and family income with three ordered categories. Software provides the results shown in Table 8.28.

(a) Use gamma to summarize the association.

(b) Test independence of educational aspirations and family income using the chi-squared test.

Interpret.

(c) Find the 95% confidence interval for gamma.

Interpret.

(d) Conduct an alternative test of independence that takes category ordering into account.

Why arc results so different from the chisquared test?

TABLE 8.28 Statistic DF Value Prob Chi-Square 6 8.871 0.181 Statistic Value ASE Gamma 0.163 0.080