A study on educational aspirations of high school students (S. Crysdale, Internat. J. compar. Sociol. 16: 19–36, 1975) measured aspirations with the scale (some high school, high school graduate, some college, college graduate). The student counts in these categories were (11, 52, 23, 22) when family income was low, (9, 44, 13, 10) when family income was middle, and (9, 41, 12, 27) when family income was high.

a. Test independence of educational aspirations and family income using X² or G². Explain the deficiency of this test for these data.

b. Find the standardized Pearson residuals. Do they suggest any association pattern?

c. Conduct an alternative test that may be more powerful. Interpret.