A study on educational aspirations of High School Students ( S. Crysdale, Intern
ID: 3434785 • Letter: A
Question
A study on educational aspirations of High School Students ( S. Crysdale, International Journal of Comparative Sociology, Vol 16, 1975, pp 19-36) measured aspirations using the scale (some high school, high school graduate, some college, college graduate). For students whose family income was low, the counts in these categories were (9, 44, 13, 10); when family income was middle, the counts were (11, 52, 23, 22); when family income was high, the counts were (9, 41, 12, 27)
A. Construct a suitable contingency table for the above data.
B. Find the conditional distribution on aspirations for those whose family income was high.
C. Conduct a Chi-square test of Independence between educational aspirations and income levels.
D. Explain what further analyses you could do that would be more informative than a chi-squared test.
Explanation / Answer
Chi-Squared Test for Homogeneity of Several Categorical Populations
Null Hypothesis: populations of people are homogeneous with respect to the four levels of education (low, med, high income groups educated same)
Alternative Hypothesis: populations not homogeneous.
Chi-Square Test: Some High School, Grad High School, Some College, Grad College
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
Chi-Square Test: Some High School, Grad High School, Some College, Grad College
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
Some Grad
High High Some Grad
School School College College Total
Low Income
9 44 13 10 76 [observed counts]
8.07 38.14 13.36 16.42 [expected counts]
0.106 0.901 0.010 2.513 [Chi-Square contr]
Medium Income
11 52 23 22 108
11.47 54.20 18.99 23.34
0.019 0.089 0.847 0.077
High Income
9 41 12 27 89
9.45 44.66 15.65 19.23
0.022 0.300 0.851 3.135
Total 29 137 48 59 273
Chi-Sq = 8.871, DF = 6, P-Value = 0.181
"P-Value" = 0.181 > 0.10 [90% confidence interval]; thus Null Hypothesis of homogeneity should be rejected (low, med, high income groups educated same). Alternative Hypothesis should be accepted (education dependent upon income level)
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