Homework #7: X
2
Chi-Square Analysis
Chi-Square Analysis, pronounced “Kai-Square”, is a technique for analyzing variations of
qualitative data. The most frequently used applications of this technique are, first, Goodness of Fit
in which an observed distribution of data is compared with a theoretical or historical distribution of
same type of data. Second, Test of Independence of Qualitative Variables for determining if a crosstabulation of the values of two qualitative variables is completely random or follows a pattern
indicating dependence. The general formula for Chi-Square is:
The outcome of this formula is compared with a random distribution that has similar degrees of
freedom, equivalent to (number of rows of data-1) x (number of columns of data-1). If the observed
value of chi-square is equal or greater than certain number corresponding to the desired level of
probability -e.g. alpha = 0.01, then the observed distribution is significantly different to the
theoretical. The null hypothesis is rejected.
The data used in this exercise correspond to typical data about employees such as gender, age,
salary, etc. Students would test the following hypotheses using Chi-Square. Each hypothesis requires
to prepare first a cross-tabulation of data.
Commands in SPSS: Analyze→Descriptive Statistics→Crosstabs
Commands in SPSS: Analyze→Nonparametric Tests (includes several other tests)
Homework Questions: Hypotheses Testing
1. Do a table of salary category vs. gender. Then, test the hypothesis “Women have lower
salaries than men”.
2. Do a table of salary category vs. educational category. Then, test the alternative hypothesis
“Salaries and educational level are dependent”.
3. Do a table of salary category vs minority classification. Then, test the alternative hypothesis
“Minority members have lower salaries than majority members”
4. Do a table of age category vs. salary category. Then, test the alternative hypothesis: “Salary
increases with age”.
5. Apply Analyze→Correlate→Bivariate to Projected Salary (Independent Variable) and
Current Salary (Dependent Variable). Then, test the alternative hypothesis: “The projected
salary, based on double of initial salary of career, is positively correlated with the current
salary after years in the career.”
Your answers must have at least the following: crosstabulation of variables, chi-square table and
a paragraph of comments indicating if the null hypothesis is rejected or failed to reject and the
significance or probability level used.
Criteria for Comments to Tables and Graphs:
1. Comments must be present, if missing the points per question are discounted 40%
2. Comment refers to the meaning of the statistic, not simply reproduce the statistics in the table;
for instance, “Mean height of females is 62.5”, lower than the US Average (64.0”)” instead of
simply “Mean height of females is 62.5”.
3. If the outcome refers to test of hypothesis, the comment must indicate clearly the null
hypothesis being tested and whether it is rejected or failed to be rejected. In addition, the alpha
or Sig. level used in the test; for instance: “not significant at Alpha = 0.05”, “not significant at
Alpha = 0.01 but significant at Alpha = 0.05”, “significant at Sig. 0.01 or better”.