1. Chi-Square Test of Independence Practice Problem – 1
This question asks you to use a chi-square test of independence to answer the question. First of all, the level of measurement for the independent and the dependent variable can be any level that defines groups (dichotomous, nominal, ordinal, or grouped interval). "Marital status" [marstat] is nominal and "sex" [sex] is dichotomous, so the level of measurement requirements are satisfied.

2. Chi-Square Test of Independence in SPSS (1)
You can conduct a chi-square test of independence in crosstabulation of SPSS by selecting:
Analyze > Descriptive Statistics > Crosstabs…

3. Chi-Square Test of Independence in SPSS (2)
First, select and move the variables for the question to “Row(s):” and “Column(s):” list boxes.
The variable mentioned first in the problem, sex, is used as the independent variable and is moved to the “Column(s):” list box.
The variable mentioned second in the problem, marital status, is used as the dependent variable and is moved to the “Row(s)” list box.
Second, click on “Statistics…” button to request the test statistic.

4. Chi-Square Test of Independence in SPSS (3)
First, click on “Chi-square” to request the chi-square test of independence.
Second, click on “Continue” button to close the Statistics dialog box.

5. Chi-Square Test of Independence in SPSS (4)
Now click on “Cells…” button to specify the contents in the cells of the crosstabs table.

6. Chi-Square Test of Independence in SPSS (5)
Make sure both “Observed” and “Expected” in the “Counts” section in “Crosstabs: Cell Display” dialog box are checked and click on “Continue” and “OK” buttons.

7. Chi-Square Test of Independence in SPSS (6)
The chi-square test of independence requires that the expected frequency for all cells be 5.0 or higher.
The crosstabulated table contains the count and expected counts for each cell in the table.
We can see that none of the expected counts are less than 5, and the smallest expected count is 5.9.

8. Chi-Square Test of Independence in SPSS (7)
In the table Chi-Square Tests result, SPSS also tells us that “0 cells have expected count less than 5 and the minimum expected count is 5.93”.
The sample size requirement for the chi-square test of independence is satisfied.

9. Chi-Square Test of Independence in SPSS (8)
The probability of the chi-square test statistic (chi-square= ) was p<0.001, less than the alpha level of significance of 0.05.
The null hypothesis that differences in "marital status" are independent of differences in "sex" (the actual frequencies are equal to the expected frequencies in the cross-tabulated table) is rejected.
In other words, the research hypothesis that differences in “sex" are related to differences in "marital status" is supported by this analysis.
The answer to the question is True.

10. Chi-Square Test of Independence Practice Problem – 2
This question asks you to use a chi-square test of independence to answer the question. First of all, the level of measurement for the independent and the dependent variable can be any level that defines groups (dichotomous, nominal, ordinal, or grouped interval). “Employment status" [empstat] is nominal and "sex" [sex] is dichotomous, so the level of measurement requirements are satisfied.

11. Chi-Square Test of Independence in SPSS (8)
Conduct a chi-square test of independence in crosstabulation of SPSS by selecting:
Analyze > Descriptive Statistics > Crosstabs…

12. Chi-Square Test of Independence in SPSS (9)
Select and move [empstat] to Row(s): box and make sure [sex] is still in the Column(s): box .
Then, click OK.

13. Chi-Square Test of Independence in SPSS (10)
The chi-square test of independence requires that the expected frequency for all cells be 5.0 or higher.
Since the Chi-Square Tests result shows that “2 cells have expected count less than 5” , the sample size requirement for the chi-square test of independence is not satisfied.
The chi-square statistic may lead to erroneous conclusions, so it should not be interpreted.
The answer to the question is incorrect application of a statistic.

14. Steps in solving chi-square test of independence problems - 1
The following is a guide to the decision process for answering
homework problems about chi-square test of independence problems:
Is the dependent and independent variable nominal, ordinal, dichotomous, or grouped interval?
Incorrect application of a statistic No
Yes

15. Steps in solving chi-square test of independence problems - 2
Compute the Chi-Square test of independence
Yes
Expected cell counts less than 5?
Incorrect application of a statistic No
Is the p-value for the chi-square test of independence <= alpha? No
False
Yes
True