Chi-Square Test for Independence

Question 1

What are the hypotheses for a chi-square test of independence?

Answer 1

• H0: There is no relationship between the two categorical variables
• H1: There is a relationship between the two categorical variables

Question 2

What assumptions must be met for chi-square?

Answer 2

• Data must be categorical
• Each observation should be independent
• Expected frequency in each cell should be at least 5

Question 3

How to interpret SPSS output for Chi-square test?

Answer 3

• Chi-square statistic (xsquared): Measures difference between observed and expected frequencies
• Df: based on number of categories in each variable
• P Value: If P<a (e.g. 0.05) , reject the null hypothesis, indicating a significant relationship
• Cramers V: Measures strength of association between variables (0-1)

Question 4

Methodology for a chi-square test?

Answer 4

• State null and alternative hyp
• Create contingency table of observed frequencies
• Calculate expected frequencies or each cell
• Compute chi-square-statistic
• Compare the test statistic to the critical value or use p-value to make a decision