- If you want to test the relationship between two categorical variables you can do this with Pearson's chi-square test or the likelihood ratio statistic.
- Look at the table labelled Chi-Square Tests; if the Exact Sig. value is less than .05 for the row labelled Pearson Chi-Square then there is a significant relationship between your two variables.
- Check underneath this table to make sure that no expected frequencies are less than 5.
- Look at the contingency table to work out what the relationship between the variables is: look out for significant standardized residuals (values outside of ±1.96), and columns that have different letters as subscripts (this indicates a significant difference).
- Calculate the odds ratio.
- Report the Χ2 statistic, the degrees of freedom, the significance value and odds ratio. Also report the contingency table.
- If you want to test the relationship between more than two categorical variables you can do this with loglinear analysis.
- Loglinear analysis is hierarchical: the initial model contains all main effects and interactions. Starting with the highest-order interaction, terms are removed to see whether their removal significantly affects the fit of the model. If it does then this term is not removed and all lower-order effects are ignored.
- Look at the table labelled K-Way and Higher-Order Effects to see which effects have been retained in the final model. Then look at the table labelled Partial Associations to see the individual significance of the retained effects (look at the column labelled Sig. – values less than .05 indicate significance).
- Look at the Goodness-of-Fit Tests for the final model: if this model is a good fit of the data then this statistic should be non-significant (Sig. should be bigger than .05).
- Look at the contingency table to interpret any significant effects (percentage of total for cells is the best thing to look at).
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