In this lesson, we focused on the analysis of two-way tables. Beginning with the \(2 \times 2\) case we described the concept of independence for two discrete random variables and showed how to do the Chi-Square test of independence. Then, we discussed three different measures of associations, e.g., the difference in conditional proportions, relative risk and odds-ratios, and their relations to the test of independence. We also saw how the residuals can be used to assess which cells, in particular, may have led to a significant result and how to apply an "exact" version of the independence test to tables of very small cell counts.
The concepts of independence, associations and marginal and conditional probabilities are very important for the analysis of categorical data. We will find the same concepts in more complex contingency tables, and throughout the course and methodology for analysis of categorical data. In the next lesson, we consider data that has a natural ordering and structure measures of association that take advantage of this.