Section 10.3: Contingency Tables: Independence and Homogeneity

1. Relate association to statistical independence.
2. State an appropriate test statistic for testing a claim of association between two categorical variables.
3. State under what conditions the \(\chi^{2}\) test for independence is appropriate.
4. Relate the contingency tables from this section to the frequency / count tables from Chapter 3.
5. Compute estimates of probabilities from contingency tables for two categorical variables \(X\) and \(Y\), including estimates of \(P(X = x, Y = y)\), \(P(X = x)\), \(P(Y = y)\), \(P(X = x \mid Y = y)\), and \(P(Y = y \mid X = x)\).
6. Explain how to compute the expected frequencies (counts) under the null model of independence using the multiplication rule for independent events.
7. Distinguish between statistical association and causation.