Chapter 22

Two-way tables

1. Explain how a two-way table can be used to summarize counts of a categorical variable across two or more populations.
2. Give an analogy between one-, two-, and multi-sample tests for population means and a two-way table for testing claims about proportions of a category across one, two, and more than two populations.
3. State the convention we will use in the class in terms of what rows and columns correspond to in a two-way table.

Hypotheses for two-way tables of counts

1. Explain what we mean by two variables being associated.
2. Explain what we mean by two variables being independent.
3. Describe how independence between two variables manifests in a two-way table.
4. State the generic form of the null and alternative hypotheses about two categorical variables in a population.
5. Given a problem about two categorical variables, identify the relevant null and alternative hypotheses from the problem.

Expected counts and the chi-square statistic

1. Explain under what hypothesis the expected counts for the \(\chi^{2}\) statistic for association are calculated.
2. State the \(\chi^{2}\) statistic for association.
3. State the sampling distribution of the \(\chi^{2}\) statistic for association under the null hypothesis.
4. Construct a matrix from a two-way table using matrix in R.
5. Compute the \(\chi^{2}\) statistic for association using xchisq.test from mosaic.
6. Interpret the output of xchisq.test in terms of the \(\chi^{2}\) statistic for association.

The chi-square test

1. Interpret the output of xchisq.test in terms of the \(\chi^{2}\) test for association.
2. Perform a hypothesis test for association using xchisq.test.

Conditions for the chi-square test

1. State the assumptions on the data for the \(\chi^{2}\) statistic for association to follow a \(\chi^{2}\) distribution.