Chi-Square Tests of Hypotheses About Frequency Tables

Like the second course in this sequence, this third course builds on the first course, Introducing Null Hypothesis Significance Testing With the z-Test, in this case by applying the logic of Null Significance Hypothesis Testing (NHST) to research designs involving inferences about frequency counts using the chi-square test.

The course begins with a thorough examination of contingency tables and the research contexts in which they are used, including several examples from a variety of situations. The course also covers how to identify and distinguish which chi-square test, the goodness-of-fit test or the test of independence, is appropriate for a given research design, how to state hypothesis appropriate to a given design, and how to recognize when assumptions and conditions for the appropriate use of these tests have been met.

In turn, the course considers how to set up and complete the calculations for the chi-square statistic with both the goodness-of-fit test and the test of independence, including how to make these calculations using raw data or summaries of frequency counts within the jamovi statistical program. In both cases, the steps of NHST are made explicit, from stating hypotheses to making the statistical decision.

The course also considers calculation of effect size for contingency tables, as well as issues surrounding the interpretation of the results of contingency table analysis, including cautions about making cause and effect inferences.

Learning objectives

• Explain when to use chi-square analyses.
• Identify hypotheses appropriate for chi-square analyses.
• Explain the logic of chi-square analyses.
• Explain the assumptions of chi-square analyses.
• Conduct a chi-square goodness-of-fit test.
• Conduct a chi-square test of independence.
• Analyze effect size for chi-square analyses.