This chapter introduces the chi-square family of statistical tests, focusing on their application in categorical data analysis using R. Using both a hypothetical planetary dataset and the CPS85 dataset, readers learn to construct contingency tables, compute observed and expected frequencies and apply the chi-square equation to test hypotheses about associations between categorical variables. The chapter covers both the Goodness of Fit test for single categorical variables and the Test of Independence for two-variable analyses, illustrating step-by-step calculations and interpretation. Key statistical concepts are addressed, including null and alternative hypotheses, p-values, degrees of freedom, and statistical significance. Additionally, assumptions of chi-square tests and effect size measures, such as Phi, Cramér’s V, and contingency coefficients, are explained. Readers are guided through implementing these analyses in R, generating tables and plots, calculating effect sizes, and preparing results for reporting, providing a practical foundation for performing and interpreting chi-square tests in research.

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The Chi-Square Family of Tests

  • Mark A. Perkins

摘要

This chapter introduces the chi-square family of statistical tests, focusing on their application in categorical data analysis using R. Using both a hypothetical planetary dataset and the CPS85 dataset, readers learn to construct contingency tables, compute observed and expected frequencies and apply the chi-square equation to test hypotheses about associations between categorical variables. The chapter covers both the Goodness of Fit test for single categorical variables and the Test of Independence for two-variable analyses, illustrating step-by-step calculations and interpretation. Key statistical concepts are addressed, including null and alternative hypotheses, p-values, degrees of freedom, and statistical significance. Additionally, assumptions of chi-square tests and effect size measures, such as Phi, Cramér’s V, and contingency coefficients, are explained. Readers are guided through implementing these analyses in R, generating tables and plots, calculating effect sizes, and preparing results for reporting, providing a practical foundation for performing and interpreting chi-square tests in research.