10. Categorical data analysis

This chapter introduces the foundational concepts and methods of categorical data analysis, focusing on the chi-square (χ²) tests. It begins by exploring the theory and application of the χ² goodness-of-fit test, a statistical tool used to compare observed frequencies in categorical data against expected distributions under a null hypothesis. Through examples such as simulated randomness in human behaviour and card choice experiments, the chapter elucidates the importance of translating observed phenomena into statistical hypotheses. The mathematical notation, calculation of test statistics, and interpretation of results are explained in detail, including how to assess the rejection of null hypotheses and the role of degrees of freedom in shaping test outcomes. The chapter also describes how to undertake these analyses in jamovi.

In addition to the goodness-of-fit test, the chapter examines the χ² test of independence, which assesses relationships between two categorical variables. By employing contingency tables and statistical constructs, the text illustrates hypothesis formulation and testing in scenarios where category associations are analysed. Alternative methods, such as the Fisher exact test and McNemar test, are introduced to address specific challenges like small sample sizes and repeated measures designs. The chapter emphasises practical considerations, such as ensuring independence of data and sufficient expected frequencies, and provides guidance on reporting results with clarity and relevance. For further exploration, the text recommends resources for advanced study in categorical data analysis.