Chi-Square Testing

Pearson’s chi-squared (χ²) test is a statistical method used to evaluate whether observed categorical frequencies differ from those expected under a specified hypothesis (Pearson, 1900). It is one of the most widely applied techniques for analyzing categorical data in the social and educational sciences, where researchers frequently work with survey responses, program participation counts, course modality preferences, demographic variables, or other frequency-based outcomes (Agresti, 2019; Agresti et al., 2021). All chi-square procedures rely on comparing observed counts to expected counts derived from a model representing the null hypothesis. Depending on the research question, Pearson’s chi-square test can take three forms: A test of independence, used to determine whether two categorical variables measured in a single population are associated. A test of homogeneity, used to evaluate whether the distribution of a categorical variable is the same across multiple populations or groups. A goodness-of-fit test, used when assessing whether the distribution of a single categorical variable aligns with a theoretical or hypothesized distribution. Across all forms, the χ² test uses the same underlying statistic but applies it to different designs and hypotheses (Agresti, 2013). In educational research, chi-square tests are commonly used to examine questions such as whether instructional preferences vary by student subgroup, whether course outcomes differ across departments, or whether observed usage patterns of student support services match institutional expectations. By comparing observed and expected distributions, researchers can determine whether the patterns present in categorical data are likely due to chance or reflect meaningful differences that warrant further investigation (Field, 2013; McHugh, 2013).