Aspects of Contingency Tables

Abstract

Background. From a simple two-by-two table to one with higher dimensions, there are many aspects of contingency tables besides dimensions to consider. Some aspects, like contradictory context (e.g., smoking and lung disease) have been studied repeatedly, but others like whether there is a clear explanatory and response variable or not are absent from the literature. These aspects can impact how students reason and should be considered when sequencing instructional material. Limited work exists to understand how these different aspects impact student reasoning. Methods. I completed a literature review to identify different aspects of contingency tables and related findings. Furthermore, I conducted a series of clinical interviews with students working with contingency tables based on protocols that were developed in consideration of these aspects. I analyzed the information resulting from the interviews, including video recordings, transcripts, and written work. I started with an initial framework that was informed by past literature and a pilot study. As the analysis ensued, I made modifications to the framework in order to account for emergent themes that could not be captured by current forms of the framework. Findings. In this poster, I present the aspects of contingency tables (1. Context, 2. Population Comparison vs. Association of Variables, 3. Explanatory & Response Variables, 4. Direct and Indirect Association, 5. Positive and Negative (Inverse) Association, 6. Symmetric and Asymmetric, 7. Table Dimension & Size, 8. Variation, 9. Numbers) and include a summary of past studies. Additionally, I present the result of my analysis of clinical interviews, which is a revised framework and a flowchart of student reasoning. Implications. It is important to consider different aspects of contingency tables when designing instruction, curriculum, or professional development. For example, problems with a clear explanatory and response variable, population comparisons, and symmetric variables might be easier for students. Instructional sequences should consider these aspects as well, and the numbers should be selected based on real or realistic context and in consideration of the ways students reason.