ABOUT ASSOCIATION IN CONTINGENCY TABLES

The aim of this research was to identify students' preconceptions concerning statistical association in contingency tables. An experimental study was carried out with 213 preuniversity students, and it was based on students' responses to a written questionnaire including 2 x 2, 2 x 3, and 3 x 3 contingency tables. In this article, the students' judgments of association and solution strategies are compared with the findings of previous psychological research on 2 x 2 contingency tables. We also present an original classification of students' strategies, from a mathematical point of view. Correspondence analysis is used to show the effect of item task variables on students' strategies. Finally, we include a qualitative analysis of the strategies of 51 students, which has served to characterize three misconceptions concerning statistical association. The concepts and procedures involved in the study of correlation and regression are intended to determine statistical dependence relationships between numerical variables. The extension of the idea of correlation to qualitative variables has originated the general concept of association, the teaching of which is a fundamental topic in the statistics curricula of many different university degrees. In secondary education and preuniversity courses, three different topics are included in the teaching of association: the analysis of contingency tables, the determination of correlation between quantitative variables, and the comparison of a numerical variable in two or more samples. The concept of association or statistical dependence has great relevance to mathematics education, because it extends functional dependence and is fundamental for many statistical methods, allowing us to model numerous phenomena in different sciences (e.g., biology, economics, medicine, education). This topic has significant connections with research on functional thinking and other areas of mathematics education, such as probability and proportional reasoning. The main goal in many of these applications is to find causal explanations that permit us to understand our environment. However, the association does not necessarily imply a causal relationship. Sometimes, because of the influence of concurrent factors, it is possible to find a high coefficient of association among variables when there is no causal link (spurious correlation). Besides this epistemological difficulty, psychological research has shown that judging association is not an intuitive ability. Adults sometimes base their judgment on