Enhancing Statistical Reasoning through Descriptive Models and exploratory approach

Information

This work aims to demonstrate how, through an exploratory approach and the use of what we can call descriptive models, statistical reasoning can be developed around independence tests for categorical data. In the context of graduate (2024-II) and undergraduate programs (2020-2022), we have used the independence test for categorical variables as a bridge between descriptive statistics and inferential statistics, starting with the exploration of a two-factor bar plot, first reading the row profile and then comparative distributions. The results have shown better performance in solving word problems; the observed approval rate has been 80% for graduate students and 60-70% among undergraduate students. Qualitative evaluation has revealed a better understanding of concepts such as the meaning of independence for categorical variables, the assimilation of the chi-squared statistical test as a measure of distance between observed and expected distributions, the need to establish a limit for the rejection region and why it can be 5% or usual significance values, how to find a p-value under the Chi squared distribution, and writing the conclusion according to the context where they comparing the graphical analysis and the  chi-squared independence test conclusion.