Comparing Fisher Information in Continuous, Dichotomized, and Discretized Data: A Pedagogical Perspective with Illustrations

In this pedagogical paper we provide an illustration of Fisher information through examples based on the dichotomization and discretization of continuous variables following a Gaussian distribution. In these examples, we demonstrate the information loss and quantify the increase in sample size necessary to recover this loss. To facilitate understanding and application, we also provide R codes for performing illustrative simulations. This approach aims to improve the teaching and learning experience of Fisher information in statistical education.