Modelización de la variabilidad muestral en diferentes metodologías de la inferencia

Abstract

Statistical inference allows the results obtained in the study of samples to be extended to the populations from which the samples have been collected. Current teaching favours the frequentist methodology, based on the consideration of the sampling distribution of the statistic and in which numerous difficulties of interpretation by students and professionals have been described. In statistical practice, however, other modelling approaches are used, such as Bayesian and resampling inference, and recently the so-called informal inference approach has been introduced into the teaching of statistics. The aim of this paper is to analyze how sampling variability is taken into account in these different approaches. Using elements of the ontosemiotic approach, we show that learning is concentrated on different mathematical objects, but that modelling plays an important role in all of them. Some frequent errors in learning inference are also interpreted as semiotic conflicts. We finish with some reflections on the teaching of statistical inference.