Informal inference – Some thoughts to r...

Informal inference is a term used more recently in statistics education to unify various approaches starting from simulation of probabilistic models (to illustrate their impact and to solve the problems), or using re-randomisation methods to reduce the required assumptions (as done in non-parametric statistics), and going on to use bootstrap to replace statistical inference by a data-oriented approach, as was the intention by Efron and Tibshirani. There are special needs in applications to modify the traditional methods of statistical inference that ask for the specific approaches (reduce assumptions; find tractable solutions where parametric models do not fit). It is pertinent to analyse these approaches from an educational perspective. Vital questions and issues are: What is the role of probability and can it be reduced to a purely frequentist concept? What are the consequences of this approach to the perception of modelling – as all information is contained in the given data? How smooth is the educational path from informal inference towards statistical inference as type-II errors are not embedded in a pure re-randomisation and bootstrap approach? Informal inference as it is intended in the current developments goes beyond informally exploring probabilistic models by simulation and aims to replace traditional statistical inference. Is this the way forward both logically and educationally?

Keywords: comparative statistical inference; statistical thinking; foundations; statistics education.