Many paths lead to statistical inference (original) (raw)
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A Comparative Educational Study of Statistical Inference
2013
In his “Comparative Statistical Inference”, Barnett (1982) investigates the various approaches towards statistical inference from a mathematical and philosophical perspective. There have been a few isolated endeavours to develop varied teaching approaches of statistical inference. ‘Comparative statistical inference from an educational perspective’ is long overdue. After discussing Barnett, we give an overview on various attempts to simplify the concepts for teaching. Informal inference is a major endeavour among such projects; resampling and Bootstrap is a newer development in statistical inference, which has also some appeal for teaching. In the light of Barnett’s comparative evaluation we develop some essential alternatives for teaching like Bayes or non Bayes. References to Barnett will illustrate that simple solutions might bias the concepts. Rather than optimizing isolated approaches towards teaching statistical inference, a comparative educational study is suggested. The aim o...
Informal inference – approaches towards statistical inference
Decision Making Based on Data Proceedings IASE 2019 Satellite Conference, 2019
The development of methods suitable to tackle the problem of inductive logic – how to justify arguments that generalise findings from data – has been signified by great controversies in the foundations and – later – also in statistics education. There have been several attempts to reconcile the various approaches or to simplify statistical inference: EDA, Non-parametric statistics, and the Bootstrap. EDA focuses on a strong connection between data and context, non parametrics reduces the complexity of the model, and Bootstrap rests solely on the data. Informal inference subsumes two different areas of didactic endeavour: teaching strategies to simplify the full complexity of inference by analogies, simulations, or visualisations on the one hand, and reduce the complexity of inference by a novel approach of Bootstrap and re-randomisation. The considerations about statistical inference will remain important in the era of Big Data. In this paper, the various approaches are compared for...
A framework for thinking about informal statistical inference
Statistics Education Research Journal, 2009
Informal inferential reasoning has shown some promise in developing students’ deeper understanding of statistical processes. This paper presents a framework to think about three key principles of informal inference – eneralizations ‘beyond the data,’ probabilistic language, and data as evidence. The authors use primary school classroom episodes and excerpts of interviews with the teachers to illustrate the framework and reiterate the importance of embedding statistical learning within the context of statistical inquiry. Implications for the teaching of more powerful satistical concepts at the primary school level are discussed.
A Framework for Thinking About Informal Statisical Inference
SERJ EDITORIAL BOARD, 2009
Informal inferential reasoning has shown some promise in developing students’ deeper understanding of statistical processes. This paper presents a framework to think about three key principles of informal inference – generalizations ‘beyond the data,’ probabilistic language, and data as evidence. The authors use primary school classroom episodes and excerpts of interviews with the teachers to illustrate the framework and reiterate the importance of embedding statistical learning within the context of statistical inquiry. Implications for the teaching of more powerful statistical concepts at the primary school level are discussed.
A comparative study of statistical inference from an educational point of view
2015
Inferential statistics is the scientific method for evidence-based knowledge acquisition. The underlying logic is difficult and the mathematical methods created for this purpose are based on advanced concepts of probability, combined with different epistemological positions. Many different approaches have been developed over the years. Following the classical significance tests of Fisher and the statistical tests by Neyman and Pearson, and decision theory, two more approaches are considered here using qualitative scientific argument: the Bayesian approach, which is linked to a contested conception of probability, and the rerandomization and bootstrap strand, which is bound to simulation. While Barnett (1982) analysed statistical inference from a mathematical/philosophical perspective to shed light on the various approaches, we analyse from the grand scenario of statistics education and investigate the relative merits of each approach. Some thoughts are developed to reconsider inform...
A Framework for Thinking About Informal Statistical INFERENCE7
2009
Informal inferential reasoning has shown some promise in developing students' deeper understanding of statistical processes. This paper presents a framework to think about three key principles of informal inference - generalizations 'beyond the data,' probabilistic language, and data as evidence. The authors use primary school classroom episodes and excerpts of interviews with the teachers to illustrate the framework and reiterate
why is it difficult to understand statistical inference?", 2020
Difficulties in learning (and thus teaching) statistical inference are well reported in the literature. We argue the problem emanates not only from the way in which statistical inference is taught but also from what exactly is taught as statistical inference. What makes statistical inference difficult to understand is that it contains two logics that operate in opposite directions. There is a certain logic in the construction of the inference framework, and there is another in its application. The logic of construction commences from the population, reaches the sample through some steps and then comes back to the population by building and using the sampling distribution. The logic of application, on the other hand, starts from the sample and reaches the population by making use of the sampling distribution. The main problem in teaching statistical inference in our view is that students are taught the logic of application while the fundamental steps in the direction of construction are often overlooked. In this study, we examine and compare these two logics and argue that introductory statistical courses would benefit from using the direction of construction, which ensures that students internalize the way in which inference framework makes sense, rather than that of application.
The Role of Probability for Understanding Statistical Inference
Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics, 2022
Probability is the basis for intelligent actions and decisions in the face of uncertainty. That includes statistical inference as well as considerations of reliability, risk, and decision-making. Curricula have reduced approaches with respect to the nature of probability. With easy access to computer technology, simulation has become the predominant approach to teaching. Although simulation is an effective method to replace complicated mathematics, it reduces concepts to their frequentist part. This culminates in an approach to informal inference that makes probability and conditional probability redundant. However, the relevant properties of statistical inference require a comprehensive conception of probability to be shaped in the individual's cognitive system.
The reasoning behind informal statistical inference
Informal statistical inference (ISI) has been a frequent focus of recent research in statistics education. Considering the role that context plays in developing ISI calls into question the need to be more explicit about the reasoning that underpins ISI. This paper uses educational literature on informal statistical inference and philosophical literature on inference to argue that in order for students to generate informal statistical inferences, there are a number of interrelated key elements that are needed to support their informal inferential reasoning. In particular, we claim that ISI is nurtured by statistical knowledge, knowledge about the problem context, and useful norms and habits developed over time, and is supported by an inquiry-based environment (tasks, tools, scaffolds). We adopt Peirce's and Dewey's view that inquiry is a sense-making process driven by doubt and belief, leading to inferences and explanations. To illustrate the roles that these elements play in supporting students to generate informal statistical inferences, we provide an analysis of three sixth-graders' (aged 12) informal inferential reasoning—the reasoning processes leading to their informal statistical inferences
Parallel Discussion of Classical and Bayesian Ways as an Introduction to Statistical Inference
International Electronic Journal of Mathematics Education, 2009
The purpose of this paper is to report on the conception and some results of a long-term university research project in Budapest. The study is based on an innovative idea of teaching the basic notions of classical and Bayesian inferential statistics parallel to each other to teacher students. Our research is driven by questions like: Do students understand probability and statistical methods better by focussing on subjective and objective interpretations of probability throughout the course? Do they understand classical inferential statistics better if they study Bayesian ways, too? While the course on probability and statistics has been avoided for years, the students are starting to accept the "parallel" design. There is evidence that they understand the concepts better in this way. The results also support the thesis that students' views and beliefs on mathematics decisively influence work in their later profession. Finally, the design of the course integrates reflections on philosophical problems as well, which enhances a wider picture about modern mathematics and its applications.