An Early Start on Inference (original) (raw)

A Modern way to teach Statistics, with an application

Advances in Image and Video Processing

The traditional way when teaching statistics is that Statistics has two main branches, namely Descriptive and Inferential statistics, with probability as a "link" between them. The Descriptive statistics are brief descriptive coefficients that summarize a given data set, which can be either a representation of the entire or a sample of a population, While Inferential statistics are based on a random sample of data taken from a population to describe and make inferences about the population. The modern way we suggest for teaching statistics is to divide the Statistics into three branches. Namely Descriptive, Diagnostic and Predictive Statistics. In this paper, we will reclassify the inferential Statistics tests to Diagnostic Statistics tests and Predictive Statistics tests and give an applied example.

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...

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...

The Role of the Sampling Distribution in Developing Understanding of Statistical Inference

2000

There has been widespread concern expressed by members of the statistics education community in the past few years about the lack of any real understanding demonstrated by many students completing courses in introductory statistics. This deficiency in understanding has been particularly noted in the area of inferential statistics, where students, particularly those studying statistics as a service course, have been inclined to view statistical inference as a set of unrelated recipes. As such, these students have developed skills that have little practical application and are easily forgotten. This thesis is concerned with the development of understanding in statistical inference for beginning students of statistics at the post-secondary level. This involves consideration of the nature of understanding in introductory statistical inference, and how understanding can be measured in the context of statistical inference. In particular, the study has examined the role of the sampling dis...

Predict! Teaching statistics using informal statistical inference.

In this article for teachers, informal statistical inference is introduced as an approach to teaching statistics. This idea has now been researched from primary school through university classrooms around the world. Informal statistical inference can help students better appreciate the usefulness of statistics for both everyday life and future careers. Informal statistical inference is introduced and how it differs from the way we usually teach statistics. A unit from a middle school classroom is used to illustrate how the class were learning statistics while making informal inferences. Finally, some ideas are provided for turning a regular statistics lesson into one that lets your students make inferences.

Students and Teachers’ Knowledge of Sampling and Inference

New ICMI Study Series, 2011

Ideas of statistical inference are being increasingly included at various levels of complexity in the high school curriculum in many countries and are typically taught by mathematics teachers. Most of these teachers have not received a specific preparation in statistics and therefore could share some of the common reasoning biases and misconceptions about statistical inference that are widespread among both students and researchers. In this chapter the basic components of statistical inference, appropriate to school level, are analysed, and research related to these concepts is summarised. Finally, recommendations are made for teaching and research in this area.

A New Way of Teaching Statistics

Journal of Educational Technology Systems, 1995

Teaching statistics through computer-assisted simulations eliminates the constraints and challenges associated with teaching the course using mathematics. It also provides students with a practical means for solving real-life problems and a solid conceptual grasp of the problem-solving nature of the discipline. A text that dcemphasizcs mathematics and introduces simulation as a means of understanding concepts, along with software designed for computer-intensive statistical methods and a workbook of journal article selections provide the foundation materials for such a study of statistics. A special course guide also was developed to provide a clear introduction to the software for naive users, show how the software and the text are related, and connect the simulation techniques to standard statistical tests. Altogether these materials not only provide a positive experience for students studying statistics, but they allow them to study the subject independently and at a distance.

Students\u27 Understanding of the Concepts Involved in One-Sample Hypothesis Testing

2019

Hypothesis testing is a prevalent method of inference used to test a claim about a population parameter based on sample data, and it is a central concept in many introductory statistics courses. At the same time, the use of hypothesis testing to interpret experimental data has raised concerns due to common misunderstandings by both scientists and students. With statistics education reform on the rise, as well as an increasing number of students enrolling in introductory statistics courses each year, there is a need for research to investigate students’ understanding of hypothesis testing. In this study we used APOS Theory to investigate twelve introductory statistics students’ reasoning about one-sample population hypothesis testing while working two real-world problems. Data were analyzed and compared against a preliminary genetic decomposition, which is a conjecture for how an individual might construct an understanding of a concept. This report presents examples of Actions, Proce...

Bootstrapping" students' understanding of statistical inference

2013

2 "BootStrAPPing" StudentS' underStAnding oF StAtiStiCAl inFerenCe introduction this report summarises the research activities and findings from the tlri-funded project conducted in year 13, introductory university and workplace classes, entitled "'Bootstrapping' Statistical inferential reasoning". the project was a 2-year collaboration among three statisticians, two researchers, 16 year 13 teachers, seven university lecturers, one workplace practitioner, three teacher professional development facilitators, and one quality assurance advisor. the project team designed innovative computer-based approaches to develop students' inferential reasoning and sought evidence that these innovations were effective in developing students' understanding of statistical inference. Key findings the bootstrapping and randomisation methods using dynamic visualisations especially designed to enhance • conceptual understanding have the potential to transform the learning of statistical inference.