Other

• Promoting statistics thinking amongst secondary school students in the national context

Although secondary school students in many countries (like Ireland) get a limited and basic introduction to Statistics, it is often of a mechanical and tedious nature with little or no emphasis on data analysis and practical examples. In particular they, together with their teachers, rarely see the applicability and challenging nature of statistical thinking. Statisticians need to promote these aspects of statistics to the young, their teachers and the public at large. It is suggested that the use of examples of a local (often of a national) nature should be encouraged in an effort to emphasize the relevance of statistical thinking. With this in mind, several examples which have been successfully used in the Irish context are discussed.

• Toward A Statistically Literate Citizenry: What Statistics Everyone Should Know

In my paper 'Statistical Literacy - Statistics Long After School' presented at ICOTS V in Singapore, I discussed creating a course 'Citizens Statistics 101' and suggested what topics should be included in such a course. Unfortunately, the project has not happened, but I continue to think about it and present in this paper a practice exam that illustrates its content. The bottom line hope is that someday there will be no need for such a course as students will learn the statistics in school that will enable them to be statistically literate citizens.

• What Educated Citizens Should Know About Statistics And Probability

Much has changed since the widespread introduction of statistics courses into the curriculum in the 1960s and 1970s, but the way introductory statistics courses are taught has not kept up with those changes. This paper discusses the changes, and the way the introductory syllabus should change to reflect them. In particular, seven ideas are discussed that every student who takes elementary statistics should learn and understand in order to be an educated citizen. Misunderstanding these topics leads to cynicism among the public at best, and misuse of study results by physicians and others at worst.

• How Far Can We Go In The Statistics Curriculum Development At The Secondary School Level To Reach Successfully The Objective?

In most countries at the secondary school level, the statistics curriculum is a part of the mathematics curriculum. If we have a look at the papers on statistical education at the college or at the university published ten years ago, we can see that the requirements are practically adaptable to the actual secondary level. With the changes occurring in mathematical education at the secondary school level, with the development of interdisciplinary class projects especially for higher grades (9-12), with the increasing availability of computers at school, the teaching of statistics has changed. But first, we have to define the objective or more precisely the objectives, then the ways to get them and conclude with the limits and their reasons of the approach.

• Some Lessons To Be Learned From Curriculum Developments In Statistics

Over the past 40 years or more there have been many attempts to improve the curriculum in school statistics. They have had varying degrees of success. Referring mainly to experience in the UK, but also noting developments in the USA, I shall try to identify the lessons to be learned if such curriculum development is to be successful.

• Statistics At Foundation School Level In South Africa The Way Forward

Historically, little or no statistics has been taught at schools in South Africa. This is about to change dramatically with the introduction of a new curriculum. The dilemma however, is that statistics will have to be taught by teachers who have had little or no training in statistics! The authors propose a plan, aimed at the foundation phase, to assist teachers to cope with the challenges of teaching statistics successfully. They emphasize that it is of cardinal importance that statistical training is developed according to the age of the learners, bearing in mind the mathematical tools that they have at their disposal at that time.

• Statistical Consulting With Undergraduates - A Community Outreach Approach

At Sonoma State University, we offer a 2-hour per week class in Statistical Consulting. All our statistics majors must take the class twice, and other students may also take the class. The only prerequisite for the class is a semester of Elementary Statistics. This leads to a very varied class, in terms of statistical ability and experience. Our clients at the Statistical Consulting Center are largely from two sources, namely other departments at the university, and local non-profit organizations. Both these sources typically have projects that are suitable for our consulting class, so that both unsophisticated and advanced students can benefit from it. I will present some examples of these projects, and discuss the perhaps surprisingly high levels of satisfaction of the students, in terms of their learning objectives, and of the clients, in terms of their needs. Faculty also enjoy teaching the class, and the university gets much positive publicity in the community.

• Accessible Methodologies For Estimating Density Functions

It is often the case that the moments of a distribution can be readily determined, while its exact density function is mathematically intractable. We show that the density function of a continuous distribution defined on a closed interval can be easily approximated from its exact moments by solving a linear system involving a Hilbert matrix. When sample moments are being used, the same linear system will yield density estimates. A simple formula that is based on an explicit representation of the elements of the inverse of a Hilbert matrix is being proposed as a means of directly determining density estimates or approximants without having to resort to kernels or orthogonal polynomials. As illustrations, density estimates will be determined for the 'Buffalo snowfall' data set and the density of the distance between two random points in a cube will be approximated. Finally, an alternate methodology is proposed for obtaining smooth density estimates from averaged shifted histograms.

• Interpretation Of Regression Output: Diagnostics, Graphs, and the Bottom Line

A standard approach in presenting the results of a statistical analysis of regression data in scientific journals is to focus on the question of statistical significance of regression coefficients. The reporting of p-values in conjunction with a description of the various positive and negative associations between the response and the factors in question ensues. The real question of interest beyond these initial assessments ought to be, "how well does the treatment work?" The point of view taken here will be that this standard presentation, while important, constitutes only a first order approximation to a complete analysis, and that the bottom line ought to involve the quantification of regression effects on the scale of observable quantities. This will mainly be accomplished graphically. It is also emphasized that diagnostic assessment of the compatibility of the data to the model should be based on similar considerations.

• Understanding The Sign Of A Correlation Coefficient: An Example

In many books on Statistics, it is often stated that correlation between two variables X and Y is positive if, as X increases Y also increase. Equivalently, correlation between X and Y is positive, if large values of X most often correspond to the large values of Y and small values X, most often correspond to small values of Y. The correlation is negative if large values of X most often correspond to small values of Y and visa versa. With an example we show that this statement in not always correct. We also give the correct interpretation for the sign of the correlation and its relation to the behavior of the two random variables.