Past present and future of statistical science pdf
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- Teaching the Past, Present, and Future of Statistics
- Публикация:Statistical Science 2014
Over the past quarter century, information in the form of digital data has become the foundation on which governments, industries, and organizations base many of their decisions. In our modern world, there exists a deluge of data that grows exponentially each day. Companies and institutions have come to the awareness that not only must they have access to the right data at the right time, but they must also have access to analysis of the raw data to make correct decisions.
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Statistics education is the practice of teaching and learning of statistics , along with the associated scholarly research. Statistics is both a formal science and a practical theory of scientific inquiry , and both aspects are considered in statistics education. Education in statistics has similar concerns as does education in other mathematical sciences , like logic , mathematics , and computer science.
At the same time, statistics is concerned with evidence-based reasoning, particularly with the analysis of data.
Therefore, education in statistics has strong similarities to education in empirical disciplines like psychology and chemistry , in which education is closely tied to "hands-on" experimentation. Mathematicians and statisticians often work in a department of mathematical sciences particularly at colleges and small universities.
Statistics courses have been sometimes taught by non-statisticians, against the recommendations of some professional organizations of statisticians and of mathematicians. Statistics education research is an emerging field that grew out of different disciplines and is currently establishing itself as a unique field that is devoted to the improvement of teaching and learning statistics at all educational levels.
Statistics educators have cognitive and noncognitive goals for students. For example, former American Statistical Association ASA President Katherine Wallman defined statistical literacy as including the cognitive abilities of understanding and critically evaluating statistical results as well as appreciating the contributions statistical thinking can make.
In particular, educators currently seek to have students: "design investigations; formulate research questions; collect data using observations, surveys, and experiments; describe and compare data sets; and propose and justify conclusions and predictions based on data. Despite the fact that cognitive goals for statistics education increasingly focus on statistical literacy, statistical reasoning, and statistical thinking rather than on skills, computations and procedures alone, there is no agreement about what these terms mean or how to assess these outcomes.
A first attempt to define and distinguish between these three terms appears in the ARTIST website  which was created by Garfield , delMas and Chance and has since been included in several publications. Further cognitive goals of statistics education vary across students' educational level and the contexts in which they expect to encounter statistics. Statisticians have proposed what they consider the most important statistical concepts for educated citizens.
For example, Utts published seven areas of what every educated citizen should know, including understanding that "variability is normal" and how "coincidences… are not uncommon because there are so many possibilities. Non-cognitive outcomes include affective constructs such as attitudes, beliefs, emotions, dispositions, and motivation. Beliefs are defined as one's individually held ideas about statistics, about oneself as a learner of statistics, and about the social context of learning statistics.
Students' web of beliefs provides a context for their approach towards their classroom experiences in statistics. Many students enter a statistics course with apprehension towards learning the subject, which works against the learning environment that the instructor is trying to accomplish. Therefore, it is important for instructors to have access to assessment instruments that can give an initial diagnosis of student beliefs and monitor beliefs during a course.
For examples of such instruments, see the attitudes section below. Disposition has to do with the ways students question the data and approach a statistical problem. Dispositions is one of the four dimensions in Wild and Pfannkuch's  framework for statistical thinking, and contains the following elements:. Scheaffer states that a goal of statistics education is to have students see statistics broadly. He developed a list of views of statistics that can lead to this broad view, and describes them as follows: .
Since students often experience math anxiety and negative opinions about statistics courses, various researchers have addressed attitudes and anxiety towards statistics. Some instruments have been developed to measure college students' attitudes towards statistics, and have been shown to have appropriate psychometric properties.
Examples of such instruments include:. Careful use of instruments such as these can help statistics instructors to learn about students' perception of statistics, including their anxiety towards learning statistics, the perceived difficulty of learning statistics, and their perceived usefulness of the subject. Nevertheless, one of the goals of statistics education is to make the study of statistics a positive experience for students and to bring in interesting and engaging examples and data that will motivate students.
According to a fairly recent literature review,  improved student attitudes towards statistics can lead to better motivation and engagement, which also improves cognitive learning outcomes.
In New Zealand , a new curriculum for statistics has been developed by Chris Wild and colleagues at Auckland University. Rejecting the contrived, and now unnecessary due to computer power, approach of reasoning under the null and the restrictions of normal theory, they use comparative box plots and bootstrap to introduce concepts of sampling variability and inference. In the United Kingdom , at least some statistics has been taught in schools since the s.
In the Smith inquiry made the following statement:. On the one hand, there is widespread agreement that the Key Stage 4 curriculum is over-crowded and that the introduction of Statistics and Data Handling may have been at the expense of time needed for practising and acquiring fluency in core mathematical manipulations.
Many in higher education mathematics and engineering departments take this view. On the other hand, there is overwhelming recognition, shared by the Inquiry, of the vital importance of Statistics and Data Handling skills both for a number of other academic disciplines and in the workplace. The Inquiry recommends that there be a radical re-look at this issue and that much of the teaching and learning of Statistics and Data Handling would be better removed from the mathematics timetable and integrated with the teaching and learning of other disciplines e.
The time restored to the mathematics timetable should be used for acquiring greater mastery of core mathematical concepts and operations. In the United States , schooling has increased the use of probability and statistics, especially since the s. Topics in probability and statistical reasoning are taught in high school algebra or mathematical science courses; statistical reasoning has been examined in the SAT test since The College Board has developed an Advanced Placement course in statistics , which has provided a college-level course in statistics to hundreds of thousands of high school students, with the first examination happening in May The framework contains learning objectives for students at each conceptual level and provides pedagogical examples that are consistent with the conceptual levels.
Estonia is piloting a new statistics curriculum developed by the Computer-Based Math foundation based around its principles of using computers as the primary tool of education. Statistics is often taught in departments of mathematics or in departments of mathematical sciences.
At the undergraduate level, statistics is often taught as a service course. By tradition in the U. My view is that statistics as a theoretical discipline is better taught late rather than early, whereas statistics as part of scientific methodology should be taught as part of science.
In the United Kingdom , the teaching of statistics at university level was originally done within science departments that needed the topic to accompany the teaching of their own subjects, and departments of mathematics had limited coverage before the s. Psychologist Andy Field British Psychological Society Teaching and Book Award created a new concept of statistical teaching and textbooks that goes beyond the printed page.
Enrollments in statistics have increased in community colleges , in four-year colleges and universities in the United States.
At community colleges in the United States, mathematics has experienced increased enrollment since The report includes a brief history of the introductory statistics course and recommendations for how it should be taught.
In many colleges, a basic course in "statistics for non-statisticians" has required only algebra and not calculus ; for future statisticians, in contrast, the undergraduate exposure to statistics is highly mathematical. Students wanting to obtain a doctorate in statistics from "any of the better graduate programs in statistics" should also take " real analysis ". The ASA recommends that undergraduate students consider obtaining a bachelor's degree in applied mathematics as preparation for entering a master program in statistics.
Historically, professional degrees in statistics have been at the Master level, although some students may qualify to work with a bachelor's degree and job-related experience or further self-study. For a doctoral degree in statistics, it has been traditional that students complete a course in measure-theoretic probability as well as courses in mathematical statistics.
Such courses require a good course in real analysis , covering the proofs of the theory of calculus and topics like the uniform convergence of functions.
The question of what qualities are needed to teach statistics has been much discussed, and sometimes this discussion is concentrated on the qualifications necessary for those undertaking such teaching. The question arises separately for teaching at both school and university levels, partly because of the need for numerically more such teachers at school level and partly because of need for such teachers to cover a broad range of other topics within their overall duties.
Given that "statistics" is often taught to non-scientists, opinions can range all the way from "statistics should be taught by statisticians", through "teaching of statistics is too mathematical" to the extreme that "statistics should not be taught by statisticians".
In the United States especially, statisticians have long complained that many mathematics departments have assigned mathematicians without statistical competence to teach statistics courses, effectively giving " double blind " courses. The principle that college-instructors should have qualifications and engagement with their academic discipline has long been violated in United States colleges and universities, according to generations of statisticians.
For example, the journal Statistical Science reprinted "classic" articles on the teaching of statistics by non-statisticians by Harold Hotelling ;    Hotelling's articles are followed by the comments of Kenneth J.
Arrow , W. Moore , James V. Sidek, Shanti S. Gupta, Robert V. Hogg , Ralph A. Bradley, and by Harold Hotelling, Jr. Examining data from , Schaeffer and Stasny  reported. The principle that statistics-instructors should have statistical competence has been affirmed by the guidelines of the Mathematical Association of America , which has been endorsed by the ASA. The unprofessional teaching of statistics by mathematicians without qualifications in statistics has been addressed in many articles.
The literature on methods of teaching statistics is closely related to the literature on the teaching of mathematics for two reasons. First, statistics is often taught as part of the mathematics curriculum, by instructors trained in mathematics and working in a mathematics department.
Second, statistical theory has often been taught as a mathematical theory rather than as the practical logic of science as the science that "puts chance to work" in Rao's phrase and this has entailed an emphasis on formal and manipulative training, such as solving combinatorial problems involving red and green jelly beans.
Statisticians have complained that mathematicians are prone to over-emphasize mathematical manipulations and probability theory and under-emphasize questions of experimentation , survey methodology , exploratory data analysis , and statistical inference.
In recent decades, there has been an increased emphasis on data analysis and scientific inquiry in statistics education. In the United Kingdom, the Smith inquiry Making Mathematics Count suggests teaching basic statistical concepts as part of the science curriculum, rather than as part of mathematics. Besides an emphasis on the scientific inquiry in the content of beginning of statistics, there has also been an increase on active learning in the conduct of the statistics classroom.
Sessions on statistics education area also offered at many conferences in mathematics educations such as the International Congress on Mathematical Education , the National Council of Teachers of Mathematics , the Conference of the International Group for the Psychology of Mathematics Education, and the Mathematics Education Research Group of Australasia. The International Research Forums on Statistical Reasoning, Thinking, and Literacy offer scientific gatherings every two years and related publications in journals, CD-ROMs and books on research in statistics education.
Only three universities currently offer graduate programs in statistics education: the University of Granada ,  the University of Minnesota ,   and the University of Florida. These dissertations are archived on the IASE web site. Two main courses in statistics education that have been taught in a variety of settings and departments are a course on teaching statistics  and a course on statistics education research.
Teachers of statistics have been encouraged to explore new directions in curriculum content, pedagogy and assessment. In an influential talk at USCOTS, researcher George Cobb presented an innovative approach to teaching statistics that put simulation , randomization , and bootstrapping techniques at the core of the college-level introductory course, in place of traditional content such as probability theory and the t -test.
Other researchers have been exploring the development of informal inferential reasoning as a way to use these methods to build a better understanding of statistical inference. Another recent direction is addressing the big data sets that are increasingly affecting or being contributed to in our daily lives. Statistician Rob Gould, creator of Data Cycle, The Musical dinner and theatre spectacular, outlines many of these types of data and encourages teachers to find ways to use the data and address issues around big data.
Driving both of these changes is the increased role of computing in teaching and learning statistics. From Wikipedia, the free encyclopedia. Practice of teaching and learning of statistics, along with the associated scholarly research. Not to be confused with "education statistics", the use of statistics in education research.
The examples and perspective in this section deal primarily with the United States and do not represent a worldwide view of the subject.
You may improve this section , discuss the issue on the talk page , or create a new section, as appropriate.
Teaching the Past, Present, and Future of Statistics
The Committee of Presidents of Statistical Societies COPSS is celebrating its 50th anniversary with this magnum opus not only about statistics and science but also about people and their passion for discovery. Through the contributions of a distinguished group of 50 statisticians who are past winners of at least one of the five awards sponsored by COPSS, this volume showcases the breadth and vibrancy of statistics, describes current challenges and new opportunities, highlights the exciting future of statistical science, and provides guidance to future generations of statisticians. Skip to content Skip to navigation. Search form Search. Past, Present, and Future of Statistical Science.
PDF | On Jan 1, , Xihong Lin and others published Past, Present, and Future of Statistical Science Preface | Find, read and cite all the.
Публикация:Statistical Science 2014
The module is not intended to be a competitor to third-party libraries such as NumPy, SciPy, or proprietary full-featured statistics packages aimed at professional statisticians such as Minitab, SAS and Matlab. Quantitative Analysis. No attempt has been made to issue corrections for errors in typing, punctuation, etc. Mathematical statistics by Rietz, H.
The world is becoming increasingly complex, with larger quantities of data available to be analyzed.