Statistics education
Encyclopedia
Statistics education is concerned with the teaching and learning of statistics
.
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 statistician
s 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.
, at least some statistics has been taught in schools since the 1930s. At present, A-level qualifications (typically taken by 17-18 year olds) are being developed in "Statistics" and "Further Statistics". The coverage of the former includes: Probability; Data Collection; Descriptive Statistics; Discrete Probability Distributions; Binomial Distribution; Poisson Distributions; Continuous Probability Distributions; The Normal Distribution; Estimation; Hypothesis Testing; Chi-Squared; Correlation and Regression. The coverage of "Further Statistics" includes: Continuous Probability Distributions; Estimation; Hypothesis Testing; One Sample Tests; Hypothesis Testing; Two Sample Tests; Goodness of Fit Tests; Experimental Design; Analysis of Variance (Anova); Statistical Process Control; Acceptance Sampling. The Centre for Innovation in Mathematics Teaching (CIMT) has online course notes for these sets of topics. Revision notes for an existing qualification indicate a similar coverage. At an earlier age (typically 15–16 years) GCSE qualifications in mathematics contain "Statistics and Probability" topics on: Probability; Averages; Standard Deviation; Sampling; Cumumulative Frequency Graphs (including median and quantiles); Representing Data; Histograms. The UK's Office for National Statistics
has a webpage leading to material suitable for both teachers and students at school level. In 2004 the Smith inquiry made the following statement:
, schooling has increased the use of probability and statistics, especially since the 1990s. Summary statistics and graphs are taught in elementary school in many states. 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 1994. 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 1997.
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 1930s. For the twenty years subsequent to this, while departments of mathematics had started to teach statistics, there was little realisation that essentially the same basic statistical methodology was being applied across a variety of sciences. Statistical departments have had difficulty when they have been separated from mathematics departments.
At community college
s in the United States, mathematics has experienced increased enrollment since 1990. At community colleges, the ratio of the students enrolled in statistics to those enrolled in calculus rose from 56% in 1990 to 82% in 1995.
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."Undergraduate major programs should include study of probability and statistical theory, along with the prerequisite mathematics, especially calculus and linear algebra. Programs for nonmajors may require less study of mathematics. Programs preparing for graduate work may require additional mathematics." As undergraduates, future statisticians should have completed courses in multivariate calculus, linear algebra, computer programming, and a year of calculus-based probability and statistics. Students wanting to obtain a doctorate in statistics from "any of the better graduate programs in statistics" should also take "real analysis
". Laboratory courses in physics, chemistry and psychology also provide useful experiences with planning and conducting experiments and with analyzing data. The American Statistical Association
recommends that undergraduate students consider obtaining a bachelor's degree in applied mathematics as preparation for entering a master program in statistics.The American Statistical Association makes the following recommendations for undergraduates wishing to become statisticians: "Major in applied mathematics, or a closely related field. If you do major in a nonstatistical field, minor in mathematics or statistics. Develop a background in mathematics, science, and computers and gain knowledge in a specific field of interest. A master's degree or PhD is very helpful and often recommended or required for higher-level positions."
Historically, professional degrees in statistics have been at the Master level, although some students may qualify to work with an bachelor's degree and job-related experience or further self-study."A master's degree or PhD is very helpful and often recommended or required for higher-level positions." Professional competence requires a background in mathematics---including at least multivariate calculus, linear algebra, and a year of calculus-based probability and statistics. In the United States, a master program in statistics requires courses in probability, mathematical statistics, and applied statistics (e.g., design of experiments, survey sampling, etc.).
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 proof
s of the theory of calculus and topics like the uniform convergence of functions. In recent decades, some departments have discussed allowing doctoral students to waive the course in measure-theoretic probability by demonstrating advanced skills in computer programming
or scientific computing.Stanford University statisticianPersi Diaconis
wrote that "I see a strong trend against measure theory in modern statistics departments: I had to fight to keep the measure theory requirement in Stanford's statistics graduate program. The fight was lost at Berkeley."
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. Edwards Deming
, Ingram Olkin
, David S. Moore
, James V. Sidek, Shanti S. Gupta, Robert V. Hogg
, Ralph A. Bradley, and by Harold Hotelling, Jr. (an economist and son of Harold Hotelling).
Data on the teaching of statistics in the United States has been collected on behalf of the Conference Board of the Mathematical Sciences
(CBMS
). Examining data from 2000, 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 American Statistical Association
. The unprofessional
teaching of statistics
by mathematicians (without qualifications in statistics) has been addressed in many articles.
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
. In the United States, the American Statistical Association
's (ASA's) guidelines for undergraduate statistics specify that introductory statistics should emphasize the scientific method
s of data collection
, particularly randomized experiment
s and random sample
s: further, the first course should review these topics when the theory of "statistical inference
" is studied. Similar recommendations occur hold for the Advanced Placement (AP) course in Statistics. The ASA and AP guidelines are followed by contemporary textbooks in the USA, such as those by Freedman, Purvis & Pisani (Statistics) and by David S. Moore
(Introduction to the Practice of Statistics with McCabe and Statistics: Concepts and Controversies with Notz ) and by Watkins, Schaeffer & Cobb (Statistics: From Data to Decisions and Statistics in Action).
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.
The fact remains that randomized experiments have been rare in the evaluation of teaching methods in recent decades. For decades, many scholars in educational schools have raised objections against increasing the number of randomized experiments, often because of philosophical objections to the use of alleged "physical-scientific" or "quantitative" methods on human subjects. While statisticians have urged an increase in the number of randomized experiments---which again have been rare in all areas of pedagogy
and didactics
in recent decades---statisticians recognize that observational studies remain valuable in education---just as observational studies remain valuable in epidemiology
, political science, economics, etc.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
.
Statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
is both a formal science
Formal science
The formal sciences are the branches of knowledge that are concerned with formal systems, such as logic, mathematics, theoretical computer science, information theory, systems theory, decision theory, statistics, and some aspects of linguistics....
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
Mathematical sciences
Mathematical sciences is a broad term that refers to those academic disciplines that are primarily mathematical in nature but may not be universally considered subfields of mathematics proper...
, like logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
, mathematics
Mathematics education
In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research....
, 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
Chemistry education
Chemistry education is a comprehensive term that refers to the study of the teaching and learning of chemistry in all schools, colleges and universities...
, in which education is closely tied to "hands-on" experimentation.
Mathematicians and statistician
Statistician
A statistician is someone who works with theoretical or applied statistics. The profession exists in both the private and public sectors. The core of that work is to measure, interpret, and describe the world and human activity patterns within it...
s 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.
United Kingdom
In the United KingdomUnited Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
, at least some statistics has been taught in schools since the 1930s. At present, A-level qualifications (typically taken by 17-18 year olds) are being developed in "Statistics" and "Further Statistics". The coverage of the former includes: Probability; Data Collection; Descriptive Statistics; Discrete Probability Distributions; Binomial Distribution; Poisson Distributions; Continuous Probability Distributions; The Normal Distribution; Estimation; Hypothesis Testing; Chi-Squared; Correlation and Regression. The coverage of "Further Statistics" includes: Continuous Probability Distributions; Estimation; Hypothesis Testing; One Sample Tests; Hypothesis Testing; Two Sample Tests; Goodness of Fit Tests; Experimental Design; Analysis of Variance (Anova); Statistical Process Control; Acceptance Sampling. The Centre for Innovation in Mathematics Teaching (CIMT) has online course notes for these sets of topics. Revision notes for an existing qualification indicate a similar coverage. At an earlier age (typically 15–16 years) GCSE qualifications in mathematics contain "Statistics and Probability" topics on: Probability; Averages; Standard Deviation; Sampling; Cumumulative Frequency Graphs (including median and quantiles); Representing Data; Histograms. The UK's Office for National Statistics
Office for National Statistics
The Office for National Statistics is the executive office of the UK Statistics Authority, a non-ministerial department which reports directly to the Parliament of the United Kingdom.- Overview :...
has a webpage leading to material suitable for both teachers and students at school level. In 2004 the Smith inquiry made the following statement:
"There is much concern and debate about the positioning of Statistics and
Data Handling within the current mathematics GCSE, where it occupies some
25 per cent of the timetable allocation. 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 (eg biology or geography). The time restored to the mathematics timetable should be used for acquiring greater mastery of core mathematical concepts and operations."
United States
In the United StatesUnited States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
, schooling has increased the use of probability and statistics, especially since the 1990s. Summary statistics and graphs are taught in elementary school in many states. 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 1994. The College Board
College Board
The College Board is a membership association in the United States that was formed in 1900 as the College Entrance Examination Board . It is composed of more than 5,900 schools, colleges, universities and other educational organizations. It sells standardized tests used by academically oriented...
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 1997.
General
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.United Kingdom
By tradition in the U.K., most professional statisticians are trained at the Master level.A difficulty of recruiting strong undergraduates has been noted by Smith (with Staetsky): "Very few undergraduates positively choose to study statistics degrees; most choose some statistics options within a mathematics programme, often to avoid the advanced pure and applied mathematics courses. 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." (page 622)In the United Kingdom
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
, 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 1930s. For the twenty years subsequent to this, while departments of mathematics had started to teach statistics, there was little realisation that essentially the same basic statistical methodology was being applied across a variety of sciences. Statistical departments have had difficulty when they have been separated from mathematics departments.
United States
Enrollments in statistics have increased in community colleges, in four year colleges and universities in the United States.At community college
Community college
A community college is a type of educational institution. The term can have different meanings in different countries.-Australia:Community colleges carry on the tradition of adult education, which was established in Australia around mid 19th century when evening classes were held to help adults...
s in the United States, mathematics has experienced increased enrollment since 1990. At community colleges, the ratio of the students enrolled in statistics to those enrolled in calculus rose from 56% in 1990 to 82% in 1995.
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."Undergraduate major programs should include study of probability and statistical theory, along with the prerequisite mathematics, especially calculus and linear algebra. Programs for nonmajors may require less study of mathematics. Programs preparing for graduate work may require additional mathematics." As undergraduates, future statisticians should have completed courses in multivariate calculus, linear algebra, computer programming, and a year of calculus-based probability and statistics. Students wanting to obtain a doctorate in statistics from "any of the better graduate programs in statistics" should also take "real analysis
Real analysis
Real analysis, is a branch of mathematical analysis dealing with the set of real numbers and functions of a real variable. In particular, it deals with the analytic properties of real functions and sequences, including convergence and limits of sequences of real numbers, the calculus of the real...
". Laboratory courses in physics, chemistry and psychology also provide useful experiences with planning and conducting experiments and with analyzing data. The American Statistical Association
American Statistical Association
The American Statistical Association , is the main professional US organization for statisticians and related professions. It was founded in Boston, Massachusetts on November 27, 1839, and is the second oldest, continuously operating professional society in the United States...
recommends that undergraduate students consider obtaining a bachelor's degree in applied mathematics as preparation for entering a master program in statistics.The American Statistical Association makes the following recommendations for undergraduates wishing to become statisticians: "Major in applied mathematics, or a closely related field. If you do major in a nonstatistical field, minor in mathematics or statistics. Develop a background in mathematics, science, and computers and gain knowledge in a specific field of interest. A master's degree or PhD is very helpful and often recommended or required for higher-level positions."
Historically, professional degrees in statistics have been at the Master level, although some students may qualify to work with an bachelor's degree and job-related experience or further self-study."A master's degree or PhD is very helpful and often recommended or required for higher-level positions." Professional competence requires a background in mathematics---including at least multivariate calculus, linear algebra, and a year of calculus-based probability and statistics. In the United States, a master program in statistics requires courses in probability, mathematical statistics, and applied statistics (e.g., design of experiments, survey sampling, etc.).
For a doctoral degree in statistics, it has been traditional that students complete a course in measure-theoretic probability
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
as well as courses in mathematical statistics
Statistical inference
In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation...
. Such courses require a good course in real analysis
Real analysis
Real analysis, is a branch of mathematical analysis dealing with the set of real numbers and functions of a real variable. In particular, it deals with the analytic properties of real functions and sequences, including convergence and limits of sequences of real numbers, the calculus of the real...
, covering the proof
Mathematical proof
In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true. Proofs are obtained from deductive reasoning, rather than from inductive or empirical arguments. That is, a proof must demonstrate that a statement is true in all cases, without a single...
s of the theory of calculus and topics like the uniform convergence of functions. In recent decades, some departments have discussed allowing doctoral students to waive the course in measure-theoretic probability by demonstrating advanced skills in computer programming
Computer programming
Computer programming is the process of designing, writing, testing, debugging, and maintaining the source code of computer programs. This source code is written in one or more programming languages. The purpose of programming is to create a program that performs specific operations or exhibits a...
or scientific computing.Stanford University statisticianPersi Diaconis
Persi Diaconis
Persi Warren Diaconis is an American mathematician and former professional magician. He is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University....
wrote that "I see a strong trend against measure theory in modern statistics departments: I had to fight to keep the measure theory requirement in Stanford's statistics graduate program. The fight was lost at Berkeley."
Who should teach statistics?
The question of what qualities are needed to teach statistics has been much discussed, and sometimes this discussion in 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".Teaching at university level
In the United States especially, statisticians have long complained that many mathematics departments have assigned mathematicians (without statistical competence) to teach statisticsStatistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
courses, effectively giving "double blind
Double-blind
A blind or blinded experiment is a scientific experiment where some of the people involved are prevented from knowing certain information that might lead to conscious or subconscious bias on their part, invalidating the results....
" courses. The principle
Professional ethics
Professional ethics encompass the personal and corporate standards of behaviour expected of professionals.- Professional ethics :Professional people and those working in acknowledged professions exercise specialist knowledge and skill...
that college-instructors should have qualifications and engagement with their academic discipline
Academic discipline
An academic discipline, or field of study, is a branch of knowledge that is taught and researched at the college or university level. Disciplines are defined , and recognized by the academic journals in which research is published, and the learned societies and academic departments or faculties to...
has long been violated in United States colleges and universities, according to generations of statisticians. For example, the journal Statistical Science
Statistical Science
Statistical Science is a review journal published by the Institute of Mathematical Statistics. The founding editor was Morris H. DeGroot.-External links:*...
reprinted "classic" articles on the teaching of statistics by non-statisticians by Harold Hotelling
Harold Hotelling
Harold Hotelling was a mathematical statistician and an influential economic theorist.He was Associate Professor of Mathematics at Stanford University from 1927 until 1931, a member of the faculty of Columbia University from 1931 until 1946, and a Professor of Mathematical Statistics at the...
; Hotelling's articles
are followed by the comments of Kenneth J. Arrow, W. Edwards Deming
W. Edwards Deming
William Edwards Deming was an American statistician, professor, author, lecturer and consultant. He is perhaps best known for his work in Japan...
, Ingram Olkin
Ingram Olkin
Ingram Olkin is a professor emeritus and chair of statistics and education at Stanford University and the Stanford University School of Education...
, David S. Moore
David S. Moore
David S. Moore is an American statistician, who is known for his leadership of statistics education for many decades.In statistics education, David S...
, James V. Sidek, Shanti S. Gupta, Robert V. Hogg
Robert V. Hogg
Robert Vincent Hogg is an American statistician and professor of statistics of the University of Iowa. Hogg is known for his widely used textbooks on statistics and on mathematical statistics...
, Ralph A. Bradley, and by Harold Hotelling, Jr. (an economist and son of Harold Hotelling).
Data on the teaching of statistics in the United States has been collected on behalf of the Conference Board of the Mathematical Sciences
Conference Board of the Mathematical Sciences
The Conference Board of the Mathematical Sciences is an umbrella organization of seventeen professional societies in the mathematical sciences in the United States.-Member societies:* AMATYC American Mathematical Association of Two-Year Colleges...
(CBMS
Conference Board of the Mathematical Sciences
The Conference Board of the Mathematical Sciences is an umbrella organization of seventeen professional societies in the mathematical sciences in the United States.-Member societies:* AMATYC American Mathematical Association of Two-Year Colleges...
). Examining data from 2000, Schaeffer and Stasny reported
By far the majority of instructors within statistics departments
have at least a master’s degree in statistics or biostatistics (about
89% for doctoral departments and about 79% for master’s departments).
In doctoral mathematics departments, however, only
about 58% of statistics course instructors had at least a master’s
degree in statistics or biostatistics as their highest degree earned.
In master’s-level mathematics departments, the corresponding
percentage was near 44%, and in bachelor’s-level departments
only 19% of statistics course instructors had at least a master’s
degree in statistics or biostatistics as their highest degree
earned. As we expected, a large majority of instructors in statistics
departments (83% for doctoral departments and 62% for
master’s departments) held doctoral degrees in either statistics
or biostatistics. The comparable percentages for instructors of
statistics in mathematics departments were about 52% and 38%.
The principle
Professional ethics
Professional ethics encompass the personal and corporate standards of behaviour expected of professionals.- Professional ethics :Professional people and those working in acknowledged professions exercise specialist knowledge and skill...
that statistics-instructors should have statistical competence has been affirmed by the guidelines of the Mathematical Association of America
Mathematical Association of America
The Mathematical Association of America is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists;...
, which has been endorsed by the American Statistical Association
American Statistical Association
The American Statistical Association , is the main professional US organization for statisticians and related professions. It was founded in Boston, Massachusetts on November 27, 1839, and is the second oldest, continuously operating professional society in the United States...
. The unprofessional
American Association of University Professors
The American Association of University Professors is an organization of professors and other academics in the United States. AAUP membership is about 47,000, with over 500 local campus chapters and 39 state organizations...
teaching of statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
by mathematicians (without qualifications in statistics) has been addressed in many articles.
Teaching methods
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 theoryStatistical theory
The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that...
has often been taught as a mathematical theory rather than as the practical logic of science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
--- 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
Design of experiments
In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
, survey methodology
Sampling (statistics)
In statistics and survey methodology, sampling is concerned with the selection of a subset of individuals from within a population to estimate characteristics of the whole population....
, exploratory data analysis
Exploratory data analysis
In statistics, exploratory data analysis is an approach to analysing data sets to summarize their main characteristics in easy-to-understand form, often with visual graphs, without using a statistical model or having formulated a hypothesis...
, and statistical inference
Statistical inference
In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation...
.
In recent decades, there has been an increased emphasis on data analysis
Exploratory data analysis
In statistics, exploratory data analysis is an approach to analysing data sets to summarize their main characteristics in easy-to-understand form, often with visual graphs, without using a statistical model or having formulated a hypothesis...
and scientific inquiry
Scientific method
Scientific method refers to a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry must be based on gathering empirical and measurable evidence subject to specific principles of...
in statistics education. In the United Kingdom, the Smith
Adrian Smith (academic)
Sir Adrian Frederick Melhuish Smith FRS is a distinguished British statistician and formerly Principal of Queen Mary, University of London. He was previously at Imperial College, London where he was head of the Mathematics Department. He is a member of the governing body of the London Business...
inquiry Making Mathematics Count
Making Mathematics Count
Making Mathematics Count is the title of a report on mathematics education in the United Kingdom . The report was written by Adrian Smith as leader of an "Inquiry into Post–14 Mathematics Education", which was commissioned by the UK Government in 2002...
suggests teaching basic statistical concepts
Statistical literacy
Statistical literacy is a term used to describe an individual's or group's ability to understand statistics. Statistical literacy is necessary for citizens to understand material presented in publications such as newspapers, television, and the Internet. Numeracy is a prerequisite to being...
as part of the science curriculum, rather than as part of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
. In the United States, the American Statistical Association
American Statistical Association
The American Statistical Association , is the main professional US organization for statisticians and related professions. It was founded in Boston, Massachusetts on November 27, 1839, and is the second oldest, continuously operating professional society in the United States...
's (ASA's) guidelines for undergraduate statistics specify that introductory statistics should emphasize the scientific method
Scientific method
Scientific method refers to a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry must be based on gathering empirical and measurable evidence subject to specific principles of...
s of data collection
Data collection
Data collection is a term used to describe a process of preparing and collecting data, for example, as part of a process improvement or similar project. The purpose of data collection is to obtain information to keep on record, to make decisions about important issues, to pass information on to...
, particularly randomized experiment
Randomized experiment
In science, randomized experiments are the experiments that allow the greatest reliability and validity of statistical estimates of treatment effects...
s and random sample
Random sample
In statistics, a sample is a subject chosen from a population for investigation; a random sample is one chosen by a method involving an unpredictable component...
s: further, the first course should review these topics when the theory of "statistical inference
Statistical inference
In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation...
" is studied. Similar recommendations occur hold for the Advanced Placement (AP) course in Statistics. The ASA and AP guidelines are followed by contemporary textbooks in the USA, such as those by Freedman, Purvis & Pisani (Statistics) and by David S. Moore
David S. Moore
David S. Moore is an American statistician, who is known for his leadership of statistics education for many decades.In statistics education, David S...
(Introduction to the Practice of Statistics with McCabe and Statistics: Concepts and Controversies with Notz ) and by Watkins, Schaeffer & Cobb (Statistics: From Data to Decisions and Statistics in Action).
Besides an emphasis on the scientific inquiry in the content of beginning of statistics, there has also been an increase on active learning
Active learning
Active learning is an umbrella term that refers to several models of instruction that focus the responsibility of learning, on learners. Bonwell and Eison popularized this approach to instruction . This "buzz word" of the 1980s became their 1990s report to the Association for the Study of Higher...
in the conduct of the statistics classroom.
Rarity of randomized experiments
In the scholarly literature in mathematics education, relatively few articles report random experiments in which teaching methods were randomly assigned to classes. Randomized experiments have been done to evaluate non-pedagogical programs in schools, such as programs to reduce teenage-pregnancy and to reduce drug use. Randomized experiments were commonly done in educational psychology in the 1880s at American universities. In recent decades, however, randomized experiments have been relatively rare in education. In other disciplines concerned with human subjects, like biomedicine, psychology, and policy evaluation, controlled, randomized experiments remain the preferred method of evaluating treatments. See articles on No Child Left Behind, National Mathematics Advisory Panel, Scientifically-based research and What Works Clearinghouse. Educational statisticians and some mathematics educators have been working to increase the use of randomized experiments to evaluate teaching methods.The fact remains that randomized experiments have been rare in the evaluation of teaching methods in recent decades. For decades, many scholars in educational schools have raised objections against increasing the number of randomized experiments, often because of philosophical objections to the use of alleged "physical-scientific" or "quantitative" methods on human subjects. While statisticians have urged an increase in the number of randomized experiments---which again have been rare in all areas of pedagogy
Pedagogy
Pedagogy is the study of being a teacher or the process of teaching. The term generally refers to strategies of instruction, or a style of instruction....
and didactics
Didactics
A didactic method is a teaching method that follows a consistent scientific approach or educational style to engage the student’s mind.The didactic method of instruction is often contrasted with dialectics and the Socratic method; the term can also be used to refer to a specific didactic method,...
in recent decades---statisticians recognize that observational studies remain valuable in education---just as observational studies remain valuable in epidemiology
Epidemiology
Epidemiology is the study of health-event, health-characteristic, or health-determinant patterns in a population. It is the cornerstone method of public health research, and helps inform policy decisions and evidence-based medicine by identifying risk factors for disease and targets for preventive...
, political science, economics, etc.
Journals
- Journal of Statistics Education published by the American Statistical AssociationAmerican Statistical AssociationThe American Statistical Association , is the main professional US organization for statisticians and related professions. It was founded in Boston, Massachusetts on November 27, 1839, and is the second oldest, continuously operating professional society in the United States...
- Statistics Education Research Journal published by the International Association for Statistical Education (IASE)
- Teaching Statistics: An International Journal for Teachers
- Technology Innovations in Statistics Education (TISE) "reports on studies of the use of technology to improve statistics learning at all levels, from kindergarten to graduate school and professional development".
Associations
- International Association for Statistics Education – a subgroup within the International Statistical InstituteInternational Statistical InstituteThe International Statistical Institute is a professional association of statisticians. The Institut International de Statistique or International Statistical Institute was founded in 1885 although there had been international congresses from 1853.. The Institute publishes a variety of books and...
- The International Research Forums on Statistical Reasoning, Thinking, and LiteracyThe International Research Forums on Statistical Reasoning, Thinking, and LiteracyThe International Statistical Reasoning, Thinking, and Literacy Research Forums began in 1999 to foster current and innovative research studies that examine the nature and development of statistical literacy, statistical reasoning, and statistical thinking, and to explore the challenge posed to...
– promoting statistics education
Journals
- Journal of Statistics Education published by the American Statistical AssociationAmerican Statistical AssociationThe American Statistical Association , is the main professional US organization for statisticians and related professions. It was founded in Boston, Massachusetts on November 27, 1839, and is the second oldest, continuously operating professional society in the United States...
- Statistics Education Research Journal published by the International Association for Statistical Education (IASE)
- Teaching Statistics: An International Journal for Teachers
- Technology Innovations in Statistics Education (TISE) "reports on studies of the use of technology to improve statistics learning at all levels, from kindergarten to graduate school and professional development".
Associations and Centers
- Web pages of the Royal Statistical SocietyRoyal Statistical SocietyThe Royal Statistical Society is a learned society for statistics and a professional body for statisticians in the UK.-History:It was founded in 1834 as the Statistical Society of London , though a perhaps unrelated London Statistical Society was in existence at least as early as 1824...
Centre for Statistical Education - Maths, Stats & OR Network: Supports lecturers in Mathematics, Statistics and Operational Research in the UK
- Quotes on "Who should teach statistics?"