This file contains quotes related to statistics, tenure, evaluation, and relationships between statistics and mathematics. These may be useful to statisticians for: * seeking fair evaluations and tenure, particularly those statisticians housed in mathematics or other departments besides statistics, * seeking recognition (and workload adjustment) for consulting, * seeking a workload adjustment for teaching, like (other) lab courses get, * reforming statistics; convincing colleagues (particular in a math department) of the importance of non-mathematical aspects of statistics. At the top references to articles, then come the quotes. Tim Hesterberg, quotes collected Fall 95.Please send any corrections to email@example.com
Statistics at Liberal Arts Colleges, Thomas L. Moore & Rosemary A. Roberts The American Statistician, 42(3), August 1988, 80-85. Improving the Teaching of Applied Statistics: Putting the Data Back Into Data Analysis Judith D. Singer and John B. Willett The American Statistician 44(3) August 1990, 223-230. Why is Introductory Statistics Difficult to Learn? And What Can We Do to Make It Easier? Donald G. Watts The American Statistician 44(3) November 1991, 290-291. An Undergraduate Concentration in Applied Statistics for Mathematics Majors Marie Gaudard and Gerald J. Hahn The American Statistician, 42(2), May 1991, 115-122 Statistical Consulting in a University: Dealing With People and Other Challenges Roger E. Kirk The American Statistician, February 1991, 41(1), 28-34 Teaching Statistics to Engineers Soren Bisgaard The American Statistician, Nov 1991, 45(4), 274-283 What's Missing in Statistical Education? Ronald D. Snee, The American Statistician, May 1993, 47(2), 149-154 Embracing the "Wider View" of Statistics C. J. Wild The American Statistician, May 1994, 48(2), 163-171 Statistical Education Fin de Siecle David S. Moore, George W. Cobb, Joan Garfield, and William Q. Meeker The American Statistician, August 1995, 49(3), 250-260. Responses: What Industry Needs, Jon R. Kettenring What Academia Needs, Peter J. Bickel Modernizing Statistics Ph.D. Programs, John Lehoczky Joan B. Garfield Carl N. Morris Providing a Statistical "Model": Teaching Applied Statistics using Real-World Data John B. Willett and Judith D. Singer in F. Gordon and S. Gordon (eds.) Statistics for the Twenty-first Century, Washington DC: Mathematical Association of America, MAA Notes, Number 26, 83-98. UCLA Launches Statistics Department Jan de Leeuw, Amstat News, No. 224, Oct 1995, page 10. Statistics Needs Academic Independence Ibrahim A. Ahmad, Amstat News, No. 224, Oct 1995, page 14. The Visibility of Statistics as a Discipline Paul D. Minton The American Statistician, Nov 1983, 37(4), 284-289 Towards Lean and Lively Courses in Statistics Robert Hogg in F. Gordon and S. Gordon (eds.) Statistics for the Twenty-first Century, Washington DC: Mathematical Association of America, MAA Notes, Number 26, 3-13 A Multidisciplinary Conversation on the First Course in Statistics Walter Chromiak, Jim Hoefler, Allan Rossman and Barry Tessman (all from Dickinson) in F. Gordon and S. Gordon (eds.) Statistics for the Twenty-first Century, Washington DC: Mathematical Association of America, MAA Notes, Number 26, 26-36 Mathematics and Statistics: An Uneasy Marriage Gudmund R. Iversen (Swarthmore) in F. Gordon and S. Gordon (eds.) Statistics for the Twenty-first Century, Washington DC: Mathematical Association of America, MAA Notes, Number 26, 37-44. Remedial Statistics?: The Implications for Colleges of the Changing Secondary School Curriculum Ann Watkins, Gail Burrill, James M. Landwehr, Richard L. Scheaffer. in F. Gordon and S. Gordon (eds.) Statistics for the Twenty-first Century, Washington DC: Mathematical Association of America, MAA Notes, Number 26, 45-55. Student-Conducted Projects in Introductory Statistics Courses Harry V. Roberts. in F. Gordon and S. Gordon (eds.) Statistics for the Twenty-first Century, Washington DC: Mathematical Association of America, MAA Notes, Number 26, 109-128. Should Mathematicians Teach Statistics? (with discussion). David S. Moore College Mathematics Journal 19, 3-35. Response by A. Blanton Godfrey "Should Mathematicians Teach Statistics?" Response by Judith Tanur, "No! But Who Should Teach Statistics?" Response by R. Gnanadesikan and J. R. Kettenring, "Statistics Teachers Need Experience With Data" Response by Barbara A. Bailar, "The Mathematicians' Statistics has a Subsidiary Role. Response by Gudmund R. Iversen, "Statistician, Examine Thyself" Response by Henry L. Alder, "The Need for Good Teaching of Statistics" Response by David L. Hanson, "Let the Experts Teach and Judge" Response by Michael Reed, "Who Teaches What to Whom?" Response by Gerald J. Hahn, "What Should the Introductory Statistics Course Contain?" Response by Ronald D. Snee, "Mathematics is Only One Tool that Statisticians Use" Let Us Change the Most Disliked Course on Campus Gudmund R. Iversen, Jeffrey Witmer SLAW Technical Report No. 91-004 Department of Mathematics, Pomona College. Difficulties in Learning Basic Concepts in Probability and Statistics: Implications for Research Joan Garfield, Andrew Ahlgren Journal for Research in Mathematics Education, 1988, Vol 19, No 1, 44-63 Curricular Reform in Statistics: Report on a National Science Foundation Conference George Cobb SLAW Technical Report No. 93-002 Department of Mathematics, Pomona College. CUPM, Recommendation for a General mathematical Sciences Program MAA, 1981 (as quoted in Moore, "Getting More Data into Theoretical Statistics Courses") Thomas L. Moore Getting More Data into Theoretical Statistics Courses SLAW Technical Report No. 91-001 Department of Mathematics, Pomona College. Low-tech ideas for Teaching Statistics Robin Lock and Thomas L. Moore SLAW Technical Report No. 91-008 Department of Mathematics, Pomona College. Consulting: An Aid in Recruiting Statistics Students, or Statistical Consulting in Training Students Donald Bentley SLAW Technical Report No. 90-006 Department of Mathematics, Pomona College. Data Analysis: An Adjunct to Mathematical Statistics at Oberlin College Jeffrey Witmer SLAW Technical Report No. 91-003 Department of Mathematics, Pomona College. Opportunities for Statisticians at 4-year Undergraduate Institutions Rosemary Roberts Technical Report No. 90-005 Alternative Introductions to Applied Statistics for Mathematics Majors Robin Lock SLAW Technical Report No. 90-008 Department of Mathematics, Pomona College. Teaching Statistics as a Respectable Subject David S. Moore in F. Gordon and S. Gordon (eds.) Statistics for the Twenty-first Century, Washington DC: Mathematical Association of America, MAA Notes, Number 26, 14-25 Ask Dr. Stats, column in Stats, the Magazine For Students of Statistics, Fall 1994, Number 12, p. 23 Statistics within Departments of Mathematics at Liberal Arts Colleges Thomas L. Moore, Jeffrey A. Witmer The American Mathematical Monthly, May 1991, 431-436. Applied Introductory Statistics Courses for Mathematics Majors at Liberal Arts Colleges Rosemary A. Roberts SLAW Technical Report No. 90-002 Department of Mathematics, Pomona College. Teaching Statistics Draft report (late 1995) of the joint Mathematical Association of America/American Statistical Association Statistics Focus Group. George Cobb, Robert Hogg, 37 others. The Teaching of Statistics: Content Versus Form Oscar Kempthorne The American Statistican, February 1980, 34(1), 17-21 To receive an index of SLAW (Statistics in the Liberal Arts Workshop) technical reports, or to receive the reports, contact: Kathy Sheldon
Mathematics Department Pomona College 610 N. College Ave. Claremont, CA 91711-6348 909-621-8409 (Phone) 909-607-1247 (Fax)
Statistics at Liberal Arts Colleges, Thomas L. Moore & Rosemary A. Roberts The American Statistician, 42(3), August 1988, 80-85. Statisticians and others who teach statistics at liberal arts colleges enjoy opportunities and encounter difficulties that are unique to the liberal arts setting. A statistician at a liberal arts college has an exciting, important, and demanding role. As a "one-person department" - few liberal arts colleges have more than one statistician-the statistician works in an environment that is professionally isolated, assuming the responsibility for the well-being of both statistical education and consulting within the college community. Statistics, as it is concerned with gathering, organizing, and analyzing data, and with inferring from these data to the underlying reality, is a powerful intellectual method that can be applied in many contexts. In academia, statistics is a part of the curriculum in psychology, sociology, biology, and economics to name but a few disciplines. In industry and government decisions are made that are increasingly dependent upon the collection and interpretation of data, and employers are demanding greater quantitative sophistication of the graduates they hire. Indeed, in almost every aspect of our daily lives we are confronted with data and asked to make judgments based on them, about issues ranging from airline safety to the spread of AIDS. H. G. Wells anticipated that statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write. We believe this day has come. It is widely agreed that the critical reading and analysis of texts, the methodology of experimental science, and the deductive reasoning of mathematics are broad intellectual methods that should be part of any liberal education. We believe that reasoning from numerical data - that is, statistics - deserves a similar stature. To give statistics a prominent position in the liberal arts curriculum, we must address several current problems. First, we must change the attitude of our students toward statistics. To this end, we argue for the teaching of data-driven courses. It is also important to realize that in most liberal arts colleges statistics courses are offered in several departments and are often taught by faculty whose primary professional training is not in statistics. Even in mathematics departments, statistics courses are often taught by nonstatisticians. Our survey (of 99 small liberal arts colleges) found that 50% of the responding mathematics departments have no member with an advanced degree (Ph.D. or master's) in statistics. We argue that liberal arts colleges have a unique opportunity to take the lead in giving statistics a prominent position in the curriculum. But to seize this opportunity, a college must be prepared to add to its faculty someone whose primary training and interest is in statistics. Statistics is not mathematics. (See Moore 1988.) That this distinction has not been fully appreciated has had consequences for the way in which statistics has been and is being taught. Kempthorne (1980, p. 21) noted that "statistics has been captured and enslaved by mathematics" and in the process data have been shoved aside. ... Finally, although a course that is too much a slave to mathematics or to techniques may bore the student, it can be seductively easy to teach. Teaching a data-driven mathematics course, however, is not easy. Preparing a good data set for class takes work. One must find the raw data and take the time to understand them. Class time must be used to discuss issues about the data, the data collection, the questions behind the data, and appropriate ways to analyze the data. Teaching such a course requires a style of teaching different from the one with which we grew up. Since some lecture time must give way to class discussion, the teacher must be competent in leading discussion as well as lecturing. Discussing statistical issues with students is crucial, as is emphasizing the reasoning that guides data analysis and frames formal inference. A mathematics major that includes a two-term probability/mathematical statistics sequence, linear algebra, and analysis or advanced calculus is adequate preparation for most statistics graduate programs. The declining number of students going on to do graduate work, however, suggests that it is inadequate to motivate students to consider a career in statistics. We believe that students should, in addition, take at least one applied statistics course, preferably before taking mathematical statistics. This course should aim to engage the intellect of those students who ultimately have the most chance of furthering the statistics profession, and should set the stage for mathematical statistics. We recommend that the statistics offerings of a college mathematics department include an applied course at the introductory level that can count toward the math major. This applied course should involve discussion of issues about data and should also include the use of a computer package for the analysis of substantial data sets. For many students who become mathematics majors, this would provide a first exposure to data, and experience we believe to be prerequisite for the mathematical statistics course. The course would also provide an additional entry-level course to the mathematics major and promote mathematics as a career. The role of a statistician at a liberal arts college extends beyond the mathematics department. Statisticians will naturally become involved with faculty and students who are planning to collect or analyze data. We argue that this involvement should be both expected and recognized in evaluation. A liberal arts college is unlikely to have more than one or two faculty members whose primary training and scholarly interests lie in statistics. Although such faculty are appropriately housed in the mathematics department, they should be regarded as a resource for the college as a whole. Wise use of this resource requires advance consideration by the mathematics department and college. In the absence of explicit planning, statisticians will implicitly be encouraged to concentrate on the mathematical aspects of statistics and on concerns internal to the mathematics department. We believe this to be unwise. A statistician with interests that extend beyond the mathematical aspects of the subject will naturally become involved with individual faculty and students in other disciplines who are planning data collection or analyzing already existing data. Such interdisciplinary contact is helpful both to the statistician and to the other disciplines. Statisticians expand their experience and improve their background for teaching, while others profit from the specialized knowledge of the statistician. Discussion of individual problems are also a natural encouragement to greater collaboration in instruction. Problem solving with students and faculty on an individual basis is often a major component of a statistician's work load. An effective statistician whose door is open may devote more time to the problems of others in the college than does any other faculty member. Helping students with their projects is a form of teaching, and work with faculty in other disciplines contributes to the college's scholarly production whether or not the statistician is acknowledge in resulting publications. It is common in university statistics departments to assign these functions as part of the job responsibility of some individuals in the department. Performance in statistical consulting and joint research is then recognized in promotion and salary decision. In the less specialized atmosphere of a college, optimal use of a statistician's talents requires that internal consulting and collaboration should be expected, encouraged, and rewarded. The college should recognize that these are professional activities, and should reward them as such. Recognition might, for example, take the form of a reduced teaching load or extra summer pay. We offer the following suggestions concerning the role of a statistician in a liberal arts college. First, the position announcement and job description should explicitly mention that statistical work with students and faculty in other disciplines is encouraged. This implies (as does the fact that statistics is not properly a field of mathematics) that a decision should be made to seek a statistician per se rather than simply seeking a strong candidate in any area to fill a vacancy in mathematics. Second, the nature of teaching a scholarly work in statistics should be recognized in evaluation. The role just defined is a demanding one. The liberal arts statistician typically will not have the luxury of taking a difficult consulting problem "down the hall" to a colleague more experienced with that type of problem. The professional isolation of the liberal arts statistician will be typical but can be counteracted with the help of the home college, local universities, and professional organizations. Improving the Teaching of Applied Statistics: Putting the Data Back Into Data Analysis Judith D. Singer and John B. Willett The American Statistician 44(3) August 1990, 223-230. Artificial data sets are often used to demonstrate statistical methods in applied statistics courses and textbooks. ... we argue that artificial data sets should be eliminated from the curriculum and that they should be replaced with real data sets. Today, computers have revolutionized the way we analyze data and they should be permitted to revolutionize the way we teach data analysis. They have eliminated the need for simplified arithmetic; the computer does not care if the observations and summary statistics are integers. Tedious calculations should be relegated to the machine. Students need not memorize formulas whose sole purpose is computational simplification. Exploratory analyses, which previously were avoided because of the time required to conduct them, can now be appropriately incorporated into the data-analytic repertoire. Using real data sets vastly increases the time required to prepare classes, homework, and exams. For each data set that clearly illustrates a specific technique, several hours must be spent in preliminary analysis of several data sets, of which some turn out to inapplicable and others present nontrivial analytic problem. Why is Introductory Statistics Difficult to Learn? And What Can We Do to Make It Easier? Donald G. Watts The American Statistician 44(3) November 1991, 290-291. In our department (Mathematics and Statistics), a question that often crops up is "Why do statisticians claim that statistics is more difficult to teach than mathematics?" I can state many reasons, but, in my view, the major difficulty that confounds beginning students and inhibits the learning of statistics, and that distinguishes statistics >from other disciplines such as mathematics, physics, chemistry, and biology, is that the important fundamental concepts of statistics are quintessentially abstract. That is, we cannot directly demonstrate or experience or draw a picture of the most important fundamental concepts of statistics. Consider an introductory course in calculus: The main concepts that must be assimilated are those of a limit (which can be demonstrated with successive calculations), a derivative (which can be demonstrated with successive calculation, and, more importantly, graphically by drawing the tangent to a curve), and an integral (which can be demonstrated by drawing a curve and then showing that the integral is the area under the curve). But what of statistics? Can anyone draw a random variable? a mean? a variance? probability? (not just a value in a probability distribution, but probability in the same sense that one can draw a derivative). I would welcome it if someone could, or could even demonstrate a random variable, for example, but it seems to me that these concepts are in fact truly abstract. (The closest I can come to demonstrating a random variable is to describe it as "the value of the next observation in an experiment.") It is no wonder then that beginning students have difficulty learning statistics. And the problem is exacerbated by other factors, including the following. 1. Introductory statistics courses involve more concepts that are more abstract and use them to a greater extent. 2. Statistics courses are perforce primarily concerned with concepts, data, and inferences, whereas introductory mathematics courses are predominantly concerned with techniques and proofs. That is, once the concept of a derivative or an integral has been presented, the bulk of the course concerns deriving derivatives of various classes of functions (e.g., exponentials, trigonometric functions) and developing techniques for integration (e.g., by parts, by substitution). Even the most elementary statistics course, however, is concerned with drawing inferences about phenomena in the real world on the basis of data obtained from experiments. Consequently, students in elementary statistics courses must not only grapple with truly abstract concepts, but they must immediately relate and apply these concepts to reality. 3. Statistics problems are always open to interpretation, often have several solutions, and no one will ever know the correct answer (if indeed there is one). 4. Mathematics and statistics use the same currency - numbers. But there are important, real, differences between the numbers that are obtained from calculations (mathematics) and those obtained from experiments (statistics). In my classes, I sometimes suggest that it would be handy if teachers had upper- and lowercase voices so as to be able to distinguish between symbols when speaking. I think now that it would also be useful if we had different voices, and even different symbols, for numbers - one for numbers used in calculations of functions, for examples, and another for data. Data numbers could be wiggly, diminishing in size as the number of significant figures increased, and even written in slowly vanishing ink.) 5. Statistical notation and terminology are ambiguous and confusing. Terms are applied to both the random variable and its distribution (e.g. mean, variance) and furthermore, to real quantities calculated from data! For example, what is mean by "the variance of the mean"? Is the meaning clearer by saying the variance of the sample mean"?-especially when we also use the term sample mean to refer to the average from a real sample? An Undergraduate Concentration in Applied Statistics for Mathematics Majors Marie Gaudard and Gerald J. Hahn The American Statistician, 42(2), May 1991, 115-122 Statistics in Practice (a course similar to our Math 116), which surveys the uses of statistics, is to be taken no later than the sophomore year to provide an introduction to the discipline and applications of statistics and to motivate subsequent, more theoretical statistics courses. (they recommend a "two-semester course that introduces the mathematical foundations of probability and statistics" for the junior year.) Statistical Consulting in a University: Dealing With People and Other Challenges Roger E. Kirk The American Statistician, February 1991, 41(1), 28-34 University administrators have traditionally rewarded research, teaching, and service, in that order. This reward system puts consultants at a disadvantage in achieving tenure and advances in rank and salary. Unfortunately, most universities do not have special criteria for evaluating faculty whose job descriptions contain a significant service component. In the universities with which I am familiar, statistical consultants are expected to publish and obtain grants at the same rate as their nonconsulting colleagues. Obviously, this is not possible, and those consultants who try to compete with their nonconsulting colleagues become candidates for early burnout. As part of an ongoing, educational campaign, consultants should periodically forward reports of their consulting activities to their university administration and chairperson. In these reports, it is important to emphasize the consultant's academic contribution to each project ... Let the administration know that the statistician's contribution goes beyond just cranking out numbers. Teaching Statistics to Engineers Soren Bisgaard The American Statistician, Nov 1991, 45(4), 274-283 Statistics is not just applied probability. As a corollary to this, what is important for the science of statistics should not be judged by how complicated it is mathematically. Graphics and exploratory data analysis are examples of methods that require only a minimum of mathematics but are of extreme importance for engineering statistics. I personally consult with any engineers from the University of Wisconsin-Madison campus and from industry. I do not see how I could teach statistics without the experience that this consulting gives me. Moreover, I know my students appreciate the relevance and realism it brings to my teaching. Consulting certainly has taught me a lot about what the real problems are. In fact, I think it ought to be as inconceivable to be a statistician who never consults as it is to be a "theoretical" physician who never sees a patient. In teaching engineers statistics, we can learn a great deal from the physicists. The are not shy about teaching physics, starting with mostly qualitative insights, experiments, and applications. And, they use numerous well-chosen physical experiments, demonstrated right in front of the students, to explain the theory. Only later, when a certain level of qualitative understanding and intuition has been built up, do they introduce differential equations, calculus of variations arguments, and so on. We should do the same! Moreover, we should teach fun things and methods the students can use, so that they become enthusiastic. Once they are "hooked" on statistics and can see just how much fun it can be, they will have the energy to study in more detail. Sir Ronald A. Fisher, Presidential Address, First Indian Statistical Conference, Sankhya, 4, 1938, p. 16 I want to insist on the important moral that the responsibility for the teaching of statistical methods in our universities must be entrusted, certainly to highly trained mathematicians, but only to such mathematicians as have had sufficient prolonged experience of practical research, and of responsibility for drawing conclusions from actual data, upon which practical action is to be taken. Mathematical acuteness alone is not enough. Statistical Education: Improvements Are Badly Needed Robert V. Hogg, The American Statistician, November 1991, 45(4), 342-343. We do not encourage enough teamwork, with students working together on projects, particularly in beginning courses. Instead of asking students to work on "old data, even though real, is it not better to have them find or generate their own data? Projects give students experience in asking questions, defining problems, formulating hypotheses and operational definitions, designing experiments and surveys, collecting data and dealing with measurement error, summarizing data, analyzing data, communicating findings, and planning "follow-up" experiments suggested by the findings. (My note - only "analyzing data" falls within the purview of the typical Mathematical Statistics course, and that to only a small extent.) Strong mathematical backgrounds are extremely important in the development of professional statisticians. However, at the beginning level, statistics should not be presented as a branch of mathematics. Good statistics is not equated with mathematical rigor or purity but is more closely associated with careful thinking. In particular, students should appreciate how statistics is used in the endless cycle associated with the scientific method: We observe Nature and ask questions, we collect data that shed light on these questions, we analyze the data and compare the result to what we previously thought, we raise new questions, and so on and on. What's Missing in Statistical Education? Ronald D. Snee, The American Statistician, May 1993, 47(2), 149-154 There is growing consensus that the "content side" of statistical education should move away from the mathematical and probabilistic approach and place greater emphasis on data collection, understanding and modeling variation, graphical display of data, design of experiments, surveys, problem solving, and process improvement (ASA 1980, 1982; Easton et al. 1988; Hogg 1985, 1991; Snee 1988). Embracing the "Wider View" of Statistics C. J. Wild The American Statistician, May 1994, 48(2), 163-171 Much has been written about the ideal statistics teacher at the university or college level. He or she should be actively involved in both statistical research and applied statistical practice and be able to bring the fruits of this experience into the classroom to give the course the relevance and gritty realism it requires. In addition, he or she should have the time to run courses with heavy project requirements. The reality is usually far from these ideals. The majority of teachers of statistical service courses are overworked, and many are underqualified (e.g. inexperienced graduate students) (my note - or mathematicians with little statistical experience). They cannot afford to have their teaching commitments eat up large proportions of their research time. Their own personal experiences may only rarely be able to be used directly. ... Looking for sufficient recent, exciting, relevant, real-world examples takes enormous effort and more time and general knowledge than most teachers have. Statistical Education Fin de Siecle David S. Moore, George W. Cobb, Joan Garfield, and William Q. Meeker The American Statistician, August 1995, 49(3), 250-260. (David Moore) Statisticians have not been slow to take advantage of fast and cheap computing. Old methods such as regression now come equipped with a bewildering variety of diagnostic tools. More general classes of models (generalized linear models, generalized additive models) describe a wider variety of phenomena. Bootstrapping and subsampling produce error estimates and confidence intervals in previously intractable settings. Each year seems to bring new ways of smoothing data by fitting general classes of functions. The natural of both statistical research and statistical practice has changed dramatically under the impact of technology. I have tried to change my classroom style in the direction suggested by the reformers. Here are a few observations. Your mileage, as the saying goes, may vary. I found the new style more effective with graduate students than with undergraduates; in smaller classes as opposed to larger classes; for teaching applied statistics rather than theory; and in courses where students could absorb the basics from the text, rather than struggling to read the book. In some courses I was satisfied that the students learned more, even though we "covered" slightly less material than in the past. In one course, on statistical theory for average mathematics undergraduates, the interactive approach flopped completely. The students were unsure of their mathematical foundations, had difficulty reading the text, did no want to talk in front of others, and resented being asked to do more work (as they perceived it) than in comparable courses. The new style is quite time-consuming. Preparing material for discussion and interaction takes longer than preparing clear lectures. (Joan Garfield) David's experiences when he moved toward more active learning are familiar to researchers on teaching. I would add that instructors who incorporate more in-class students activities also find that they have less control over the course, which may be discomforting to them. Their new role is that of a facilitator of and partner in learning. Class discussions do not always lead to predictable conclusions, and it may be hard to come to closure at the end of a class session and to stress the points intended to be learned that day. Students' reactions to a nontraditional course format may not be uniformly favorable, as David experienced in his statistical theory class. When I changed my classroom style from lectures to small group activities, my teaching evaluations initially went down. Over the next two years, however, as I became more experienced and learned how to better construct and facilitate activities, my evaluations improved. ... Secondary schools and faculty in other disciplines are also experimenting with alternative instructional methods. As students encounter more classes where they engage in active learning, they will more readily accept this format in a statistics course. Question 2: What, in particular, does the unstable state of higher education portend for statistics? (answer) Statistics is a particularly interesting case. We have several advantages. Statistics has a substantial presence (larger than mathematics, for example) outside academe. We can offer direct contributions to problems of visible value to the public and to politicians. Training in statistics has job market value to students in a variety of disciplines. Simultaneously, an understanding of data and chance is increasingly recognized as one of the central intellectual competencies that a liberal education should foster, so that as core curricula return to fashion, they often include a quantitative literacy component. Strong trends suggest that statistics may (as it should) replace calculus as the capstone mathematical study for many students. Here again from Albers et al. (1992) are data on statistics enrollments in two-year colleges as a percentage of calculus enrollments: Year 1966 1970 1975 1980 1985 1990 Percent 10 19 37 27 36 52 These data also reflect David's observation that statistics is larger than mathematics in the world outside the academy. Were it not for the real-world need for statistics, mathematics departments would not be offering so much of it in place of topics dearer to the mathematical heart. What Industry Needs Jon R. Kettenring The American Statistician, Feb 1995, 49(1), 2-4 Basic building blocks of any program should continue to be well-rounded statistical knowledge including subjects such as data analysis, statistical computing, sampling, linear models, experimental design, time series, multivariate analysis, and so forth. To make these courses really click, one suggestion is to make sure that they are interspersed with as much real data experience as possible (refs). A related suggestion is to assign instructors to these key courses who themselves have had substantial real experience with data (ref). Would a medical student want to learn surgery from professors who have never done it? These suggestions take on special urgency for courses on data analysis. For these courses, data-savvy instructors are essential. What Academia Needs Peter J. Bickel The American Statistician, Feb 1995, 49(1), 5-6 Statistics is a peculiar kind of enterprise of contradictory character because it is at the same time so special and so general. Statistics exists only at the interface of chance and empirical data. But it exists at every such interface, which I propose to be both necessary and sufficient for an activity to be properly called statistics. It has a special and proscribed function whenever and wherever empirical data are treated; in scientific research of any kind; in government, commerce, industry, and agriculture; in medicine, education, sports, and insurance; and so on for every human activity and every discipline. So what is the platonic ideal statistician? George Box's rhetorical description of Fisher serves well: "We may ask of Fisher Was he an applied statistician? Was he a mathematical statistician? Was he a data analyst? Was he a designer of investigations? It is surely because he was all of these that he was much more than the sum of the parts. He provides an example we can seek to follow." The ideal is, as it has to be, far beyond our reach, but we can and should reasonably expect our Ph.D.'s to emerge with great strength in at least one of these categories and a serious acquaintance with all. (Lists graduate curriculum for the ideal statistics department, and notes specifically his "failure to include advanced mathematics courses in say, functional analysis, numerical analysis, discrete mathematics, and so forth." Modernizing Statistics Ph.D. Programs John Lehoczky The American Statistician, Feb 1995, 49(1), 12-17 Projects are drawn from many different sources. For example, one pair might work with an analyst in the CMU planning office to develop insights into the CMU undergraduate dropout rate or why freshman applicants to CMU decide to attend schools other than CMU. (Statistics departments would do well to recognize that they can help to solve the problems that their own universities face. Many problems such as forecasting research revenues, student enrollments, dropout rates, etc. are wonderful examples for projects. Statistics departments are uniquely positioned to offer such assistance, and successful contributions to important university problems will cause administrators to gain first-hand experience about the importance of statistics.) The reward system in most department must change to value cross-disciplinary activities, in promotion and tenure proceedings and in year-to-year performance appraisals. Traditionally, this is the most difficult for departments that have close associations with (or are administered by) mathematics departments. Respondent (to articles by Kettenring, Bickel, Ross, Bailar, Lehoczky) Joan B. Garfield The American Statistician, Feb 1995, 49(1), 18-20 I heard some recurrent themes interwoven into these papers. I want to highlight a few... (1) Teamwork and collaboration: the need for statisticians to be able to work together, solving problems and working on projects, and the need for them to bring to these teams not only their statistical expertise, but also their knowledge of other disciplines involved so that they may contribute as full partners in the research effort. (2) Communications skills ... (3) Solving real problems with real data: the need for statisticians to be able to apply skills to a variety of contexts, know how to frame meaningful research questions, and help select appropriate methods. (4) The increased amount of knowledge ... (5) The need for internships and real-world experience in analyzing data and working on projects. Keeping in mind the five themes I just outlined, I should like to share with you some findings from educational research that have implications for teaching and learning statistics. Then I will return to these five themes and relate them to the findings from educational research. (1) Learning is a constructive activity. Students learn by constructing knowledge and by being actively involved in learning activities. This contradicts the model of a student as an empty vessel or a blank slate, waiting to be filled with knowledge, as if knowledge is something that can be given or transmitted. ... (2) Students learn to do well only what they practice doing. ... (3) Students learn to value what they know will be assessed. Students are astute at figuring out what they will be tested on and how they will be tested. Even if instructors profess to have other educational goals, such as learning to work together cooperatively or being able to understand important ideals, these will be taken seriously only if they also are included in assessment and grading. .... This leads us to the theme of teamwork and collaboration. Since students learn to do well only what they have practiced doing, teamwork and collaborative activities need to be an ongoing part of students' educational experience, and not just one isolated class in which students work on projects. Teamwork and collaboration should be modeled by the sharing of experience by faculty involved in cross disciplinary projects. Encouraging collaboration and teamwork may not be an easy component to add to courses. Remember that students are used to being in competitive academic environments, where they are used to competing against each other, rather than working collaboratively with each other. Some may resist working on group projects, especially with group grades assigned. The third theme I mentioned was solving real problems. We heard recommendations for courses to be built on real problems, real data, taught by people with experience analyzing real data, who can provide role models in data analysis. We agree that students need to experience solving or seeing problems solved in a variety of different disciplines and settings, involving resources or resource people from those disciplines. Again, these kinds of experiences can build collaboration and teamwork, give students practice in solving problems, and help them construct knowledge of how problems are solved in different contexts and disciplines. Respondent (to articles by Kettenring, Bickel, Ross, Bailar, Lehoczky) Carl N. Morris The American Statistician, Feb 1995, 49(1), 21-23 Joan Garfield's comments are important. I have tried to implement some of the things she said in my graduate classes, and I cannot do it very well. It has to do with the way we were taught. I was taught in the lecture mode, and I find it too easy to slip back into that same mode. I do not know if others here have also had this experience, but I will try again to follow Joan's advice because I think it is terribly important to help make that change. It will change the environment to a much more cooperative one. Ideally, I view statistics departments through a "hub-and-spoke" metaphor. In it, statistics sits as the center of the university, as the hub, and the other departments that use statistics are the spokes. The statistics department is in contact with every other department. ... We learn from the other departments, and they learn >from us. Statistical information flows between departments, often first through the statistics hub. ... ideas, such as regression, do not have to be rediscovered in every field. But somebody does have to communicate the idea. This is why I believe statistics departments are needed; this is their principal role. ... Departments of statistics (and perhaps even more so, our mathematics ancestors) are formed to play this role of contact hub... Providing a Statistical "Model": Teaching Applied Statistics using Real-World Data John B. Willett and Judith D. Singer in F. Gordon and S. Gordon (eds.) Statistics for the Twenty-first Century, Washington DC: Mathematical Association of America, MAA Notes, Number 26, 83-98. Service sources in applied statistics abound in collage and graduate school curricula around the world ... The clear consensus, among students and professors alike, is that too many of these applied statistics courses are far from successful [3, 9, 25, 33]. In Dallal's  words, "the field of statistics is littered with students who are frustrated by their courses, finish with no useful skills, and are turned off to the subject for life" (p. 266). Joiner  gave service courses in statistics "a grade of F" for being unmitigated failures (p. 53). These courses frequently receive the worst evaluations in a school. Many students enrolled in applied statistics courses are hamstrung further by false perceptions of their own inadequacy. They regard "stats" courses as a necessary evil, an unavoidable rite of passage, and they view data analysis with fear and trepidation. (goes on to recommend instructional methods utilizing real-world data) Not all real data sets are equally effective vehicles for teaching applied statistics. We have no doubt that using real data sets increases the amount of time required to prepare classes, homework and exams. To identify a single data set which permits illustration of a specific statistical technique, and instructor must spend hours analyzing different data sets, some of which do not support interesting findings, others of which present analytic problems out of line with the curriculum. This is especially true when developing materials for elementary courses, in which students are still learning basic skills, not how to cope with non-standard problems. UCLA Launches Statistics Department Jan de Leeuw, Amstat News, No. 224, Oct 1995, page 10. Meanwhile, statistics faculty continued to encounter difficulties within the Mathematics Department. Most felt that there was no intrinsic connection between statistics and mathematics and were greatly concerned with the low opinion mathematics faculty demonstrated in regard to statistics. Further aggravating the situation were expectations of extensive service teaching with few resources and low priority in the hiring process. Statistics Needs Academic Independence Ibrahim A. Ahmad, Amstat News, No. 224, Oct 1995, page 14. Many departments do teach "their own statistics courses" either through the hiring of a "statistically trained" person in the field or simply through assigning anyone who would be willing to do the job. At best some departments hire a statistician for such a task. Such practices do not occur in other disciplines that demonstrate concern for their students education. A business school would not dare teach their students Calculus, Algebra, or Physics in such a manner. The Visibility of Statistics as a Discipline Paul D. Minton The American Statistician, Nov 1983, 37(4), 284-289 There has always been a short supply of students for graduate degree programs in statistics; they are often within undergraduate disciplines that have already shaped the students' views away from statistics. Statistics has completely missed the opportunities for recruitment that occur during freshman college enrollment. Towards Lean and Lively Courses in Statistics Robert Hogg in F. Gordon and S. Gordon (eds.) Statistics for the Twenty-first Century, Washington DC: Mathematical Association of America, MAA Notes, Number 26, 3-13 Statistics is too often presented as a branch of mathematics, and good statistics is often equated with mathematical rigor or purity, rather than with careful thinking. (As George Box said: "Statistics has no reason for existence except as a catalyst for learning and discovery.") They (teachers) often fail to use the wide variety of simulations, experiments and individual or group projects which can make statistics come alive while simultaneously enhancing student understanding. Some obstacles are posed by the students themselves. While the instructors must try to motivate students, it is difficult to change the attitudes of many of them. Students often have a fear of formulas and mathematical reasoning. An even more serious problem is the desire for having problems with quick and clean answers that avoid the need for students to think, but make it easier for them to perform well on examinations. some students may even like formulas because they are props for such problems. Students may be used to reading large volumes of materials relatively superficially, rather than a relatively few pages carefully, as is more suitable in statistical instruction. Unlike some courses, statistics is cumulative and does not lend itself to crash cramming sessions at the end of the term. Our aim in a first course is to develop critical reasoning skills necessary to understand our quantitative world. The focus of the course is the process of learning how to ask appropriate questions, how to collect data effectively, how to summarize and interpret that information, and how to understand the limitations of statistical inferences. Statistical thinking is central to education. Unfortunately the typical introductory statistics course does not meet this goal, as it stresses mathematically precise statements and formulas applied to artificial data that are of little, if any, interest to most students. A typical textbook example begins with a question that has been formed to address one feature of data that has already been collected. Students gain little insight into how and why data are collected, how experiments are designed, and how analysis of one set of data leads to new questions, new experiments, and subsequent analyses in a continuing cycle of scientific inquiry. All too often, statistics is presented as a formal ritual, rather than as a dynamic study of processes There was widespread agreement among workshop participants that students should work more with real data and with graphs. Many advocated projects in which students collect their own data and analyze them in written reports. ... projects give students experience in asking questions, defining problems, formulating hypotheses and operational definitions, designing experiments and surveys, collecting data and dealing with measurement error, summarizing data, analyzing data, communicating findings, and planning "follow-up" experiments that are suggested by their findings. It also has the further bonus of improving communication, writing, and organizational skills, all essential attributes for future careers. Properly used, the computer is a powerful and effective tool in teaching students about variability in data, particularly through statistical graphics. Most participants strongly support the use of the computer in introductory statistics courses. Having a computer available during class facilitates "on the spot" analyses of data, which teach students that there are often many analyses that can shed light on a problem and that simple graphics can tell one a great deal. Classroom demonstrations and data collection add variety, as do experiments that are run in class. A Multidisciplinary Conversation on the First Course in Statistics Walter Chromiak, Jim Hoefler, Allan Rossman and Barry Tessman (all >from Dickinson) in F. Gordon and S. Gordon (eds.) Statistics for the Twenty-first Century, Washington DC: Mathematical Association of America, MAA Notes, Number 26, 26-36 M=Mathematician, S=Statistician, PSY=Psychologist, POL=Political Scientist M: I don't think that, as a mathematician, I am automatically the person most qualified to teach elementary statistics. I would imagine that there are a dozen or more faculty members, from the social and natural sciences, better prepared than I to teach the course. S: I think that's actually an enlightened opinion. My impression is that many mathematicians who teach statistics do not realize that their training might have been insufficient to prepare them for the experience. I'm reminded of David Moore's paper, Should Mathematicians Teach Statistics?, which he answered with a resounding No! Psy: Come on, a mathematician who can't teach statistics?! I can hear people saying, "Statistics is all about numbers, isn't it? Who knows numbers better than a mathematician?" Right? POL: I would imagine that most mathematicians have had more statistics than I've had. M: I never had a single course in statistics as either an undergraduate math major or as a Ph.D. student in mathematics. In fact, I can't think of any of my fellow graduate students who took a statistics course while in graduate school. And I don't think my experience is unusual among mathematicians. S: As I recall, many of the respondents to the Moore article pointed out that mathematicians are often pressed into service as statistics instructors, simply because there aren't enough statisticians to go around. PSY: We want students to have a common framework from which to explore more advanced topics in statistics, but it sounds as if we're arguing that we shouldn't expect math departments to take sole responsibility for statistics courses. In fact, we seem to be saying that a variety of disciplines should have a hand in organizing and possibly even teaching a first course in statistics. S: But it certainly makes sense to have a statistician oversee the course content and organization. After all, each discipline tends to focus on a handful of techniques, while the statistician has the broadest training and expertise. POL: But what about those schools that are not graced with the luxury of having a trained statistician on staff? M: Maybe some serious thought should be given to hiring one. Just think about it. If this were a history course, they would certainly hire a historian. "Statistical Consulting is Scholarship" by William J. Wilson, The American Statistician, Nov 1992, 46(4). The abstract for that article reads: Statistical Consulting is an integral part of the duties of most statisticians employed as faculty at universities or colleges. The recognition given for this activity has traditionally been in the area of "service" and the weight assigned this activity in the present reward system is that of any other service activity. A recently released report by the Carnegie Foundation for the Advancement of Teaching offers a new definition of scholarship which includes the scholarship of application - the application of knowledge to solve consequential problems. This means a formal recognition of scholarship for the activities of consulting statisticians. What is needed for this recognition to become an integral part of the reward system is adequate documentation and evaluation procedures. Mathematics and Statistics: An Uneasy Marriage Gudmund R. Iversen (Swarthmore) in F. Gordon and S. Gordon (eds.) Statistics for the Twenty-first Century, Washington DC: Mathematical Association of America, MAA Notes, Number 26, 37-44. Statistics as a Liberal Art There is a new trend in many disciplines cutting across the more traditional approaches to teaching. This trend reflects a wish of many instructors to present their material in such a way that the students become as excited about the topic as the instructor is, without getting bogged down in trivial details. Currently not many students come out of their introductory statistics courses with this kind of an attitude towards the subject. Mostly, they feel they have spent the semester learning how to plug data into a set of unrelated formulas. It is not surprising that they do not have much of a sense of what statistics is all about. Instead, what if we could manage to share with the students the central focus of what statistics really is all about? What if we could convey why statistics is so interesting that it was worth spending the effort to get a Ph.D. in the subject, and that statisticians would not wan to trade their occupation for anything else? What if we could share with our students the beauty of the subject and the importance of statistics in their personal lives as well as for the rest of the world? It is hard to convey such a sense of excitement about mathematics. Students do not begin to see the essentials of mathematics until they are halfway through a college mathematics major. The barrier seems to be that a person has a great deal of technical, mathematical knowledge before he or she can begin to understand what mathematics really is all about. There have been attempts at such an approach to the teaching of mathematics, but these attempts have perhaps not been as successful as people had hoped. Statistics is different enough from mathematics that it is possible to teach such a course in statistics. The course needs to be taught by an individual who has had considerable experience with data and with the sues of statistical methods. Such a course should try to convey the nature of uncertainty and how seemingly random events have patterns to them; patterns that statistics is created to look for. Indeed, it may be possible to define statistics as the set of methods used to study regularities in the face of variability. Statistical reasoning will also help a person make a more critical evaluation of reports that two or more variables are related. We know that correlation between two variables does not necessarily mean that they are causally related. But it is often hard to distinguish between spurious and causal relationships. Anyone who has had a course in statistics containing a discussion of the role of control variables, is much more tuned in to the notion that we have to examine the role of possible control variables before we can draw any conclusions about cause and effect. This way of looking at statistics means we should think of statistics more as part of a liberal arts education than as a set of methods and techniques. It may be easier to teach such a liberal-arts-type course now than some time ago because of the advances in computer hardware and software. The existence of good statistical software and the easy access to computers on our campuses has eliminated the need to teach much of the material we used to include in introductory statistics courses. Liberal arts should be more than the original seven classical subjects; it should be a learning process that helps a person develop into an understanding and contributing member of society. An important part of that learning is the ability to understand how the empirical world functions with it social, biological and physical variables. Those who intend to become statisticians need to learn statistics in terms of specific methods and techniques the way any trade or profession is taught. But only a small minority of students become statisticians, and many of the large numbers of students taking introductory statistics may be better served by being exposed to statistics as a liberal arts course than the more usual course with its emphasis on the nuts and bolts of statistics. We must remember that for most students, their first course in statistics is also their last course in statistics. A good liberal arts course can awaken an interest in statistics that may lead some students to consider it as a career. A dreary nuts-and-bolds course can turn them away. Need for a Statistician Many mathematicians realize that they cannot possibly teach this elementary, introductory statistics course. They may be able to teach themselves the actual statistical techniques. But they typically lack the statistician's experience and sense of data to teach such a course. Having one or more statisticians as part of a mathematics department is not without its problems. The number of statisticians is usually small, which means that there is a certain amount of professional isolation. The other members of the department typically work in fields that have little overlap with statistics. It may well even be that the statisticians know more about mathematics than the mathematicians know about statistics. This does not make it simple for the statistician who want to talk to somebody about a current research problem or a recent publication in the statistical literature. Formal evaluations for promotions and tenure decisions also get more difficult when the evaluations within the department are done by people who do not share the same professional interests. But it also broadens the scope of a mathematics department to have statisticians on the staff. more than that, colleges and universities need to have statisticians on their faculty, and there is no more natural place for such people than in a mathematics department when a separate statistics department does not exist. The largest limitation for mathematicians who are asked to teach statistics is their lack of experience dealing with data. After all, mathematics is a language of symbols, and most mathematicians hardly ever run across many numbers. Remedial Statistics?: The Implications for Colleges of the Changing Secondary School Curriculum Ann Watkins, Gail Burrill, James M. Landwehr, Richard L. Scheaffer. in F. Gordon and S. Gordon (eds.) Statistics for the Twenty-first Century, Washington DC: Mathematical Association of America, MAA Notes, Number 26, 45-55. Articles of Faith The principles guiding the major statistics education projects of the past decade are remarkably similar. Perhaps this is because they are based on the conviction that statistics is not a branch of mathematics. ... In the common emphases below, one can see both the belief that statistics should not be taught as a branch of mathematics and the influence of the reform movement in mathematics education. 1. Data analysis should be central. Data analysis, as the term is generally used in secondary schools, refers to defining a problem, collecting data, organizing and summarizing it, and interpreting it with the help of graphical analyses. The battle over whether the statistics curriculum should be taught from a data-analytic point of view has essentially been won. Almost every expert, panel, committee, and commission studying the problems in mathematics education agree that data analysis is central. 2. Statistics is not probability. The study of probability does not need to precede the study of statistics. Students should first learn elementary data analysis with probability being taught as the need for it arises. Traditional topics taught in introductory statistics - standard deviation, the normal distribution, least squares fit, t-test, type I and type II errors, permutations and combinations, and Bayes' theorem - should be taught after the more basic ideas of data analysis, informal probability, simulation, and an intuitive introduction to statistical inference. 3. Resistant statistics should have a larger role. Students more readily understand statistics based on the median and there are powerful statistical reasons for emphasizing resistant statistics (which aren't sensitive to outliers). 4. There is often more than one way to approach problems in statistics and probability. This means that discussion and evaluation of different approaches can take u a large part of class time. Students must be encouraged to attach problems from different angles and be prepared to support their conclusions. 5. Real data that are interesting and important to the students should be used whenever possible. Real data give the study of statistics both its legitimacy and its excitement. the data should drive the statistical methods rather than vice versa, and each set of data should itself be worthy of study. In addition, students, who are accustomed to the neatness of the numbers in the typical mathematics classroom, need experience in dealing with the messier numbers of the real world. 6. The emphasis should be on good examples and on building intuition. Showing how to lie with statistics and stressing probability paradoxes destroy a student's confidence. 7. Students enjoy and profit from project work, experiments, and other activities designed to give them practical experience in statistics. 8. Students should write more and compute less. The emphasis should be in interpreting plots and numerical summaries rather than on the technicalities of construction plots and computing statistics. (My note-This does not mean not to use a computer, it means one should not concentrate on how to compute statistics by hand.) 9. The statistics and probability taught in secondary schools should be important and useful to students in its own right and not serve just to prepare students for college courses. (My note - the statistics we teach our college students should be important and useful to students in its own right and not serve just to prepare students for statistics graduate school.) Students and teachers do not expect ambiguity in their mathematics classes. The shift from exact answers to approximation, and the emphasis on words such as "explore", "analyze", and "describe" are significant changes in the way most teachers and students deal with numbers. A simulation problem inevitably brings "What is the real answer?" The teachers and students have trouble adjusting to "mathematics" in which there is not necessarily a unique answer. The nontraditional classroom environment necessary when working with statistics and probability causes uneasiness. The structure of a statistics class is not as predictable. One set of homework exercises may take three days as students work their way through a problem or an experiment. The answers cannot be read, but must be discussed. Often new avenues are suggested by the students in the middle of a lesson. Unlike the solitary mathematics assignment, statistics is more appropriately done by students in groups where they can exchange ideas. The bell may ring before the teacher has time to pull ideas together and make an appropriate homework assignment. Student-Conducted Projects in Introductory Statistics Courses Harry V. Roberts. in F. Gordon and S. Gordon (eds.) Statistics for the Twenty-first Century, Washington DC: Mathematical Association of America, MAA Notes, Number 26, 109-128. Introductory statistics courses have a reputation, often deserved, for being dull. In part, this reputation comes from the common dislike of anything smacking of mathematics, but this is only part of the problem. For statistics is widely taught with major emphasis on theory and only token attention to applications to real problems. Hence the fascination of statistical thinking - which lies in its usefulness in thinking about and acting on real problems - does not get communicated to most students. The distinguished statistician, George Box, sums it up in one sentence: "In my view statistics has no reason for existence except as the catalyst for investigation and discovery." Box likens the preoccupation with theory in statistical teaching to the teaching of students by theoretical training alone. Unfortunately, many statistics teachers don't even let students get their feet wet with nontrivial applications, let alone require that they actually try to swim. This is understandable: in many academic subjects besides statistics, students aren't required to swim. Moreover, statistical applications are not easy for instructors to direct, manage, and provide feedback and evaluation, especially when classes are large. In statistics teaching, projects are the best way I know to achieve learning through doing. ... 1. People learn best when directly involved in real problems and issues. 2. One-shot classroom training doesn't change behavior. Practice and feedback work far better. 3. The best learning is active, not passive. In an organization, active problem-solving works extremely well in cross-functional groups and in unfamiliar situations. 4. Learning by example - seeing it done - is more effective than hearing about it. But the most important benefit is that projects provide the best way I know to make students aware of the relevance of statistics to the real world. Without that awareness, any statistics course must be judged a failure, however well, say, the students learn to construct and interpret a 95 percent confidence interval. Students should be responsible for finding or collecting their own data, and I urge that the data be brought up to the current data whenever possible: the projects should take place in real time. it would not be hard to supply data sets from past projects, but much of the excitement and realism would be lost. There is more to a statistical application than the analysis of a canned data set, even a good canned data set. Projects place a substantial, almost intimidating, responsibility on the teacher, but no teacher, however inexperienced in applications, should hesitate to try. How Inexperienced Teachers Can Get Started on Projects The answer is simple: Just jump in and do them, and learn as you go. The rewards will be immediate, and they will continue indefinitely. Never-ending improvement is possible. Don't worry about making mistakes, but learn from them. Should Mathematicians Teach Statistics? (with discussion). David S. Moore College Mathematics Journal 19, 3-35. No! Statistics is no more a branch of mathematics than is economics, and should no more be taught be mathematicians. It is a separate discipline that makes heavy and essential use of mathematical tools, but has origins, subject matter, foundational questions and standards that are distinct from those of mathematics. It is true that many advanced texts and research papers in statistics use formidable mathematics, but this is misleading. After all, many a graduate microeconomics text cites the Kuhn-Tucker theorem on the first page, and many research papers in physics are intensely mathematical. Statistics is as much a distinct discipline as are economics and physics. Its subject matter is data and inference from data. It is unprofessional for mathematicians who lack training and experience in working with data to teach statistics. To see clearly that statistics is in o sense a branch of mathematics, we should note first that statistics does not originate within mathematics. ... Statistics is therefore a broad, and not wholly mathematical, science. It is a measure of the narrow scope of much academic statistics that basic texts rarely touch the substance of design of experiments, arguably the most practically important subject in statistics" Second, the aims and foundational controversies of statistics are unrelated to those of mathematics. Statistics is concerned with the gathering, organization, and analysis of data, and with inferences >from data to the underlying reality. ... The problem of inference >from data to reality is very different from the mathematical exploration of the consequences of a model" Given the distinct aims of statistics, it is not surprising that the standards of excellence in statistics differ from those of mathematics. Contributions to statistics are significant in proportion to their usefulness in the study of data, not in proportion to their mathematical depth. ... Mathematicians, trained in a different tradition, are incapable of judging statistical work. Finally, and to a mathematician most compelling, statistics does not participate in the interrelationships among subfields that characterize contemporary mathematics. This fact clearly distinguishes statistics from probability, which is a branch of mathematics. ... while statistics makes essential use of mathematical concepts and tools, there is no traffic in the other direction. Who Should Teach, and What? The fact that statistics is a separate discipline from mathematics has implications for teaching that are being increasingly recognized. First, the mathematical theory of statistics is of secondary importance in teaching. Almost any first course in statistics could be improved by less emphasis on both theory and recipes, and more emphasis on what statisticians do and why. What is needed is broader content (even at the expense of detail) and more hand-on experience with appropriate data, usually with the aid of interactive computing. Even in training statisticians, where a firm grounding in theory is essential, statistics should not be taught as mathematics. The American Statistical Association is in the process of preparing guidelines for an undergraduate major in statistics . Not surprisingly, these reflect the status of statistics as a separate discipline. ... This program resembles a major in physics or economics more than an option within an undergraduate mathematics major. Second, graduate training in mathematics is no more sufficient for teaching statistics than for teaching economics. ... (compares t-test for comparing means and F-test for comparing variances) the F-test is so sensitive to deviations from normality as to be almost useless in practice. The equal theoretical standing of the two procedures is irrelevant. Knowledge of facts such as this is a matter of scholarship in the discipline of statistics; mathematicians (or psychologists) who lack this scholarship should feel appropriately embarrassed if they teach a subject in which they are untrained. Satisfactory teaching of the science of data requires experience with data. Mathematics should be taught by mathematicians. Psychology should be taught by psychologists. And statistics should be taught by statisticians. What could be more obvious? Response by A. Blanton Godfrey "Should Mathematicians Teach Statistics?" Should mathematicians teach statistics? What an absurd question. Of course not. In summary, a compelling reason mathematicians should not teach statistics is that they are too far removed from the problems that statistics tries to solve. Response by Judith Tanur, "No! But Who Should Teach Statistics?" I agree with David Moore's argument that statistics is not a branch of mathematics and thus mathematicians should not teach statistics. His argument that mathematical theory is of secondary importance in statistics is most compelling to me. Response by R. Gnanadesikan and J. R. Kettenring, "Statistics Teachers Need Experience With Data" Because data are the focus of statistics, its teaching can benefit >from those with the experience and wisdom gained from successfully confronting, analyzing, and interpreting data. The most striking feature of modern statistics is its synergy with other disciplines. As a "data science," it has applications to a gamut of scientific and technological problems. Thinking of statistics as subsumed under mathematics is neither accurate nor exciting. Response by Barbara A. Bailar, "The Mathematicians' Statistics has a Subsidiary Role. Professor Moore notes that statistics is not a branch of mathematics. Indeed so; the whole of applied mathematics is merely a branch of statistics in which random error is reduced to zero. Some of the most critical aspects of statistics have no place in the usual mathematics curriculum; framing questions and hypotheses, developing research proposals to examine them, assuring the quality of the data, dealing with bias, drawing inferences from a broad range of relevant but imperfect data, and generalizing results to populations not examined. Response by Gudmund R. Iversen, "Statistician, Examine Thyself" Moore's conclusion - that statistics should be taught by statisticians, and not by mathematicians - seems so right that we may even ask ourselves why the question in his title is an issue. It is an issue because statistics is not taught well - not because some courses are taught by mathematicians, but because statisticians abdicate their responsibilities and let people from other disciplines teach statistics. Response by Henry L. Alder, "The Need for Good Teaching of Statistics" There are two points in Moore's provocative article with which I agree: "Statistics is notorious among students as a dull and poorly taught subject." "It is the misfortune of statistics to be a small and methodological discipline." If the lack of students entering the statistics profession is to be properly addressed, the teaching of introductory courses in statistics needs to be made so exciting that more students are enticed to enter the profession. To advocate, as Moore does, that such introductory courses should only be taught by statisticians does not address the real problem since there are not enough statisticians available to teach all these courses. Response by David L. Hanson, "Let the Experts Teach and Judge" It seems hard to disagree with the statement that a subject should be taught by an expert in the area and, in particular, that statistics should not be taught by nonexperts (whether they be mathematicians, psychologists, engineers, or ..). In the case of statistics, I claim that the "ideal" expert is one who has a strong theoretical foundation (including the relevant mathematics), a "feel for" probabilistic and statistical thinking, and considerable experience with a variety of types of data. Unfortunately, there is a shortage of individuals possessing all these qualifications, certainly not enough to do both the teaching and the applied work that needs to be done. Response by Michael Reed, "Who Teaches What to Whom?" I completely agree with the four italicized statements in Moore's first section "A Separate Discipline," and I applaud the new emphasis on applied statistics and methodological research described in his second section "Changing Times." It is clear that statistics is a vigorous discipline with fundamental and exciting intellectual questions. Most of the teaching is in State I (beginning statistics, no calculus) and Stat II (beginning statistics assuming three terms of calculus). The real question is how to staff such courses at universities, at four-year colleges, and at two-year colleges. Here is where Moore's article is very misleading. How many of these excellent statisticians who know that analyzing data is "as exciting as mathematics" and who are experts on the new computer methods will actually teach Stat I or Stat II? We all know that answer: Not many! In universities, they will prefer to teach the advanced courses; colleges will have great difficulties in attracting and hiring them. Response by Gerald J. Hahn, "What Should the Introductory Statistics Course Contain?" As an industrial statistician, I find the statistics course that my clients have taken to be one strike against me. A typical reaction is "It was one of the most boring (or most useless) courses I had in college." We fail to impart the excitement of drawing information >from data. But it does not have to be that way! Statistics should not be presented as a narrow technical subject - and as Moore clearly indicates, certainly not as another course in applied mathematics - but as something that is encountered in daily life, and has relevance to just about every profession. The major emphasis in presenting such investigations should be on the planning needed to get the right data and on the underlying assumptions, rather than in focusing on the analysis. If fully agree with Moore that the planning of experiments is "the most practically important subject in statistics." We need to make students aware of the many real, and often unexpected, difficulties that arise in implementing a study. This is in sharp contrast to current introductory courses, where it is common practice to jump into the statistical analysis after implying, or sometimes briefly stating, that a random sample was selected from some (often poorly defined) population. An integral part of the course should be a study: selected, designed, conducted, and analyzed by each class member individually, or in small teams. This must include a clear statement of goals and a plan for obtaining the needed information. Having the right person teach the course is imperative. To be effective, the instructor must have good theoretical knowledge, practical hands-on experience, strong teaching ability, and downright enthusiasm for the subject. Response by Ronald D. Snee, "Mathematics is Only One Tool that Statisticians Use" The general consensus of these conferences and committee reports is that the teaching of statistics must move away from the mathematical and probabilistic approach, and focus on variation, data collection, graphical display of data, design of experiments, problem solving, etc. The appropriateness of the "data focus" is clear when we recognize that data collection and analysis is necessary to the solution of real world problems. This focus will make it clear that statistics is a separate and distinct discipline. Focusing on solving real world problems will also help mathematicians recognize the broad utility of statistics and the role mathematics plays in statistics. Those knowledgeable in the profession of statistics will do the best job of teaching statistics. David Moore's Response I am moreover happy to agree that people of many backgrounds have become effective statisticians, though the amount of learning and experience required to do so is much greater than most mathematicians imagine. College mathematics departments, in particular, often prefer to hire another algebraist who appears mathematically stronger than the statisticians among the applicants. The necessity to short-change statistics instruction then becomes compelling. If the principle that statisticians have a special expertise is recognized, steps can be taken to make this expertise available via hiring or retraining. Most colleges follow this path in computer science; statistics is a similar case. Let Us Change the Most Disliked Course on Campus Gudmund R. Iversen, Jeffrey Witmer SLAW Technical Report No. 91-004 Department of Mathematics, Pomona College. We teach statistics and we have a problem: too many students hate our subject. Why? Well, some hate it because they think it is mathematical and they have always hated mathematics. Others only take statistics because it is required for their major, and they hate requirements. Besides, they see no usefulness or relevance for this particular requirement. Some think statistics is a special category of lying ("Lies, damned lies, and statistics" as Disraeli is disputed to have said) and hate it because they think statistics promotes distortion and still others take introductory statistics and end up hating it because they find it so confusing and frustrating - as soon as they think they understand something they are told they are wrong and are given yet another formula to memorize. Of course, some students hate statistics for all of these reasons. Central to the field of statistics is the notion of variability, or randomness. To many students, randomness and variability represent new ways of thinking about the world. These are not obvious ways of thinking, and many students have difficulties with basic statistical concepts because of that. Turning to the second reason students have difficulties with their statistics courses; namely the teaching of statistics, we find that hundreds of thousands of students take an introductory statistics class every year. Some of these courses are taught by statisticians, but statistics courses are also taught by people from many other disciplines. Statistics may be unique in that so much of the teaching is done by people without a higher degree in statistics. A sociologist who has had some statistics and uses statistics and uses statistics in her work may well end up teaching statistics to the sociology majors. The same sociologist also has some training in English and uses English in her work, but it is unthinkable that she would teach English. Also, statistics is taught extensively by people in departments like biology, economics, psychology, and political science. Mathematicians also teach statistics course at many institutions. Statistics is heavily mathematical in its theoretical core, but that does not automatically qualify a mathematician to teach statistics. In short, there is no other subject on the college campus that is taught by so many people from some many departments. Many of these instructors are not even necessarily qualified to teach statistics. One problem arising from these varied sources of statistics instruction is that many instructors do not know enough statistics to do justice to the subject matter. They may not have had sufficient training to do justice to the subject matter. They may not have had sufficient training in statistics to start with. Also, not being statisticians, many of them have not kept up with recent developments in the field. The right match between the mathematical background of the student and the mathematical level of the statistics course is not found very often. No wonder many people dislike their statistics courses. Experienced statisticians may be some of the few people who are able to achieve this match in their courses. This may be because they are able to teach statistics without using mathematics as a crutch on which to lean. Academic administrators have to make certain that the teaching of statistics on their campuses is not left to people who are incompetent statisticians. Difficulties in Learning Basic Concepts in Probability and Statistics: Implications for Research Joan Garfield, Andrew Ahlgren Journal for Research in Mathematics Education, 1988, Vol 19, No 1, 44-63 The experience of psychologists, educators, and statisticians alike is that a large proportion of students, even in college, do not understand many of the basic statistical concepts they have studied. Inadequacies in prerequisite mathematics skills and abstract reasoning are part of the problem. In addition, research in cognitive science demonstrates the prevalence of some "intuitive" ways of thinking that interfere with the learning of correct statistical reasoning. The literature has been filled with comments by instructors about students not attaining an adequate understanding of basic statistical concepts and not being able to solve applied statistical problems (Duchastel, 1974; Jolliffe, 1976; Kalton, 1973; Urquhart, 1971). The experience of most college faculty members in education and the social sciences is that a large proportion of university students in introductory statistics courses do not understand many of the concepts they are studying. Studies in the research literature confirm this impression. Students often tend to respond to problems involving mathematics in general by falling into a "number crunching" mode, plugging quantities into a computational formula or procedure without forming an internal representation of the problem (Nodding, Gilbert-MacMilland, & Lutz, 1980). They may be able to memorize the formulas and the steps to follow in familiar, well-defined problems but only seldom appear to get much sense of what the rationale is or how concepts can be applied in new situations (Chervany, Collier, Fienberg, & Johnson, 1977; Garfield, 1981; Kempthorne, 1980). Within the conceptual underpinnings, the details they have learned or memorized, for whatever use they might be, therefore quickly fade. At any level, students appear to have difficulties developing correct intuition about fundamental ideas of probability for at least three reasons. First, many students have an underlying difficulty with rational number concepts and proportional reasoning, which are used in calculating, reporting, and interpreting probabilities (Behr, Lesh, Post, & Silver, 1983). ... Lower percentages of students had correct responses to exercises involving complex concepts and skills requiring understanding of underlying mathematics principles. Difficulties in translating verbal problem statements plague stochastics as they do the rest of school mathematics (Hansen, McCann, & Myers, 1985). Second, probabilities ideas often appear to conflict with students experiences and how they view the world (Kapadia, 1985). We discuss this conflict below in the section on misconceptions in statistical reasoning. Third, many students have already developed a distaste for probability through having been exposed to its study in a highly abstract and formal way. For many students, a considerable improvement in skills in dealing with abstractions may be necessary before they are ready for much of the probabilistic reasoning and hypothesis testing that underlie basic statistical inference. Beyond the underlying skills problems, however, there is an even more serious source of difficulty: the students' intuitive convictions about statistical phenomena. The second NAEP mathematics assessment produced evidence that students' intuitive notions of probability seemed to get stronger with age but were not necessarily more correct (Carpenter et al., 1981). Fischbein (1975) also found decrements in probabilistic performance with increasing age, which he attributed to school experience and to scientific reductionism. Students' intuitive ideas, presumably formed through their experience, may be reasonable in many of the contexts in which students use them by can be distressingly inconsistent with the statistics concepts that we would like to teach them. (in section "Misconceptions in Statistical Reasoning") Piaget and Inhelder (1975) are often cited for initiating the developmental research that has helped reveal difficulties students have with theoretical conceptions of probability. More recently, an area of inquiry referred to as judgment under uncertainly has emerged. Key studies in this area were brought together in a book edited by Kahneman, Slovic, and Tversky (1982). .... The clear story that runs through the articles in the Kahneman et al. (1982) book is that inappropriate reasoning is (widespread and persistent, (b) similar at all age levels, (c) found even among experienced researchers, and (d) quite difficult to change. Less extensive attention has been given by psychological and educational researchers to putatively simple statistical ideas such as distribution, average, sample, and randomness. But there is evidence that conceptual difficulties abound for these topics, too. (gave examples) Curricular Reform in Statistics: Report on a National Science Foundation Conference George Cobb SLAW Technical Report No. 93-002 Department of Mathematics, Pomona College. It seems a safe extrapolation from these data to suppose that, for the foreseeable future at least, a very substantial portion of beginning statistics instruction will remain in the hands of mathematicians, even though statistics is fundamentally different from mathematics, and can be taught appropriately only by someone who recognizes and understands that difference. Introductory statistics need not be taught as a survey course. As David Moore has written, "If I use regression to give students the experience they need and you use time series forecasting, that's fine. What matters most is the experience with practical reasoning about data" (quoted in Cobb, 1992). (Listed some alternatives which have been used - time series analysis, multivariate descriptive statistics, experimental design and analysis of variance, applied regression analysis. I believe these are all in place of the traditional mathematical statistics course.) CUPM, Recommendation for a General mathematical Sciences Program MAA, 1981 (as quoted in Moore, "Getting More Data into Theoretical Statistics Courses") The traditional undergraduate course in statistical theory has little contact with statistics as it is practiced and is not a suitable introduction to the subject. Thomas L. Moore Getting More Data into Theoretical Statistics Courses SLAW Technical Report No. 91-001 Department of Mathematics, Pomona College. In summary then I have argued here for the inclusion in the traditional probability/mathematical statistics course for majors of more applications in all facets of the course. Inevitably some topics in statistical theory will be left out but the students will get a broader view of statistics. This may also encourage more students to take more statistics at a later time or, perhaps, even go on to become statisticians. Low-tech ideas for Teaching Statistics Robin Lock and Thomas L. Moore SLAW Technical Report No. 91-008 Department of Mathematics, Pomona College. It is our conviction that a first course in statistics (for either mathematics majors or non-majors) should include many real examples that illustrate the full process of statistical problem solving: the initial question, the design of the study, the producing or collecting of the data, the analysis of the data, the communication of the results, and the evaluation of what questions or work constitute the next step. ... If this sounds more time-consuming you are right. Consulting: An Aid in Recruiting Statistics Students, or Statistical Consulting in Training Students Donald Bentley SLAW Technical Report No. 90-006 Department of Mathematics, Pomona College. The small four year liberal arts colleges in the United States have traditionally produced a disproportionately large percentage of graduates who have continued their educations beyond the baccalaureate to earn doctorate degrees in the sciences (2 references). Unfortunately, this phenomenon does not occur in the field of statistics. This paper discusses the causes for the low production of statistics graduates from these small colleges, and attempts to gain insight into approaches which might improve the recruiting of undergraduate students from all colleges and universities into graduate programs in statistics and related fields. These two differences, limited research requirements on faculty and use of undergraduates in research, go a long way to explain the success of small liberal arts colleges in the production of scientists. Faculty do participate in research, but the nature of the research can be limited to the level at which the undergraduate student can participate. And since there are no graduate students in competition for the research slots, undergraduates participate. Hence, the environment permits greater opportunities for the exposure of undergraduates to the thrill of scientific exploration. We statisticians are extremely dependent upon other areas of science. The substance of our professional lives comes from the data generated by scientists in other fields. There are relatively few statisticians who do not need this outside stimulation to remain professionally motivated. Working with data is an important educational exercise when trying to motivate students in statistics. Students who have a potential interest in statistics as a career should be given the opportunity to become meaningfully involved in the analysis of data from original scientific investigations. Such an exposure would allow them to experience the thrill of original research. They would have the opportunity to legitimately take ownership of the data. They would encounter the excitement of being the first to know the results of the statistical analyses, knowing that these data had never been analyzed before. Such experience is the analog of the research opportunities provided undergraduate students in the laboratory sciences. And such experiences will recruit undergraduates to careers in statistics. Statistical consulting provides the undergraduate statistics student with the analogous experience to undergraduate research in the laboratory science. Pomona College is a small liberal arts college in the greater Los Angeles area which has been successful in encouraging students to enter the field of statistics. Over the last quarter century the college has graduated only 300 students a year, yet has averaged greater than one doctorate a year earned by its alumni in statistics and the related fields of biostatistics and epidemiology. A main ingredient in this recruiting success has been the exposure of its students to applications of statistics which have been provided through consulting experiences in the biomedical industry. There are numerous benefits derived from participation in industrial consulting. Not only is there benefit to the students who are assigned to work on the actual data, but the benefits carry over into the classroom. The faculty member overseeing the project can include examples from the project for classroom lectures, exercise sets and exams. Other students will gain an interest in the work and will keep questioning the progress of the project. The opportunity to present statistics in action motivates students to consider the field as a vocation. Traditionally, the small liberal arts colleges have produced a disproportionately large percentage of the leaders in the laboratory sciences. A major factor behind this phenomena might be the opportunity that is provided the undergraduate student to participate in original research. Statistics education can take a lesson from this success, and work at providing an analogous experience for those students with an interest in a career in statistics. Such experience can be provided by involvement in statistical consulting on scientific research which is perceived by the student to be important. Data Analysis: An Adjunct to Mathematical Statistics at Oberlin College Jeffrey Witmer SLAW Technical Report No. 91-003 Department of Mathematics, Pomona College. Nonetheless, mathematical statistics presents only one side of the discipline. By offering the Data Analysis course I can show students another side of statistics. Opportunities for Statisticians at 4-year Undergraduate Institutions Rosemary Roberts SLAW Technical Report No. 90-005 Department of Mathematics, Pomona College. I will be concerned today with the problems faced by a lone professional statistician teaching in an undergraduate institution. (Regarding statistics courses in mathematics departments at liberal arts colleges) As far as statistics education is concerned, while the courses taught might be perfectly acceptable as mathematics courses, they are unlikely to be statistics courses. Tim Robertson and Bob Hogg commented in an essay in Mathematics Tomorrow, "While most traditionally trained mathematicians can pick up a textbook in mathematical statistics and teach an acceptable course, they cannot teach statistics." Equally unfortunate is the fact that many mathematicians do not realize this! The result is that a statistician who joins such a mathematics department inherits courses that need major revision, and colleagues whose perception of statistics must be changed in order to accomplish this revision. Many mathematicians tend to regard applied mathematics - under which they include statistics - as inferior to pure mathematics, indeed even as bad mathematics. Statistics courses have earned the reputation as "the worst course I've ever taken", or, as my husband likes to say, "sadistics". Statistical thinking may be conceived as a dialog between a mathematical model and data. A range of appropriate models is dictated by the context within which the data arise. Issues surrounding the data collection, their analysis and interpretation are central to statistics. They should also be a central component of any first statistics course. We now live in a time when quantitative information permeates our everyday lives, and it is more important than ever that people learn to reason from data. In small undergraduate colleges, we have an opportunity to take a lead in reforming statistics education to help achieve this goal. Even with a data-driven introductory statistics course, the statistics education of those mathematically able students who are potentially eligible to pursue a career in statistics will rarely be affected. For although mathematics majors are not precluded from taking an introductory statistics course, they are implicitly discouraged from doing so by the fact that it rarely counts for credit toward the mathematics major. Thus while graduating math majors may have taken the mathematical statistics course(s), they will have had little or no exposure to the applied side of statistics. Teaching statistics courses is just one aspect of the role of a statistician at an undergraduate institution. Often the lone statistician also provides statistical advice for students and colleagues throughout the college. A statistician who takes statistical consulting seriously may spend many hours working on the problems of others, but this activity may only be counted as service to the college, if it is counted at all. While consulting is indeed a service to the college, some takes the form of teaching, while other consulting contributes directly to the scholarly productivity of the college, regardless of whether the statistician is acknowledged in resulting publications. In large universities, statistical consulting is considered a part of a statistician's job, and taken into account in promotion and salary decisions. There is no reason that this cannot be the case at undergraduate institutions also. These institutions should expect, encourage, and support statistical consulting as a form of professional activity. Alternative Introductions to Applied Statistics for Mathematics Majors Robin Lock SLAW Technical Report No. 90-008 Department of Mathematics, Pomona College. At many colleges a typical mathematics student's introduction to the field of statistics consists of the standard two semester sequence in Probability and Mathematical Statistics. Indeed, at many smaller colleges, these are the only courses in statistics available for credit towards a math major. A group of statistics educators, with support from the Sloan Foundation's New Liberal Arts Program, has been investigating alternatives to this approach. Our goal is to capture the interest of mathematically talented students and encourage them to pursue further work in statistics. We believe that this goal can be addressed by developing an applied statistics course which exposes students more quickly to the joys of data analysis, emphasizes the applications of statistics, and utilizes their ability/interest in mathematics. The need for such an alternative course, potential pitfalls in its development, and several specific models for its implementation will be discussed. Most mathematics students first encounter statistics, if at all, as part of a two semester probability / mathematical statistics sequence. While we believe that these are important courses which should be a key part of a any mathematics curriculum, we feel that they may not be so successful in attracting students to study applied statistics. .... Even aver going through the entire year, a theoretical course in mathematical statistics often slights the applications and might never impart to students the excitement of working with real data. Another approach is for mathematics student to enroll in a standard service courses in applied statistics. Hopefully, they would then at least see some real applications, but such courses are typically designed with very modest mathematical content which wouldn't challenge most math majors. A more effective introduction could be achieved by offering a course emphasizing the applications of statistics which also assumes and uses a reasonable level of mathematical sophistication. The proper balance between solving applied solving and maintaining mathematical rigor can be very delicate. This can be complicated in some mathematics departments by a reluctance for colleagues to recognize statistics as a distinct discipline where the problems and methods may be quite different from traditional mathematics courses. Nevertheless, we feel that mathematics students should be able to take an applied statistics course at an appropriate level, preferably before taking mathematical statistics. While there are a number of possible models for implementing an introduction to applied statistics for mathematics students, we feel that certain features should be common to any such course. 1. The course should be data-driven. The best way to excite students about statistics is to demonstrate the usefulness for solving interesting problems in the real world. This requires lots of real data which motivate compelling questions. These questions should be relevant to students' interests and encourage the discussion of statistical concepts and techniques. 2. No previous background in statistics should be required. If the course is to serve as an introduction to applied statistics we should not expect students to have taken a previous course (such as mathematical statistics). 3. Fundamental concepts of statistics should be discussed. Although it is impractical for any course to cover the entire breadth of applied statistics, the course should illuminate basic principles, concepts, questions and modes of thought which are common and unique to statistics. 4. The mathematical level should be nontrivial. To attract mathematically talented students it is important that we dispel the myth that statistics is purely "number-crunching". Students need to see that there are interesting applications of mathematics and a solid theoretical framework for statistics. Thus the typical prerequisites for the course might be two or three semesters of calculus and perhaps a course in linear algebra. 5. The computer should be used liberally. Experience with a statistical computer package is essential if we want students to get an accurate feel for how a statistician works. By freeing students >from doing routine computations by hand, the computer allows them to tackle nontrivial problems with substantial data and pay more attention to the interpretation of the data and the underlying statistical concepts. Teaching Statistics as a Respectable Subject David S. Moore in F. Gordon and S. Gordon (eds.) Statistics for the Twenty-first Century, Washington DC: Mathematical Association of America, MAA Notes, Number 26, 14-25 (Three principles) Almost any statistics course can be improved by more emphasis on data and on concepts at the expense of less theory and fewer recipes. Automate calculation and graphics as much as possible. A basic statistics course should cover no more probability than is actually needed to grasp the statistical concepts that will be presented. In referring to statistics as a respectable subject, I mean first that it is a subject in its own right. Statistics, though a mathematical science, is not a subfield of mathematics. And although statistics is a methodological discipline, it is also not merely a collection of methods than can be understood as ancillary to a substantive discipline such as psychology, business, or engineering. Statistics has its own substance, its own distinctive concepts and modes of reasoning. These should be the heart of the teaching of statistics to beginners at any level of mathematical sophistication. When we teach mathematically strong students, the temptation to teach them mathematics rather than statistics is acute and must be resisted. I hope to persuade readers that the traditional math major sequence of probability followed by statistical theory is not a suitable introduction to statistics. In our imperfect world, we might consider the model of the sciences: a separate required laboratory period devoted to actually working with data, preferably via interactive computing. Alternatively, why not admit that theory is not the proper starting place and that most of our students would better master the theory after some acquaintance with practice. Even mathematics majors, I think, are better served by studying statistics before mathematical statistics. There is certainly much to study. Mathematics is an eminently respectable subject, honored at least since Plato. Statistics considered as a field of mathematics is not. The mathematics employed by statisticians is shallow by the standards of contemporary mathematics. Mathematicians therefore often consider statistics a shallow discipline. It is more just to see statistics as a field like economics or physics that makes heavy and essential use of mathematics, but is not part of mathematics and should not be taught to beginners as if it were mathematics. Statistics has its own subject matter. Statistics is the science of data. More precisely, the subject matter of statistics is reasoning >from uncertain empirical data. Statistics does not originate within mathematics. Historians have recently given a great deal of attention to the origins of statistics. Their work demonstrates that statistics is indeed a distinct discipline. (gives references and examples) The practice of statistics is not mathematical. Statistics in practice is characterized by a dialogue between data and mathematical models. A model is used to analyze the data, but the data are invited to criticize and even falsify the model. Diagnostic methods, which detect various types of disagreement between data and model, are a major field of statistical research. In recent years, the impact of ever-faster, ever-cheaper computing has turned statistical research as well as statistical practice somewhat away from the purely mathematical aspects of the subject. Statistics has its own foundational controversies. Reasoning from uncertain empirical data raises knotty philosophical issues. It is not surprising that statisticians take differing points of view on these issues. Foundational controversies in statistics are entirely unrelated to the largely dormant controversies concerning the foundations of mathematics. There is a one-way traffic between statistics and mathematics. Statistics does not participate in the close relations among subfields that characterize contemporary mathematics. Like economics, statistics imports mathematical tools and ideas but does not export its own tools and ideas into mathematics. ... Central concepts of statistical theory such as sufficient statistics, maximum likelihood, and prior and posterior distributions are not familiar to or used by mathematicians. Teaching should not be Driven by Theory Because statistics is not a subfield of mathematics, introductory instruction that presents statistics as if it were mathematics will give an inadequate picture of the field. First, the mathematical model is incomplete. It does not capture the distinction between observational and experimental studies, one of the most important distinctions in statistics. ... Second, the theoretical merit of a statistical procedure is not the same as its practical merit. ... Finally, theoretically-based procedures may require unrealistic assumptions. Here is a first principle for improving statistics instruction: Almost any statistics course can be improved by more emphasis on data and on concepts at the expense of less theory and fewer recipes. .... Beginning instruction in statistics should emphasize experience with data and variation, and the concepts and reasoning that statisticians use to understand data and variation. Some aspects of statistical reasoning are formal, even mathematical, while others are informal and not mathematical. Strategies for exploring data and principles of experimental design are examples of statistical fundamentals that don't lend themselves to either theory or recipes. Statistics taught according to this first principle will offer enough experience working with data that it resembles a laboratory science. A second principle, less important but still very helpful, then follows: Automate calculation and graphics as much as possible. If the often-forbidding calculations required by statistical procedures are automated, instruction can offer experience with realistic data and can emphasize reasoning. Students can be expected to carry on a dialogue with the data, asking repeated questions that would otherwise be hopelessly time-consuming. Students should learn to look at data in their first exposure to statistics. Because data analysis relies on simple graphical and numerical tools for displaying data, it is easy to regard it as a collection of elementary techniques that deserve only cursory treatment in college instruction. This attitude overlooks the importance of giving students actual experience working with realistic data. What is more, students must learn to "read" data as they learn to read words. Data analysis involves not only a collection of tools, but strategies for examining data intelligently. Good data are as much a human product as hybrid corn and compact disc players. The design of data production through sampling and experimentation is perhaps the most important role of working statisticians. In particular, the randomized comparative experiment has revolutionized the practice of many applied sciences and can claim to be the most influential contribution of statistics to science as a whole. Even this very brief look at data analysis and data production reveals a wealth of essentially statistical concepts and modes of reasoning that are not mathematical in nature. Until recently, it has been all too common to slight these topics in beginning instruction. ... Designs for data production are not only very important in themselves, but help justify formal inference and clarify its place in statistical practice. The final content division is formal probability-based inference. The first thing to be said is that this is a difficult subject. The reasoning of inference, particularly of tests of significance, is subtle. Worse, the reasoning rests on probability concepts, which are among the hardest to grasp in elementary mathematics. Probability is important in its own right, but its difficulty is a barrier to learning statistics. Statistical ideas are challenging enough in themselves. Here, then, is a third principle for improving statistics education: A basic statistics course should cover no more probability than is actually needed to grasp the statistical concepts that will be presented. Ask Dr. Stats, column in Stats, the Magazine For Students of Statistics, Fall 1994, Number 12, p. 23 Statistics is not a branch of mathematics. It is true that statisticians use a lot of mathematics in their work, but so do physicists, economists, and people in many other disciplines. To be a good statistician you need to have some quantitative skill, but you also have to understand how data are produced and how they should be analyzed. You need to understand the assumptions that underlie the use of a particular modeling technique and how those assumptions can be checked. You also need to be able to communicate effectively with people in a wide variety of disciplines. Most of this has little to do with mathematics. The word needs and values people who concentrate on designing experiments and analyzing data rather than on proving new theorems in statistics. All the mathematics in the world won't rescue someone who did a poor job of designing an experiment or who slanted the wording of a question on a survey. In statistical consulting it is extremely important to be able to understand the question that the client is trying to answer, to help the client collect good data from a properly designed experiment, and to communicate results of statistical analyses. Dear Dr. STATS I'm an undergraduate mathematics major with an interest in statistics. I've been told that I should skip over the elementary statistics course offered at my school and go straight into the probability and mathematical statistics sequence. Would it be a waste of time for me to study STAT 101? Few would argue that CALC I is a waste of time for someone who intends to study advanced calculus. Likewise, if you want some understanding of why certain topics and results are important in mathematical statistics, then it helps to study STAT 101 first. Mathematical derivations make more sense if you know how the resulting methods are used in practice. Moreover, there is a lot more to statistics than just the mathematical aspects of it. So my advice is that you enroll in STAT 101 - preferably with a professor who really feels the excitement of statistics applications - and learn something about how statisticians think and how statistical methods are used. Then when you study probability and mathematical statistics you will have a better appreciation for the material Statistics within Departments of Mathematics at Liberal Arts Colleges Thomas L. Moore, Jeffrey A. Witmer The American Mathematical Monthly, May 1991, 431-436. Statistics is underrepresented among mathematics faculty at liberal arts colleges in the United States. A recent survey (ref) of mathematics departments at liberal arts colleges suggests that approximately half of all such departments have no one with an advanced degree in statistics and only 12.5% have more than one such person. And, unlike the situation at many universities, if statisticians are employed at liberal arts colleges they will generally be housed in the department of mathematics, since mathematics is the traditional liberal arts discipline most closely aligned with statistics. Because the responsibility of statistics education at most liberal arts colleges rests with the mathematics department, it is imperative that the department recognize the fundamental differences between statistics and core mathematics and ensure that their statistics curriculum reflects these differences. A critical aspect of this dialog between model and data is the quality of the data. For example, by properly choosing the sample or by designing a good experiment the statistician can usually simplify analysis and strengthen the interpretability of the model. It is therefore very important to present these ideas when teaching statistics. Even an introductory course should give attention to ideas such as sampling and experimental bias, the role of randomization, the idea of pairing observations, etc. Unfortunately many introductory courses and textbooks ignore these concepts. These Statistics in the Liberal Arts Workshops (SLAW) have considered three aspects of statistics within the liberal arts setting: the teaching of statistics, the role of statistics within the mathematics major, and the role of a statistician as a general campus resource (ref). A key conclusion was that a vibrant statistics curriculum includes real data and applied statistics and that every mathematics department should offer at least one data-driven statistics course that counts for mathematics major credit and that preferably can be taken early in a student's career. Several models are possible for such a course: (1) Make an existing introductory course data-driven and count it for the major. (2) Add a (one- or two-credit) supplement to the traditional mathematical statistics course. (3) Teach new and different applied and data-driven statistics courses at the introductory level for mathematics majors. Model 1 may be the easiest to implement. Most liberal arts college mathematics departments teach a course in introductory statistics. Why not allow credit for the mathematics major for such a course? The traditional response to this question is that such a course is not mathematical enough, where "mathematical" is taken to mean "core mathematical". However, once statistics is given equal status as a mathematical science, this objection will vanish if such introductory courses are taught with statistical rigor, that is if they are data-driven explorations of the discipline of statistics, as opposed to the dry presentations of formulas that students often see. Model 1 together with the traditional mathematical statistics course then becomes similar to the model most of us now use for teaching calculus: an introduction that teaches basic techniques and the flavor of the subject followed later by a theoretical real analysis course. It is natural for mathematicians teaching statistics to emphasize the mathematical (i.e., theoretical, deductive) side of the discipline. Such an approach makes things easier for the teacher, but gives only a partial picture of statistics. For within such a curriculum students who might be drawn to statistical thinking see little of it and potential mathematical scientists (and potential mathematics majors!) are lost. A good data-driven course uses real data to teach statistical thinking. Experience suggests that real data are a far more powerful motivating force than are artificial data. Statisticians - and their students - are interested in understanding and solving real problems. The analysis of data should be the focus of an introductory course. Students should discuss the real-world problems the data were collected to solve, the quality of the data, and their effective analysis. Exercises should be built around real data sets and students might even design projects that require them to produce and analyze their own data. The emphasis of such a course is on understanding the broad concepts that apply to most statistical problem solving. At least some portion of the course should deal with larger data sets and their analysis using a statistical computer package. It is important to include large data sets and computers for several reasons. Teaching a data-driven course can be a challenge. Such a course will require a different style of teaching for most faculty, with more discussion and less lecture. More time will be spent on the computer with a statistical package and, possibly, simulations. Office time will be spent helping students work out the very nonmathematical aspects of the design and analysis of their own projects. When statistics secures a greater role in the mathematics department of a liberal arts college, everyone gains. The department becomes more properly a department of mathematical sciences as described by Steen. Students more inclined toward statistics than core mathematics have an additional point of entry into the mathematics major and the college may send more students on to careers in the mathematical sciences. At the same time, these benefits require that the differences between statistics and core mathematics be appreciated and allowed for. Applied Introductory Statistics Courses for Mathematics Majors at Liberal Arts Colleges Rosemary A. Roberts SLAW Technical Report No. 90-002 Department of Mathematics, Pomona College. The students we see in the mathematical statistics course usually have very limited experience with data. Trying to make amends for this within the context of a mathematical statistics course is not easy. There is already more than enough material to cover if an adequate introduction to the theory and methods of statistics is to be given. While textbooks are now including real data in examples and problems, this does not provide sufficient exposure for students to develop an appreciation of data. Even the inclusion of an introduction to data analysis is insufficient, because the amount of time that can be devoted to this is limited. For these reasons, we see the need for an applied course for mathematics majors. There are two general requisites for this applied course. First, the course should be taken preferably before, but at least concurrently with, the mathematical statistics course. There are several reasons for this. From a pedagogical pont of view, we believe that our students will benefit much more from the mathematical statistics course if they have a prior appreciation of data. .... Additionally, if the course is an entry level course to the mathematics major, it may attract students to the major. Second, the course must count for credit towards the mathematics major. This may be problematic for mathematics departments in which applied work is not considered to be legitimate mathematics. However, if mathematics departments are including statistics in their offerings, they have an obligation to recognize that statistics has both theoretical and applied components. If they fail to do so, statistics as a discipline is not fairly represented. Data are at the heart of statistics, and without experience with data, our students' statistics education is deficient. No wonder so few students are motivated to pursue a career in the subject! The primary goal of the applied course we are proposing is to develop in students a "data sense" through experience with real data. It is only through this kind of experience that students learn that data don't exist on their own, but within a context. The context gives rise to the reasons the data were collected, the way in which they were collected, and the questions they were collected to answer. Students must learn how to formulate these questions precisely, how to plan the data collection so that these questions can be answered efficiently, how to verify the data, and finally how to analyze the data. Emphasis must be placed on the dialog between the data and the model used during the analysis so that students learn that understanding data is an iterative process. It is this dialog that characterizes statistics and distinguishes it from the deductive thinking characteristic of mathematics. An integral part of any of these applied statistics courses is the use of a computer. This is a necessary tool for the analysis of large data sets, and essential if we want students to get an accurate feel for how a statistician works. The applied courses described above add a new dimension to the statistics education of mathematics students at small colleges. They augment the statistics offerings for mathematics majors and expose students to the excitement of working with real data. Teaching Statistics Draft report (late 1995) of the joint Mathematical Association of America/American Statistical Association Statistics Focus Group. George Cobb, Robert Hogg, 37 others. During the last two decades, statistics has been changing simultaneously on three levels, which correspond to the technique, practice, and theory. On the technical level, cheap, powerful computing has made possible a number of important innovations: graphical methods for data display, iterative methods for data description, diagnostic tools for assessment of fit between data and model, and new methods of inference based on resampling techniques such as the bootstrap. On the level of practice, such things as pattern-searching, model-free description, and systematic assessment of fit have all become more prominent, at the expense of formal inference, most especially hypothesis testing. Statisticians now put more effort into the complex process of choosing suitable models, less effort into doing those things - simpler by comparison - which take the choice of model as given. Mathematicians who teach the introductory course will probably be completely oblivious to the decreasing importance of hypothesis testing in the work of statisticians. To mathematicians, this may have the most profound implications for their introductory course because it calls into question the ultimate goals of the course. - Ann Watkins, California State at Northridge On the level of theory, one can distinguish two kinds of changes that invigorate discussions about the reasoning of statistics. First, foundational discussions of long standing (examples here) now much more often take place in the context of real applications. Second, statistical practice has partly outgrown its mathematical theories, which are consequently less relevant. Important new elements of data analysis (examples here) don't fit the older theoretical frames, while the influential area of statistical process control offers new ways, not yet mathematically developed, to frame the enterprise of learning >from data. Any introductory course should take as its main goal helping students to learn the basic elements of statistical thinking; many advanced courses would be improved by a more explicit emphasis on those same basic elements: 1. The need for data .... 2. The importance of data production It is very difficult and time-consuming to formulate problems and to get data that are of good quality and really deal with the right questions. Data generally don't represent what people initially think. Moreover, most people don't seem to realize that this is the way things work out until they go through this experience themselves. This is the most important part of actually doing statistics, because if it is not done well all the subsequent analysis can't be worth much. ... Most people I deal with would be better off if they carried realistic notions about formulating problems and getting relevant and accurate data, rather than some vague notion of significance or confidence from the course they had - Jim Landwehr I haven't had students plan studies and gather data in a couple of years, for various reasons. I wasn't very happy with the actual projects during the four semesters I did it. However, I was quite happy with the students experiences. Almost every one of them, by the time they finished, was rather sheepish about what a poor study it turned out to be, because they could see all the ways it really should be improved. - Mary Parker, Austin Community College 3. The omnipresence of variability .... 4. The quantification and explanation of variability. The key is to teach statistics like statisticians instead of like mathematicians. - Walt Pirie The introductory course in statistics should focus on a few broad concepts and principles, not a series of techniques. Suggested concepts are: graphing data (as in Cleveland's book - this is not trivial), randomness (the idea of producing a predictable pattern through randomness is difficult for a student to grasp; it is not intuitive), inferential reasoning (ideas illustrated through bootstrap-like simulations are easiest to grasp and the formulas, for those who insist on using them, are approximations), experimental design (I've seen eyes light up for some reasonably intelligent people when they were able to set a stat-a-pult right on target after collecting information on a half rep of a two to the fourth factorial experiment; they did not think it could be done). - Dick Scheaffer, Florida Thinking about the role of probability can be a useful exercise in clarifying differences between statistical and mathematical thinking. Many statistical concepts don't rely on probability theory at all, and a course which puts statistical concepts ahead of mathematical theory will recognize that fact. The distinction between mathematical theory and statistical concepts remains an important one even in thinking about the standard introduction to mathematical statistics. I don't think students who take the standard mathematical statistics course come away with even the faintest appreciation for what statistics is about. Unless students have had a previous course that does justice to data analysis, and so provides a meaningful context for the mathematical statistics, the course is mainly an opportunity to practice advanced calculus techniques. I think only three positions are tenable here: 1. The mathematical statistics course should never be taught to students who haven't first taken an applied course; 2. The mathematical statistics course must be radically revised, to integrate data analysis with the statistical theory; or 3. The mathematical theory of statistics should be introduced via an optional adjunct to the beginning applied course. - George Cobb Our mathematics majors often see little of the material taught in the introductory non-mathematical statistics courses for, say, psychology majors. This is especially true if a non-statistician teaches the course in the mathematics department. - Alan Tucker, SUNY Stony Brook I think the probability-mathematical statistics sequence is important but should be preceded by a data analysis course. - Jack Schuenemeyer, Delaware In an ideal Grinnell I'd like my students to have an applied methods course as sophomores and then have a more traditional mathematical statistics sequence. - Tom Moore, Grinnell Statistics should be taught as a laboratory science, along the lines of physics and chemistry rather than traditional mathematics. Students must get their hands dirty with data.- Dick Scheaffer Student projects can teach concepts not usually encountered in introductory or second-level statistics courses. Questions about study design, study protocols, questionnaire construction, informed consent, confidentiality, data management, data cleaning, and handling missing data may arise when students deal with collecting and analyzing their own data. ... In our experience students usually conclude that the project was one of the most useful parts of the course. Some comment that the project made them apply everything they learned as soon as they learned it. - Tom Moore and Katherine Halvorsen, "Motivating, Monitoring, and Evaluating Student Projects", Proceedings of the Section on Statistical Education of the American Statistical Association, 1991. Change must overcome four inertias: one logistical, one intellectual, one interpersonal, and one institutional. 1. Logistical Intertia: Good data sets are hard to find. Anyone reading this report could easily invent enough examples to fill a lecture on differentiating polynomials, and it would take at most five minutes or so. But how long would it take you to come up with just one real data set, say >from cognitive psychology, to illustrate the effect of outliers in one-way analysis of variance? 2. Intellectual Intertia: Learning to handle the ambiguities of statistics takes time, practice, and hard thought. Even with software installed and data sets in hand, doing a proper analysis and interpretation is a kind of challenge that many who teach statistics are not prepared to meet, mainly because, through no fault of their own, they've rarely if ever seen it done, and their training and experience have not prepared them either to do it or to value the doing of it. 3. Interpersonal Intertia: Giving up the familiar role of "I talk, you listen" doesn't always come easily. ... 4. Institutional Inertia: Most deans and department heads don't care very much whether statistics is taught well. ....many mathematics departments have not been willing to do what it takes to recruit and retain a Ph.D. statistician. According to Moore and Roberts (American Statistician, 1989, 43:2) only 26 of 80 mathematics departments at responding liberal arts colleges could claim a Ph.D. statistician. The Teaching of Statistics: Content Versus Form Oscar Kempthorne The American Statistican, February 1980, 34(1), 17-21 I also suggest that anyone who regards a commitment to teach basic statistics is being adequately achieved by teaching one of the many "introductions to mathematical statistics," which, essentially, consists of probability calculus and some elementary decision theory, or Bayesian statistics, as another example, should examine and question his thinking. What must happen is that the ideas and aims of statistics must determine the mathematics of statistics and not vice versa. Mathematics is surely a beautiful art form (in addition to being useful). If the statistics that is taught is to have this good form, then its form is determined by its mathematical form. And then, I suggest, form wins out over content, and essential ideas of statistics are lost.
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