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9 FOSTERING UNDERGRADUATE PROGRAMS IN STATISTICS How to develop, nurture, and sustain an undergraduate program in statistics is discussed by a panel of statistics adr~urustrators. Jaryaram Sethuraman (Organizer), Florida State University STATISTICS AS AN INDEPENDENT UNIT Dean L. Isaacson, Iowa State University THE CARE AND FEEDING OF UNDERGRADUATE STATISTICS PROGRAMS Walter R. Pirie, Virginia Polytechnic Institute and State University THE UNDERGRADUATE STATISTICS MAJOR James R. Thompson, Rice University 83

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FOSTERING UNDERGRADUATE PROGRAMS IN STATISTICS STATISTICS AS AN INDEPENDEN r UNIT Dean L. Isaacson Iowa State Uraversit~y It may seem somewhat paradoxical that statistics asks to be an independent unit and at the same time claims to be a part of most scientific research. How does statistics establish an identity when the subject is being taught in many departments across most campuses? The importance of data collection and analysis is spread throughout the college or university so that students do not view statistics as a separate discipline. This paradox represents both a problem and an opportunity. Statistical methods courses are often taught in departments outside of statistics by professors without a degree in statistics. Hence, there is no natural "home" for applied statisticians. The theoretical statisticians are often absorbed into mathematics departments and then tend to become mathematicians in order to get promotion and tenure. This lack of a natural home where statisticians can be nurtured has hurt the visibility of the discipline and in turn has made it difficult to establish an undergraduate program. We must pull statisticians together into a single unit so that students recognize it as a viable major. The first stepis to separate statistics from mathematics. Statisticians cannot move freely between theory end applications if tenure decisions will be made by theoretical mathematicians. Within a mathematics department there will be no incentive to do statistical consulting and collaborative research. So a significant portion of statistics will wither and die. There are also problems associated with having mathematicians teach statistics courses. The theorem-proof approach is often used, and hence students cannot see the difference between mathematics and statistics. In most colleges and universities, the number of statisticians in the department of mathematics is not great enough for the formation of a separate department. They also usually lack the breadth to satisfactorily cover the statistical methods being taught and used on their campuses. Hence, the next step should be the centralization of applied statistics. This may be a sensitive issue on many campuses, but with help from central administrations, it can be done. On most campuses there are courses in business statistics, engineering statistics, educational statistics, psychometrics, econometrics, etc. These courses should have primary listing in the department of statistics so that the material is recognized as statistics, and students who enjoy the material might consider a major in statistics, or a double major. It is not feasible to hire new faculty members to teach these courses, and so the existing faculty should be given fractional appointments in statistics. In this way, all of the "applied statisticians" would interact on a regular basis and thereby keep current in statistics. The applied courses would still be taught by individuals with expertise in the field of application. Through the above process, statistics could be centralized on campus. This would give it strength and size and hence a competitive position as a possible major. If students choose statistics as a major, there must be some flexibility in the curriculum. These students will have different career goals, and so they must have a variety of courses from which to choose. This is impossible to do if the courses are designed for statistics majors only. The theory courses should be designed and taught in such a way that undergraduate students in mathematics and engineering will also take the courses. Similarly, the applied courses should give adequate graduate credit to majors in the sciences. Hence, courses in design of experiments, survey sampling, quality control, regression, etc., will be filled primarily with graduate students from outside statistics and also will be available to the undergraduate statistics majors. By listing all of these 85

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CHAFING TO MATHEMATICAL SCIENCES DEPARTMENT OF TO 1990S courses through statistics, control is maintained so that He courses remain appropriate for an undergraduate mayor. A successful undergraduate program must also be separate from the graduate program. At many universities the graduate statistics program is strong and the undergraduate program suffers by comparison. In such cases, there must be an undergraduate coordinator who acts as the administrator for the undergraduate program. If possible, a separate "main office" with secretary should be used for undergraduate matters so that the undergraduate students do not get pushed aside when seeking advice. There also should be a core of undergraduate advisors who take the program seriously and are rewarded for doing that part of their job well. This subunit, no matter how small, gives the undergraduates a sense of unity and a home within the larger program. The resources needed to run an undergraduate program will vary. In most cases the resources are already there and simply need to be pulled together and identified as a program. Through joint appointments, selection of an undergraduate coordinator, selection of the undergraduate secretary, and centralization of statistics courses, a viable department can be formed. The main resources it needs are encouragement and respect. 86

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FOSTERING UNDERGRADUATE PROGRAMS IN STATISTICS THE CARE AND FEEDING OF UNDERGRADUATE STATISTICS PROGRAMS Walter R. Pirie Virginia Polytechnic Institute and State University I wish to tank today about how to make undergraduate programs work, both for the department and for the students. Both aspects are equally important for the success of the program. My colleagues this afternoon have provided some important insights into the administrative aspects, both nationally and within the institution. One has also discussed some unique problems for small departments. I wish to focus mostly on undergraduate programs within statistics departments in large universities that have heretofore existed primarily for their graduate programs. That is my primary interest and my background. Program Content How should a program be designed? I think the operative phrase is "by intent" and not by default. By that I mean the program designers, after some careful thought, should come to an intellectual conclusion about the desired nature of the program. Necessary actions should then be taken to allow that program to be implemented. If local conditions demand major compromises and a considerably weaker program, the project should be abandoned. This is particularly true of undergraduate statistics programs. Despite the continuing health of the discipline, demand will never warrant a statistics major at every college and university in the country as for mathematics or physics. It is in everyone's best interest that only those who can support well-designed programs should do so. Although diversity and flexibility of program content are desirable, I think most would agree on a few basics. A program should be designed around a core of required courses. That core would likely be similar in most programs, including the most commonly used statistical methods, a solid introduction to probability and statistical inference, mathematics that includes calculus and matrix algebra, and some use of computers. Beyond the core there is room for considerable flexibility, but a program should demand considerably more statistics than just the core, whichever direction it chooses. If not, it is more appropriate to call it a concentration rather than a major. The guidelines published in AMSTATNews, June 1986, cover this in more detail. Who Should Teach the Courses? Physics is not considered to be a branch of mathematics just because it uses a lot of mathematics, nor is computer science. True, advanced theoretical topics in statistics are very mathematical, but statistics is not a branch of mathematics. It is a science in its own right and cannot be adequately taught by most mathematicians (or psychologists, or Ed.D.s, etc.), at the very least, not to future statisticians. To offer an appropriately broad degree program in statistics requires a core of professionally educated statisticians. I don't claim to have a magic number, but I cannot imagine it with less than three or four professionally qualified statisticians. Can anyone envision a mathematics degree program with fewer faculty? As David Moore has said, "it is unprofessional for mathematicians who lack training and experience in working with data to teach statistics." 87

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CHASING TO MATHEMATICAL S(:~NCES DEPARTMENT OF TO 1990S Enrollments How does an undergraduate statistics program attract the students necessary to warrant a strong program with a sufficient variety of courses? The answer comes in several pieces. In the introductory-level courses, it is usually satisfactory to combine majors and general service teaching; so enrollment is often not a problem. In upper-division courses, that is often not the solution. Courses need to be designed more specifically for the statistician. In a major research institution, such courses will still attract some students from other data-oriented disciplines, and offering a minor in statistics will also be effective. Many smaller institutions will have to rely on majors only for these courses. The question becomes one of how to attract and hold not just numbers of students but also highly qualified ones. The factor that makes this difficult is that most high school seniors are not even aware of statistics as a separate discipline. One of my major points is that the traditional practice of relying on transfers from other disciplines is not satisfactory. Often the numbers will not be adequate, and few if any will be the high-quality students we need to attract. The only reliable way to consistently maintain both the quantity and quality of students is high school recruitment. The experience at my home institution over the past decade is that in years when we sent a mailing to high schools throughout the state, our freshman classes varied from 15 to 20. When we have not used a mailing, the numbers have been two to eight. We have found this to be a very effective recruitment mechanism Cat utilizes relatively modest resources in terms of cost and faculty time. The alternative of faculty visits to high schools is resource-intensive and reaches far fewer students. This year we have added a direct mailing to students whose names were selected from the PSAT list, which is available to admissions offices, and so far, that seems to be effective also. Then, of course, there is the issue of keeping the good students and building a reputation within the institution. Professor Isaacson has already discussed the importance of that. Students must feel that the department values the undergraduate program. That issue still requires a change in attitude for many statistics faculty members. What we have discussed today is not revolutionary. With the exception of a greater need for recruiting, we are simply emphasizing what happens in most good programs in any discipline. It is just that in statistics we have not paid much attention to undergraduate programs in the past. 88

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FOSTERING UNDERGRADUATE PROGRAMS IN STATISTICS THE UNDERGRADUATE STATISTICS MAJOR James R. Thompson Rice University Thinking back on my past doctoral students, I recall that two of them had undergraduate majors in English. One was a Chaucer specialist, the other a Beowulf enthusiast. Other doctoral students had done prior work in sociology, physics, electrical engineering, and medicine. Such backgrounds might seem bizarre for aspirants to doctoral work in mathematics. In statistics, they are not unusual. Each had as his major motivation for doing doctoral work in statistics not the techniques of mathematics but rather the uses to which statistics might be put in attacking the problems of science. It appears to me most appropriate that undergraduate statistics majors should have majors in other university departments as well. At Rice, all of our undergraduate statistics majors have another major in addition to statistics. We have some majors who quite frankly pick one major, such as English, independent of any prospects of a profession in the area, and another in statistics because they find it interesting and it offers promises of future employment. I do not find this strange or insulting to statistics. It seems to me, on the contrary, an intelligent approach to one 's undergraduate curriculum. Ofthese students, many will seek employmentin statistics without further academic Raining beyond the bachelor's degree. A statistician who has expertise only in the mathematical techniques of his discipline stands outside the historical mainstream of the field. Statistics began in earnest during the Victorian Enlightenment. Gallon and Pearson were not very good mathematicians. They were, however, very good scientists and individuals whose interests stretched from psychology and ethics to astronomy and agriculture. It is this fundamental curiosity which, more than any other factor, defines a statistician. If I must write down a list of fundamental statistics courses for a statistics major, I am in a much greater quandary than if I were given a similar task for a mathematics major. Every mathematics major should have an essential core of courses in algebra, complex analysis, and real analysis. This may well extend to a list of at least ten courses beyond calculus and differential equations. For a statistics major, I will grant the necessity of a Hogg and Craig type course. Beyond this, however, a wealth of paths becomes feasible. One student might, for example, spend a great deal of time in probability theory and stochastic processes, together with the pure mathematics courses required to handle them. Another student might elect a concentration in psychometrics. Still another might elect to press forward with concentrations in a classical statistics curriculum with courses in sampling, experimental design, Bayesian analysis, and linear models. Which is the correct curriculum? What is the irreducible core? I cannot answer these questions, and I am troubled by the excessive confidence of those who think they can. This may be unfortunate, for statistics is a profession, and there is a keen need for a plan to accredit undergraduate statistics programs. Such plans are currently under consideration by the American Statistical Association and the Southern Regional Committee on Statistics. Statisticians are beginning to notice that their present position as members of a subcategory of applied mathematics is serving their profession ill. They find that, in problems where their expertise is acutely needed, they may have little if any voice. Examples abound. The quality control considerations of the Challenger disaster were dealt with cursorily by a physicist. In the matter of AIDS, it was a matter of embarrassment to all when it was discovered how lacking were the Centers for Disease Control in statistical expertise. It is not simply a question of fighting over turf that is at stake here. 89

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CHASING TO MATHEMATICAL SCIENCES DEPARTMENT OF TO 1990S Rather, we have to deal with thereality that there are statistical questions of considerable importance thatreceive the shortest of shrifts because of the institutionalized impotence of the profession of statistics. So long as statistics is perceived as a proper subset of mathematics, this impotence is likely to continue. This does not mean that I side with those who would make the union card in statistics an ability to run an SAS System program. Mathematics will always continue to afford valuable transferrals of methodology to statistics, and it ought not be despised by any statistician. H.O. Hartley once observed that there is a tendency of some statisticians to regard as irrelevant any branch of mathematics that they could not readily understand. What then should be the criterion for accrediting undergraduate programs in statistics? In my view, it should be a commitment of such programs to prepare the student for doing original modeling and inferential work in science generally. The gate must be sufficiently broad that the stochastic process enthusiast and the quantitative agronomist can both pass through. It must be sufficiently narrow that the student with only a casual interest in the discipline cannot pass. The judgment must of necessity be based on the interests and orientations of the faculty who manage the undergraduate program in statistics. Do they carry out original statistical research? Do they carry out statistical consultation for industry and government? Do they show evidence of interdisciplinary research with faculty from other departments? What are the stated goals of the managers of the program? How realistic are these goals in the light of the curriculum and the student population? The questions may sound as though a great deal of subjectivity must be involved in their answers. I doubt that the subjectivity problem will be as serious as might be supposed. Statistics programs at smaller universities are presented with special challenges. First of all, such programs must rely substantially on joint faculty appointments with other scientific departments, to provide diversity and stimulation for their students. At Rice we have only four full-time statistics faculty members. (Naturally, we are doing our best to increase the number of full-time faculty.) Yet we manage to run an undergraduate program and a doctoral program. (Interestingly, of our nine doctoral students, all are U.S . citizens except for one Mexican national.) We run a weekly seminar, and both graduate and undergraduate majors are encouraged to attend. Without our joint faculty, our task would approach nonfeasibility. Joint faculty are not interested in teaching solely low-level service courses; at Rice they teach upper-level undergraduate and graduate courses as well. A good deal of care and stroking is required to ensure the cooperation of the joint faculty. As a side observation, I have noted that it is easier to obtain the participation of joint faculty within the structure of a department of statistics than it was when we were a proper subset of a department of applied mathematics. At Rice a number of upper-level undergraduate statistics majors take some graduate statistics courses. Given a choice, most statisticians would like to see a group of eight or more full-time statistics faculty in a department of statistics. With some care, however, the job can be done with fewer. If statistics is to achieve Pearson's ideal role as the grammar of sciences, then academic statisticians must turn their attention more to the scientific method itself and less to mathematical technique. The undergraduate curriculum should reflect this realization. 90

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FOSTERING UNDERGRADUATE PROGRAMS IN STATISTICS .... . QUESTION-AND-ANSWER SESSION QUESTION: How do you choose the target for your mass mailing? DR. PIRIE: What we do is quite simple. We mail a copy to every high school in the state. Also, the Department of Education publishes a list of high schools that excel. We target those in nearby states. This year, we added to that a mailing to high school juniors based on PSAT scores. The admissions department at the university or college can get a copy of the results of the PSATs. We sent letters to those who did well and expressed interest in mathematics. The budget for all of this is well under $1,000 per year. PARTICIPANT: I would like to supplement what you have said and give a slightly different view. I am from a small university. We have a mathematics and statistics department with four Ph.D. statisticians. We do not have the size or the number of majors to have a separate statistics department. We have actually been able to do what Dr. Isaacson recommended. For example, we recognize consulting as professional work. One of my goals is to attract enough majors so that statistics can become a separate department. The problem that a lot of us face is trying to get an identity for statistics. Accreditation may work against the profession. The fact is that we will not be accredited. We do not have enough students or enough statisticians, and we probably cannot offer the courses. The university has limits on what can be offered as a major. If your accrediting plans follow those of every other accrediting agency, they will be self-serving. You may end up cutting out departments, such as ours, that want to produce bachelor's degree students in statistics and eventually grow into the position of which you speak. DR. THOMPSON: You are right; it is self-serving. Many years ago, I read an argument by Milton Friedman that indicated that accreditation of lawyers, doctors, engineers, and so forth was in the interest of the professions that were accredited, but it was not necessarily in the interest of society at large. He convinced me with that argument. However, I do not see any way statistics is likely to break out of its non-identity until it considers such options as accreditation and splitting off from mathematics. None of the funding agencies from the federal government, to my knowledge, has a separate directorate for statistics. We are always included as part of mathematics. If you think that serves us well, I must respectfully disagree. QUESTION: I can easily imagine accrediting a three- or four-person mathematics department. Thus, I was expecting to hear you say that there is nothing wrong with four people in statistics if that is the right number with respect to the number of students and the nature of the university. Can you imagine accrediting a three- to four-person statistics department? DR. THOMPSON: I can do what I do with four people. I could not do it with three. There is a minimum size staff. I can see accrediting small statistics departments. However, it is very uncomfortable because there would be no slack in terms of personnel. Every day would be crisis management. Eight people would be a nice size, I think, for a statistics department 91

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APF^DICES A: 1989 COLLOQuIU~ PRESENTERS B: COMMISSION ON PHYSICAL SCIENCES, ~~HE~AT~S, AND SOURCES 93

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