G. Rex Bryce
Brigham Young University
Journal of Statistics Education Volume 13, Number 1 (2005), www.amstat.org/publications/jse/v13n1/bryce.html
Copyright © 2005 by G. Rex Bryce, all rights reserved. This text may be freely shared among individuals, but it may not be republished in any medium without express written consent from the authors and advance notification of the editor.
Key Words: Accreditation; Curriculum guidelines; Reforms in statistical education, Undergraduate degrees
de-vel-op, v.t. 1. gradually acquire new traits or characteristics. 2. to bring out the capabilities or possibilities of. 3. bring to a more advanced or effective state.
It is clear to most who have thought about the situation that there is a need to change some of academia’s paradigms concerning the education of statisticians. Various leaders in our profession have made many proposals for change. While these proposals would clearly add value to the end product of the academic endeavor, the question of how and where to implement them is less clear. Many of the published proposals for change have related to changes in how and what we teach. It is the position of this paper that we need to address the fundamental paradigm currently used for the education of professionals in our discipline. It will require the efforts of both academia and industry to make the necessary changes a reality. Throughout this paper when the word “industry” is used it should be interpreted to mean any entity that employs statisticians, whether it is business, industry or government.
When considering the development of tomorrow’s statisticians one is more likely to think of words like educate, train, or teach, rather than develop. However, the definition of develop—to gradually acquire new traits or characteristics; to bring out the capabilities or possibilities of; to bring to a more advanced or effective state—gives one the impression of an extended process that requires a variety of initiatives. This paper suggests that those efforts will need to come from the academic community, the industrial community, our professional association, and the efforts of those individuals who are the object of that development. Some may conclude that the views expressed in this paper are somewhat radical. However, whether you agree with them or not in the end, the hope is that they will at least stimulate further thinking and discussion about the issue.
In this paper, I review a few of the recommendations for changes to statistical education that have been made by various authors and discuss the limited impact of those proposals on the current practice in statistical education. With this foundation, I examine the current paradigm for developing tomorrow’s statisticians, which is primarily focused on graduate education in statistics for those with Bachelor’s degrees in other fields. The next section proposes that we heed the calls of some of the leaders in our profession to strengthen undergraduate education in statistics to move towards a new paradigm in statistical education. An example of one successful undergraduate program is discussed. The paper concludes with a discussion of some of the stake holders that will need to step forward in order for the needed changes to occur.
In 1987 I invited Ron Snee to visit Intel and speak at a summit meeting for all of Intel’s statisticians. At that time, he was in the process of polishing his ideas on statistical thinking. While there is more than one definition of the term “statistical thinking,” the one most frequently used in a business or industrial setting (Britz, Emerling, Hare, Hoerl, and Shade, 1996) is that statistical thinking is a philosophy of learning and action that comprehends that all work is a series of interconnected processes, that variation is pervasive in all such processes, and that understanding and reducing variation are keys to improvement. Snee and others have advocated that teaching statistical thinking should be at the foundation of statistical education.
For years George Box has advocated that the scientific method with the principles of inductive and deductive reasoning are central to who we are and what we do as statisticians and must be an explicit part of the education of every statistician. He says, “The theory of statistics and the teaching of statistics ought not to be concerned only with mathematical theory or dominated by deductive thinking. The theory of statistics must also include an understanding of such basic matters as scientific method, iterative investigation, exploratory design and analysis, roles of deduction and induction, [etc.].” (Box, 1994) In his 1986 Presidential Address, Marquardt adds, “The scientific method is an inherent part of all experimental sciences. Statistics is the discipline responsible for studying the scientific method with the greatest intensity and for providing in-depth expertise to other disciplines.” (Marquardt, 1987)
Brian Joiner (1985) has been an advocate of introducing more of what we might term “soft skills” to the technically oriented discipline of statistics. He says, “We must prepare to venture far beyond our familiar statistical territory to learn new skills – interpersonal skills, team-building skills, how to plan for change, and how organizations work.”
Starting with the report of the Committee on Training of Statisticians for Industry (ASA, 1980) there have been repeated reminders of the importance of improving the communications skills of statisticians—both oral and written. For example, Kettenring (1995) says, “Statistics students must somehow learn to give an effective talk, to write a report that managers can understand, and to generally cultivate their interpersonal skills for statistical consulting and cross-disciplinary collaboration.”
There have also been calls to change what we teach in the technical realm. For example, Snee (1993) has said, “There is a 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.” When we do teach theory John Bailar has urged us “to use big, real, important examples. … Any instructor who makes up a set of data to illustrate something—anything at all—has failed the students. If you cannot find a real example, there is something wrong with what you are trying to teach.” (Bailar, 1995)
A few authors have tried to move away from an emphasis on formal statistical theory towards a more data analytic approach especially at the introductory level, but the majority of the introductory texts used in the United States today are in their eighth or higher edition and reflect minor tweaking from the original editions rather than substantial changes to their content (Hinrichs, 2002).
One notable exception to this failure to respond to calls for change is the recent text by Hoerl and Snee (2002). Marquardt (1987) says that the single most important change that is needed in statistical education is to the first introductory course. He goes on to say that “its focus would be to teach a system concept of the discipline of statistics in relation to the scientific method.” The Hoerl and Snee (2002) text devotes its first four chapters to developing such a system concept in the form of clearly laid out strategies for process improvement and problem solving. They include a variety of real-life case studies to motivate the strategies, but they do not get bogged down in statistical theory, methods, or computations until the student sees the big picture.
Writing textbooks to support the calls for change in statistical education is not the only pressure being placed on the academic community, however. In 1965 Gordon Moore, one of the founders of Intel, predicted that the performance of microprocessors would double approximately every 18 to 24 months (Raymond, 1994). This has become known as Moore’s Law. Surprisingly, Moore’s Law has been proven to hold over a longer period of time than, I suspect, even Gordon Moore anticipated it would. It has proven not only to be an accurate prediction of advancement in the semiconductor industry but also to have broad implications outside the semiconductor industry. The implication for statisticians, as beneficiaries of Moore’s law, is an ever-increasing capacity for innovations in data analysis. This increased computational power allows us to develop and use methods that were only dreamed of a few years ago. Software now exists, for example, that will carry the computational load in applying Bayesian methods of data analysis or generalized linear mixed model analyses. Technology has also given us the capability to automate the data collection process and thus create voluminous amounts of data (Hahn, 1989). The challenge for academia is to decide which of the many things that could be covered in our curriculum, should be included. Like every other enterprise, our resources are limited and must be used wisely.
“Although there are jobs at the BS level, . . . it is generally agreed that the MS degree is a minimum requirement for the professional statistician. There are always exceptions, but it is recommended that someone interested in statistics as a profession obtain solid foundations in science or engineering and mathematics.” (ASA, 1980)
In the context of this quote a “solid foundation in science or engineering and mathematics” means a BS degree in one of those areas. The implication of this kind of thinking is that we take a person with a BS degree in one of the proposed areas and put them into a graduate program in statistics.
Assume for the moment that a person with such a “solid foundation” is seeking a Master’s degree at a university operating on a semester system. This means that he or she will take from eight to ten three credit-hour courses to complete the normal Master’s program. However, keep in mind that this same report also calls for balance between theory and practice. While declining to list “specific content of statistics courses,” the report does include a list of topics “most often used by industrial statisticians.” If our hypothetical student were to enroll at Brigham Young University, for example, he or she would need to take a minimum of eight courses to study just over half of the topics listed in the report. In order to approach the balance between theory and practice suggested by the report one would expect to take an additional three, or more, courses in mathematical statistics. This would put the student well over the number of courses normally required to complete the Master’s degree. Of course, if the MS degree is a consolation prize for failure to make it into the Ph.D. program, the number of courses in mathematical statistics would probably be greater, thus reducing the number of methodology courses the student could take.
One then must ask which technical courses we are to give up to provide courses to teach “team-building skills, how to plan for change, and how organizations work,” (Joiner, 1985) or how “to give an effective talk, [how] to write a report that managers can understand, and [how] to generally cultivate their interpersonal skills for statistical consulting and cross-disciplinary collaboration.” (Kettenring, 1995) And where can we include courses in modern computational statistics to take advantage of the advances due to Moore’s Law? Another important issue is identifying faculty who are qualified to teach these kinds of skills.
These are difficult choices and no single choice on these issues is going to please every constituency. However, the implication for the amount of time that is available to “place greater emphasis on data collection, understanding and modeling variation, graphical display of data, design of experiments, surveys, problem solving, and process improvement” (Snee, 1993) will not be great for the typical Master’s recipient under the current paradigm of statistical education.
Although I haven’t made a thorough study of the question, I suspect there are few if any other disciplines in which one can pursue a Master’s degree without considerably more prerequisite courses than would be required in most statistics programs. My own experience in trying to pursue a Master’s in mechanical engineering after completing many engineering core courses before I switched my undergraduate major to mathematics, suggests to me that getting a Master’s degree in any other scientific field is best done with a BS in that same field. If you do not have that BS you are likely to double the time to completion of the MS degree.
Under our current paradigm of statistical education I do not believe that anyone will be happy with the compromises that will have to be made. I am reminded of my experiences working with ABET -- The Accreditation Board for Engineering and Technology. Led by Neil Ulmann and others, several of us worked very hard getting the right people together to discuss the inclusion of statistics in the undergraduate education of engineers. At a meeting held in 1989 Craig Barrett, CEO of Intel said, “instructors of statistics courses do not teach applied statistics, instructors of engineering courses do not teach statistics, engineering professors are not statistically literate, and [industry] is not happy.” (Fong, 1989) ABET finally adopted a recommendation that the accreditation requirements for engineering and technology would include a requirement for some statistical training. When the recommendation had the force of “law,” at least in the sense that if you wanted to be accredited you had to comply, then changes began to happen across the nation. Of course, the way the requirements were implemented varied from university to university, but the existence of such requirements have and will continue to produce some significant changes in engineering education. I will come back to this idea later.
By the time of his 1986 Presidential address Marquardt (1987) had clearly changed his mind about the utility of a bachelor’s degree in statistics. After pointing out that the “marketing” program in statistics was based on producing “a small number of people trained at the graduate level,” he goes on to say:
“What is different about the marketing approach in such fields as engineering or business compared with statistics? The biggest single thing that is different is that these fields have created a large bachelor’s-level base of people. What does this accomplish?
- The field becomes legitimized and visible as a career and as a category of people available to be hired into standard jobs.
- Employers become aware of the field.
- The brightest and best from the bachelor’s program become available as candidates for graduate training.
- The field can grow in stature and importance in society because there can be enough statisticians to achieve visibility and influence as a discipline.”
“… the concept that applied statisticians must always be trained or experienced in another field before studying statistics, and the concept that statistics is inherently a graduate-level subject are inventions that fitted the era when widespread application of statistical methodology was only a futuristic vision, occurring at the dawn of the computer age in a period of heavy research funding. All of these characteristics have gradually changed. It is time to adopt some new cultural norms that are more in tune with the external and internal problems that statistics now faces.” (Emphasis added.)
It is clear from the context of the last sentence that Marquardt meant that to be fully recognized as a discipline in the way that engineering and business are, we must develop viable baccalaureate programs in statistics.
In his paper entitled “The Visibility of Statistics as a Discipline,” Minton (1983) reported that the Council of Graduate Schools declared a “discipline” to exist when it “has achieved (a) A theory and body of literature; (b) A significant number of professionals working essentially in the field; (c) More than a few professional journals regularly publishing new advances in the subject; and (d) A significant market demand for its services.” Clearly, statistics has satisfied the requirements of this definition for over 50 years. However, Minton (1983) points out, “the name Statistics does not appear in either the list of undergraduate departments or that of undergraduate majors from which entering students choose. Statistics is thus not seen as a discipline, nor as a possible career. … Statistics has completely missed the opportunities for recruitment that occur during freshman college enrollment. The availability of undergraduate degree programs would remedy this.”
Can it be done? If we build it, will they come? The BYU experience answers emphatic yeses to these questions. Unfortunately, we are one of the few departments in the nation that has a viable undergraduate program. In 1995 we invited Ronald Hocking to return for a second external review of our department. He and Ronald Iman, then president of the ASA, spent two days interviewing faculty, students, and administrators at BYU. In his report to the Dean of our college Hocking (1995) commented that when he came to BYU in 1980 he “was not enthusiastic about the potential success of this or any undergraduate program in statistics.” He went on to say that we had “succeeded beyond [his] highest expectations.” He concluded his comments by saying, “… the BYU undergraduate program in statistics is now one of the largest in the country. With regard to the breadth and depth of the course work, the quality of the teaching and the quality of the students, most would agree that it is also the best undergraduate program in the country.”
I share these things only to demonstrate what can be done. When I compare the list of topics that the ASA Committee on Training Statisticians for Industry (ASA, 1980) listed in their report as being most often used by industrial statisticians, eleven of those nineteen topics are covered in our undergraduate courses, another three in our graduate courses and all but one of the remainder is at least touched on in one or more other courses in our department. Depending on which of our six undergraduate emphases a student chooses, she or he can graduate with as many as fifteen statistics courses or 45 credit hours in statistics in addition to mathematics requirements. With this understanding it is easy to see why Iman (1995), in his external review report, would say, “Students completing their B.S. degree in statistics at BYU have the equivalent of what would serve as a Master's degree at many institutions.” In fact, many of our bachelor’s students have more course work than most Master’s degrees require.
We are able to offer such a rich program at the baccalaureate level because we have approximately 135 to 150 undergraduate majors with approximately 30 BS degrees granted each year. To maintain the program at this size, we take full advantage of the opportunity to recruit incoming freshmen with good math and communications skills. The top 25% or so of our BS graduates will go on to graduate school either at BYU for an MS degree (we do not offer a Ph.D.), or elsewhere to purse a doctorate. Those students who pursue the Master’s degree at BYU will take an additional 24 to 27 credit hours of statistics to complete their degrees. Thus a student graduating with both the BS and MS from BYU will take as many as 70 credit hours of statistics. A brief look at graduate catalogues of several institutions that offer the Ph.D. in statistics shows that course requirements vary in the neighborhood of from 54 to 59 credit hours. Of course those hours will include a more intensive grounding in mathematics and mathematical statistics than would be obtained in a combination of a Bachelor’s and Master’s degree from BYU. Again it is apparent why in his external review report Hocking (1995) could state that, “The level and number of courses required for the MS degree comes close to those required at many schools for a Ph.D.”
An examination of the listing of programs offering Bachelor’s degrees in statistics in January 2004 on the ASA home page (see www.amstat.org/education/SODS/) shows that a median of five degrees per program were awarded. Of the 97 programs offering undergraduate degrees, 76% awarded less than ten degrees and 95% awarded less than 20 degrees. Forty-three percent of these degrees were awarded through departments of mathematics having a statistics program as a subset of the department. One has to wonder whether such small programs can afford to provide the variety of courses that would prepare students to function as statisticians. In fact, we might well ask what does a Bachelor’s degree in statistics really mean in terms of the exposure to theory and methods of the discipline. Unfortunately, there is a substantial amount of variability in the curricula of the various bachelors’ programs.
The American Statistical Association has provided a means to reduce some of the variability in undergraduate level programs through the approval and publication of Curriculum Guidelines for Undergraduate Programs in Statistical Science (AmStat News, 2001). The development of these guidelines was the joint effort of a large number of individuals from a variety of organizations representing large and small educational institutions as well as representatives from industry and government. Bryce (2002) summarizes the activities leading up to the approval of the guidelines and provides a brief summary of six papers that were published from a symposium in which a variety of issues related to undergraduate education were discussed. Bryce, Gould, Notz, and Peck (2001) gives a detailed discussion of the guidelines as applied to Bachelor of Science degrees and Tarpey, Acuna, Cobb, and De Veaux (2002) discuss their application to Bachelor of Arts degrees.
If the quality movement has taught us nothing else, it has taught us that those products with the most consistency are generally the best products. The variation from program to program, as well as the lack of a standard against which to judge a program, are in all likelihood contributing factors to the reason employers are not advertising for Bachelor’s level statisticians. When that is combined with a paradigm that says that the only “real” statistician is one who holds a Bachelor’s degree in another field and a graduate degree in statistics, it is no wonder that the employers advertise for MS and Ph.D.’s, even for those jobs that could be filled by a well qualified Bachelor’s degree holder from a solid program. For example, I received a notice from AT&T advertising four different positions. One of them was described as “Support the internal analytic community with statistical programming expertise and data acquisition and management methodologies”—a job that is clearly within the capabilities of a well trained Bachelor’s degree recipient. Yet, the notice asked for Master’s or PhD’s in statistics. A related problem is the difficulty of finding good internship opportunities for Bachelor’s level students, even though between their junior and senior years many of them will have more statistical training than students from pure graduate programs.
What will be required for such a fundamental change to take place? I believe it will require the cooperation of our professional association, industrial statisticians, and the academic community. The American Statistical Association has taken the first step by approving the undergraduate curriculum guidelines. However, until we have an accrediting body such as the Accreditation Board for Engineering and Technology (ABET) there will be little incentive for institutions to adopt them. An Accreditation Board for Statistical Education (ABSE) could help to reduce the variability in Bachelor’s degree programs. While it would not mandate the exact nature of baccalaureate programs, it would allow an employer hiring someone from an accredited institution to know what to expect from such an individual. Issues such as the amount of emphasis on the scientific method, statistical thinking, interpersonal skills, communications skills, etc., could be decided by the individual departments, but the board would recommend the topics to be addressed. We have a good model for such a board in ABET.
I believe that industrial statisticians will have the most important role in creating the new paradigm. First, they need to work with their Human Resources Departments to define career ladders for statisticians that include opportunities for Bachelor’s level people. When I was at Intel, with the responsibility to develop a statistical support group, one of my first efforts was to develop such a career ladder. The existence of that kind of recognition of our discipline made a tremendous difference in our ability to recruit qualified people and in how we were viewed within the company. Second, I believe industrial statisticians must work with their recruiting people and others in their companies to get them to advertise appropriate job opportunities, both permanent employment and internships, for BS-level statisticians. Advertisements in the AmStat news, for example, will alert academic departments that there is a demand out there for Bachelor’s level statisticians. Third, industrial statisticians need to give feedback to academic departments as to their expectations for these graduates. At BYU we have developed an internship program that we feel keeps us indirectly informed about industry needs, but we are always interested in direct feedback. Finally, if industrial statisticians do not demand that an accreditation board be created and hire only graduates from accredited institutions it is unlikely to happen. After all, would they purchase any other product without a reasonable set of specifications?
Unfortunately, I suspect that these ideas will be about as popular in the academic community as a skunk at a picnic. However, I believe Marquardt (1987) was right when he said, “our current marketing approach in the field of statistics is dooming us to perpetual status as ‘hangers-on’ to the mainstream of society.” First, I believe that academia must adopt a new paradigm for statistical education that fosters a Bachelor’s level education as an appropriate, but not unique, entrance into the statistics profession. Second, as painful as it may be for academics to accept any direction from outside their world, I believe that for the long term good and recognition of our discipline we must develop an accreditation board for statistical education. Clearly, the best strategy for academics would be to take the initiative in creating such a board. However, I believe it would be a mistake, both on the part of industry and academia, for such a board to fail to include the voice of a broad range of customers of academia’s principal products. Finally, we must all remember, that change happens, but improvement comes through hard work and careful planning.
By the united collaborative effort of the American Statistical Association, industrial statisticians, and the academic community, I believe that we can work together in developing tomorrow’s statisticians. They can “gradually acquire new traits or characteristics” over an extended and fuller academic career including the knowledge and skills that have been advocated by various groups and individuals over the past twenty years. Such extended effort will “bring out the capabilities or possibilities” that they never knew they had, and ultimately “bring [them] to a more advanced or effective state.”
ASA (1980), “Preparing Statisticians for Careers in Industry: Report of the ASA Section on Statistical Education Committee on Training of Statisticians for Industry,” The American Statistician, 34, 65-75.
Bailar, J. C. (1995), “A Larger Perspective,” The American Statistician, 49, 10-11.
Boen, J. R., and Zahn, D. A. (1982), The Human Side of Statistical Consulting, Belmont, California: Wadsworth.
Box, G. E. P. (1994), “Statistics and Quality Improvement,” Journal of the Royal Statistical Society, Series A, 157, 209-229.
Britz, G., Emerling, D., Hare, L., Hoerl, R., and Shade, J. (1996), “Statistical Thinking.” Special Publication, Statistics Division, American Society for Quality, Spring, 1996.
Bryce, G. Rex, Gould, R., Notz, W. I., and Peck, R. L. (2001), “Curriculum Guidelines for Bachelor of Science Degrees in Statistical Science,” The American Statistician, 55, 7.
Bryce, G. Rex (2002), “Undergraduate Statistics Education: An Introduction and Review of Selected Literature,” Journal of Statistics Education [Online], 10 (2). (www.amstat.org/publications/jse/v10n2/bryce.html)
Fong, J. T. (1989), “Engineers’ Statistical Literacy is Key to U.S. Competitiveness,” ASME News, 9 (5), American Society of Mechanical Engineers
Hahn, G. J. (1989), “Statistics-Aided Manufacturing: A Look Into the Future,” The American Statistician, 43, 74-79.
Hinrichs, C. (2002), Personal correspondence.
Hocking, R. R. (1995), External Review Report on the Department of Statistics, Brigham Young University, February 1995.
Hoerl, R. W. and Snee, R. D. (2002), Statistical Thinking: Improving Business Processes, Pacific Grove, California: Duxbury.
Iman, R. L. (1995), External Review Report on the Department of Statistics, Brigham Young University, February 1995.
Joiner, B. L. (1985), “The Key Role of Statisticians in the Transformation of North American Industry,” The American Statistician, 39, 224- 227.
Kettenring, J. R. (1995), “What Industry Needs,” The American Statistician, 49, 2-4.
Marquardt, D. W. (1980), “External Review Report on the Department of Statistics, Brigham Young University,” 1-15.
Marquardt, D. W. (1987), “The Importance of Statisticians,” Journal of the American Statistical Association, 82, 1-7.
Minton, P. D. (1983), “The Visibility of Statistics as a Discipline,” The American Statistician, 37, 284-289.
Raymond, E. S. (1994), The New Hacker’s Dictionary, 2nd Edition, Cambridge, Massachusetts: MIT Press.
Snee, Ronald D. (1993), “What’s Missing in Statistical Education?” The American Statistician, 47, 149-153.
Tarpey, T., Acuna, C., Cobb, G., and De Veaux, R. (2002), “Curriculum Guidelines for Bachelor of Arts Degrees in Statistical Science.” Journal of Statistics Education [Online], 10 (2). (www.amstat.org/publications/jse/v10n2/tarpey.html)
G. Rex Bryce
College of Physical and Mathematical Sciences
Brigham Young University
Provo, Utah 84602
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