MARY GRAY: While I found the discussion of the students' experiences in India to be interesting, university education really is a very delicate issue from an international perspective. In particular, most statistics departments in this country are training a very large number of people who will be working internationally. Unless we believe that we are just exploiting a brain drain of statisticians from around the world, the people that we are training are going to go back and work in quite a different atmosphere, and there has not really been any consideration given to that. What the customer needs when the customer is Bellcore may be quite different from what the customer needs in some other countries of the world, particularly the countries of the south. Notwithstanding the particular experience described in India, it is my experience that the split between the theoretical and the applied is much greater in most countries — particularly countries of the south — than it is here. That is to say, it is the mathematics department that does theoretical mathematics and statistics, and then the so-called statistics is done by people in all kinds of fields with very little statistical training. There generally is very little thought given to the use of statistics in public policy. In talking about international perspectives, there needs to be more attention given to what we are doing about training people to work internationally.

S. RAO JAMMALAMADAKA: The split between the theoretical and applied statistics exists everywhere, to varying degrees. As I noted, in some places such as Sweden, it is even formalized with separate departments for mathematical statistics and statistics. In many countries, such as Japan and Australia (for instance, at the Australian National University in Canberra, where I taught), the statistics department is located in the Faculty of Economics and Commerce. In my own university, although we have a department of statistics, there are people in psychology and sociology, who are not trained in statistics, who teach their own statistics courses. This also happens at the University of California at Berkeley, as it does on many U.S. campuses. I do not think it is necessarily bad. There are some courses with large substantive content that the faculty in those other departments may be able to handle better — as long as they know when to send their students in our direction. For instance, in Sweden, the industrial engineering department sent their engineers to the mathematics department for a course that I taught on reliability, quality control, Taguchi methods, and so on. Based on a limited sample, my general conclusion is that there is no detectable "international" (as opposed to the "intranational") trend regarding the theory-versus-applied split.

CHAND MIDHA: I have heard many comments from people in statistics departments. Ours is a department of mathematical sciences that offers a master's degree, and there are many similar departments. The problem is that, although we have offered some good service courses, many of the other university departments are trying to offer different courses, some of which are being taught by so-called statisticians. We get little chance to develop any interests for these students so that they might come and consider going further in statistics. Since yesterday's session, I have had the feeling that more students should have more exposure to other things,

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Discussion
MARY GRAY: While I found the discussion of the students' experiences in India to be interesting, university education really is a very delicate issue from an international perspective. In particular, most statistics departments in this country are training a very large number of people who will be working internationally. Unless we believe that we are just exploiting a brain drain of statisticians from around the world, the people that we are training are going to go back and work in quite a different atmosphere, and there has not really been any consideration given to that. What the customer needs when the customer is Bellcore may be quite different from what the customer needs in some other countries of the world, particularly the countries of the south. Notwithstanding the particular experience described in India, it is my experience that the split between the theoretical and the applied is much greater in most countries — particularly countries of the south — than it is here. That is to say, it is the mathematics department that does theoretical mathematics and statistics, and then the so-called statistics is done by people in all kinds of fields with very little statistical training. There generally is very little thought given to the use of statistics in public policy. In talking about international perspectives, there needs to be more attention given to what we are doing about training people to work internationally.
S. RAO JAMMALAMADAKA: The split between the theoretical and applied statistics exists everywhere, to varying degrees. As I noted, in some places such as Sweden, it is even formalized with separate departments for mathematical statistics and statistics. In many countries, such as Japan and Australia (for instance, at the Australian National University in Canberra, where I taught), the statistics department is located in the Faculty of Economics and Commerce. In my own university, although we have a department of statistics, there are people in psychology and sociology, who are not trained in statistics, who teach their own statistics courses. This also happens at the University of California at Berkeley, as it does on many U.S. campuses. I do not think it is necessarily bad. There are some courses with large substantive content that the faculty in those other departments may be able to handle better — as long as they know when to send their students in our direction. For instance, in Sweden, the industrial engineering department sent their engineers to the mathematics department for a course that I taught on reliability, quality control, Taguchi methods, and so on. Based on a limited sample, my general conclusion is that there is no detectable "international" (as opposed to the "intranational") trend regarding the theory-versus-applied split.
CHAND MIDHA: I have heard many comments from people in statistics departments. Ours is a department of mathematical sciences that offers a master's degree, and there are many similar departments. The problem is that, although we have offered some good service courses, many of the other university departments are trying to offer different courses, some of which are being taught by so-called statisticians. We get little chance to develop any interests for these students so that they might come and consider going further in statistics. Since yesterday's session, I have had the feeling that more students should have more exposure to other things,

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should have double majors, and so on. I feel that if we attach some importance to these required courses and people who have other things wind up taking minors in other subjects, we may lose many of our statistics students to other areas.
JOHN TUCKER: That sort of problem is not particular to statistics. A report in the Notices of the American Mathematical Society (April 1990, pp. 408-411) pointed out that in this nation more of the advanced undergraduate mathematics instruction is being done in non-mathematics departments than is being done in mathematics departments, in terms of the total number of students taking those kinds of courses.
FIENBERG: I used to say things similar to what Chand Midha's comment suggests, but over time I have taken a somewhat different attitude and perhaps have provoked people as a result.
You have to be careful when you allow statistics courses to be taught in other departments. Yet often they are taught by people whose qualifications to do real statistics may be superior to those of people in the mathematics department or even in the statistics department, and the challenge that statisticians face on campus is how to draw those people into interaction with the students whom we want to learn statistics in a way that is not in competition with the elementary course. Rather, a distinction needs to be made between those people who are doing quality statistical analysis wherever they are based, and those people who are perhaps not qualified to do that kind of statistics instruction.
EDDY: I want to amiably disagree with my colleague. In my limited experience, the statistics courses given by other departments tend to use statistics as a collection of procedures and tools for, as someone said yesterday, feeding on particular problems: "If all you have is a hammer, everything looks like a nail." So I disagree rather vehemently with Steve Fienberg's perspective.
SNELL: I want to amiably disagree rather vehemently with Bill Eddy's view. Certain things in Dartmouth are exactly what Chand Midha is describing. The fact is that social scientists and economists long ago learned to analyze data that arises in their discipline. Having thought about the problem of how well statistics is taught in other departments, I believe they have for years been using exactly the kind of techniques everybody has been advocating, namely, motivating the theory from the application setting.
BAILAR: Perhaps we can all agree that these people in what we might think of as the hinterlands, the outlying departments, are at least perceived as offering better training than that which people who get into the statistics department are perceived as obtaining. And maybe the first task is to deal with that perception, and so to produce a greater tendency in students toward taking the courses in the statistics departments that have the solid core of understanding we believe underlies this whole enterprise.
KETTENRING: I do not really care where they are trained. What I care about is what they can do when they are on the job. In a larger sense, we really have not done a very good job in discussing the need for radical changes, and so how are we going to know if we are succeeding when we start making needed changes? We need to agree upon or have a dialogue about some measures of success or failure, because I think we can get blocked out here discussing who can teach what.
I have some criteria from my industrial perspective that I would use to judge what is being produced. I would look at the titles of the PhD theses of the statistics students who

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graduated from your departments in the last year and a half, and ask, "Why do this research? What is its impact?" I might even try to read some of them to see if I could understand them. I have my own private ways of trying to assess such things, and in the context of these discussions of changes, I believe we need to develop criteria for monitoring how the statistical community is doing in making needed changes, so as to avoid just talking.
RONALD THISTED: As to other departments offering introductory courses or even advanced courses in statistics, at the University of Chicago, we do assess the effectiveness of the statistics program.
In our department, we see other departments offering statistics courses as partly a problem and partly an opportunity. We believe that if other departments' students shy away from our courses, then perhaps we are doing something wrong and perhaps their courses are meeting a need that our courses do not. So we try to make it our business to find out what needs those courses are meeting, and if we think we can do it better — and usually we do — then we try to do two things. First, we try to change our courses to do a better job of meeting those needs, and second, we try to do a better job of communicating to our colleagues in other departments just what it is we really do as opposed to what they think we do in the courses we teach.
GRAY: Going back to the original question that started this line of discussion, if you have people teaching statistics courses in other departments, one practical suggestion is to invite them to teach some sections of the courses in your department. American University has a regulation that all the elementary statistics for undergraduates must be taught in the mathematics department, but people from psychology or economics are brought in to teach sections of the course because there are many, many sections of it. This approach also has the advantage of providing some opportunities for people to do collaborative work because they have to talk about what they are teaching.
We convinced the university administration to let this be done simply as a more economical way to do it, because if all the sections are under the control of one department, enrollments can be better managed to ensure fully enrolled courses that cost less money. Given that most universities are now worrying about costs, that is a very good reason for getting started. But I think an equally important benefit is that it is much more productive, especially in bringing in people who are doing substantial statistics, and who in many cases do have very good training and very good ideas, to work with the statistics department.
BAILAR: There are a couple of things that I am not hearing about here that might in time become pretty important. One is to explicitly acknowledge that statisticians cannot be all things to all people, and statistics graduates cannot be all things to all people. There is a need for specialization. Some of that is already recognized, as exemplified by biostatistics and by the fact that potential statisticians do spin off to other departments. But perhaps more explicit thought should be given to what kind of specialization in graduate training programs would be appropriate.
The second thing I am not hearing is comments of the form, "How can I go back and make this change?" I have the feeling that many of us think, in effect, "Gee, things are going pretty well now; it is everybody else that needs to change." This leads me to suggest, although with hesitation because I am not a CATS member, that — if they have not already planned to do

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this — perhaps CATS would develop a panel on model curricula embodying the changes discussed here that people could examine and adapt for their own use.
JOHN TUCKER: In fact, this symposium is viewed as a first effort in trying to instigate change, and producing model curricula is considered one thing that sometime has to be done as an ultimate outcome. And CATS is indeed an appropriate body to consider it.
LAWRENCE BROWN: This issue of what faculty with what background and attitudes are appropriate to teach statistics raises the question, Is statistics different from any other discipline in that respect? I do not believe so; I do not believe that social scientists who are teaching statistics courses have any different attitudes toward service courses. That is not a distinguishing characteristic.
BAILAR: Let us see if statisticians can be better than these others.
TUCKER: The observation of having years ago given up some rights to teaching these service courses in statistics is, again, not confined to statistics; mathematics has had the same thing happen, and it is also a matter of concern to mathematicians.
JOE WARD: I have been teaching at the University of Texas at San Antonio, after having taught at Clemson, and am spending a lot of time on what I believe disciplinary or institutional inertia is impeding. When we consider what a model curriculum would be, we must keep in mind where we are going, what our objectives are, how we are going to get there, and how we are going to know when we are there — that is, assessment. Those things need to be addressed, because if you decide to have more probability and statistics but continue teaching it the same old way and do not change to a way of teaching that incorporates computers and uses them routinely, substantive change in the results is unlikely. Unfortunately, people are generally still teaching the precomputer approaches to doing statistics. A new edition of a book may be 200 pages longer than the old one, but the book has the same form, style, and approach as the one somebody saw earlier because that is what sells. The objectives need to be looked at, and what is to be done with contemporary, real-world problems in technology must be decided. I call it the talk-down approach. Start with the problems, and then look down the microscope to see what the key issues are that you are trying to teach. This approach, I think, would eliminate a lot of the less crucial material.
ROTHMAN: Concerning the issue of teaching correct theory, all our theories are correct in some world. The problem we have to face is usefulness, predicting the particular situation. I do not believe the statisticians are closer to that truth than some other people are, whatever their department may be. In fact, a lot of what statisticians do is simply not useful. There are confidence intervals that allegedly work 95% of the time in the abstract world and work only 50% of the time in this world. Regarding the issue of bias, there is no question that it is a substantial fact of life with which we must deal. Statisticians are not closer to a solution than their colleagues in other fields. Statisticians need to pay attention to what those colleagues have to say.
DONALD MYERS: Stemming from what we heard on cooperative learning yesterday, should we begin to talk about cooperative rewards? To some extent, what happens to the statistics department, the mathematics department, or any other academic department is based on the reward system. The particular direction that statistics takes, the courses that are offered, and which are emphasized is largely a matter of how we are rewarded by the university. At present that reward tends to be bestowed on the basis of individual activity. Teaching, generally

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speaking, is not an individual activity; how successful you are depends on how successful your predecessor was — that is, the person who taught the students before they got to your course — and you in turn affect the next instructor. The reward system does not recognize that, nor does the way in which research money is given out recognize that.
A second point has to do with remarks that Phillip Ross made yesterday on the problem of a manager facing a decision that had to be made on the basis of imperfect information. The manager does not happen to be a statistician. He would give the statistical analysts two months to do a statistical analysis on the problem. The manager in a sense did not care what the statistics looked like. But a decision had to be made, and the decision was selecting from two different possibilities, one of which involved a $40 million investment and the other a $60 million investment. In one sense they had a relatively small amount of data, yet in another sense they had a relatively large amount of data. They also had something called soft data, namely, the expert knowledge of certain geologists, and they had to incorporate that initial information in the statistical analysis. That is a perspective I do not think I have heard in any of the comments about how to incorporate, for lack of a better word, the expert knowledge of people into the statistical analysis.
TUCKER: That situation is addressed in the 1992 CATS report entitled Combining Information that was originally published by National Academy Press, and that the American Statistical Association has just republished as Volume 1 of ASA's new Contemporary Statistics series. The report also addresses issues that arise in settings such as the one that confronts EMAP, as described yesterday by Phillip Ross.