Teaching Statistics to Engineers: An Innovative Pedagogical Experience

R. Romero, A. Ferrer, C. Capilla, L. Zunica,
S. Balasch, V. Serra, and R. Alcover
Polytechnic University of Valencia

Journal of Statistics Education v.3, n.1 (1995)

Copyright (c) 1995 by R. Romero, A. Ferrer, C. Capilla, L. Zunica, S. Balasch, V. Serra, and R. Alcover, 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: Statistics education; Total Quality University; Educational quality improvement; Active learning.


In recent years, the growing consciousness of the importance of statistics in the training of engineers has been accompanied in the western world by an increasing dissatisfaction with the teaching of statistics in universities. Within the framework of the Educational Innovation Project (PIE) of the Polytechnic University of Valencia, a group of teachers in the Department of Statistics introduced an innovation project beginning in 1989. This project has entailed a complete restructuring of the syllabus, as well as the teaching methodology. In this paper we explain different aspects of this project, emphasizing the important role of computer resources and the satisfactory results obtained.

1. The Present Demand for Statistical Knowledge

1 During the last fifteen years there has been a considerable change in the world economic situation. The most important western companies have begun to incorporate deep changes in their management philosophies. These philosophies stress the systematic use of statistical methods for continual improvement.

2 This has led to a great demand for statistical knowledge on the part of engineers and technicians of western industry. Intensive statistical courses are included in all the engineering curricula of Spanish universities. In our opinion, the results in the majority of these courses are not satisfactory; nevertheless, the problem is not exclusive to our country. Several authors have also described the need for specific changes in statistics education in the United States and Canada.

3 "Although statistics departments in universities are now commonplace, there continues to be a severe shortage of statisticians competent to deal with real problems. But such are needed" (Box 1976, p. 798).
4 "We have historically done a very poor job of teaching statistics.... It has failed year after year, semester after semester and we still persist in teaching it more or less the same way we have been teaching it for 40 years! ... This is not the real world.... The problem is compounded because most people who teach statistics have never practiced statistics" (Joiner 1986, pp. 30-31).
5 "For too long we in the statistics profession have tolerated poor statistics teaching, which produces courses that are often rated as the worst course or the most useless course that graduates in other fields claim they have ever taken. We too often teach what appears to the students a collection of unrelated methods illustrated by examples taken from coin-tossing, card-playing and dice-rolling. And then we expect the students to be able to translate this wide variety of methods with simple gambling examples to complex industrial problems involving the application of a large number of methods" (Godfrey 1986, p. 36).

6 The most common criticism of the teaching of statistics in the United States is that it is too academic in focus, excessively theoretical, and divorced from the real problems that can appear in the industrial and business world. We think that these criticisms also describe the Spanish situation.

7 "Statistics, I believe, is best defined as the science and art of obtaining and analyzing data. The key word here is data. The focus of our subject is data, not random variation ... nor is our focus probability" (Joiner 1986, p. 30).
8 "Many leading statisticians have realized this for years. I heard very clearly at the Hogg Conference last year a strong emphasis on case studies and real problems.... I think it is very important to carry this philosophy to every service course that statisticians teach. We need to show people in every field how statistics can be used to help them do their job better.... We can make remarkable progress towards this goal by combining a new dedication to excellence in teaching using real-world case studies and examples and new statistical software that makes even sophisticated methods understandable and easy-to-use" (Godfrey 1986, p. 36).

9 The report of the ASA Section on Statistical Education Committee on Training of Statisticians for Industry (1980) strongly emphasizes the need to develop students' practical skills and points out that many of the programs in the United States fail to do so. Garfield (1993, par. 13) emphasizes the importance of working cooperatively.

"... businesses are increasingly looking for employees who are able to work collaboratively on projects and to solve problems as a team."

10 These opinions contrast with the existing situation in the teaching of statistics in Spanish universities (Pena, Prat, and Romero 1990). In some cases students finish a statistics course without having worked with real data.

2. An Education Innovation Project (PIE) at the Polytechnic University

11 The Polytechnic University of Valencia currently has 14 institutions, 1,300 teachers, and 25,000 students. The Educational Innovation Project (PIE) of this University was initiated in 1989 out of the conviction that the results of the teaching/learning process were unsatisfactory. Some of the problems were a consequence of overly theoretical teaching with too little experimental training.

12 The project is managed and coordinated by the Teaching Quality Control Commission, made up of a member of the Rectorship, four teachers, and three students, with the technical and pedagogical support of experts. The main purposes of this Commission are the approval, financing, and control of Teaching Innovation Projects for every subject.

13 The growth of the PIE in our University during its first three years of application is summarized in Table 1. As shown, more than 20% of teachers, 117 subjects, and over 15,000 students have been involved in the new methodological approach.

Table 1:  Number of Institutions, Departments, Subjects, 
     Teachers, Scholarship Holders and Students Involved in the  
         Insti-                              Scholar-
  Year  tutions  Depts.  Subject  Teachers    ships   Students
  89/90     11      20       51       170       17       6235
  90/91     11      31      100       250       54       9099
  91/92     14      29      117       287       75       15650

Source:  Proyectos de Innovacion Docente (1993), Technical
Report SPUPV-93.2018, Polytechnic University of Valencia,   

14 According to the guidelines drawn in the PIE, restructuring of teaching methodology and the syllabus must be based on the following considerations.

3. Teaching Innovation Project for Statistics

3.1 Introduction

15 Within this framework, a group of teachers from the Department of Statistics implemented a pedagogical innovation plan for statistics teaching in the School of Agricultural Engineering during the academic year 1989-1990. This implied a complete restructuring of the syllabus and teaching methodology. The number of students involved during this year was 180.

16 In the light of very positive results, this innovation project was introduced in the School of Computer Science during 1990-1991; 620 fourth-year students per year have been involved.

3.2 Objectives

17 Basic knowledge is important, but not more important than creating in the student a positive attitude towards statistical methods. We must convince students of the great value of these methods as tools for data analysis and decision-making in real problems that will arise in their future professional work. The only way to succeed in this is through the formulation and solution of real, or at least realistic, problems of direct interest to students. This must be done using the scientific method and sharing the teacher's experience in real projects.

18 To encourage the students' active participation, we have reduced the time spent in lecture classes and increased individual work and discussion. The role of the teacher has changed from that of "source of information" to "facilitator of learning" (Garfield 1993).

19 Today, computers give us a chance to analyze real data more efficiently than we formerly could; therefore, it is essential to integrate suitable statistical software into the teaching of statistics. Students should carry out laboratory practical tasks as an essential part of their learning process.

20 All of this cannot be accomplished without a thorough reorganization of the syllabus and teaching methodology, to emphasize the great value of statistical methods as tools for improving the quality of real processes. "The level of theory is dictated by what is needed to understand the statistical methodology that is useful in practice..." (Committee on Training of Statisticians for Careers in Industry 1980, p. 68).

21 Finally, we want students "to improve their ability to communicate statistical information in oral and written form, to improve interaction skills and to appreciate the fact that in real life an answer must (usually) be found, however imperfect" (Anderson and Loynes 1987, p. 21).

3.3 Course Syllabus

22 Our personal experience with training and consulting work in numerous companies has convinced us that every engineer needs a good practical knowledge of multiple regression, analysis of variance, and design of experiments. Many expert committees have stated a similar opinion, including the participants in a 1984 conference on statistical education for engineers (Hogg 1985) and ABET (Accreditation Board for Engineering and Technology) in a 1989 conference on statistics and probability in the training of engineers.

23 Consequently, the whole course has been reorganized to focus on these techniques. The School of Computer Science added an introduction to stochastic processes and queueing theory. The basics of probability and statistical inference are introduced only when needed to apply the mentioned techniques. Concepts such as Type I and Type II errors and confidence intervals are explained when they are required in the development of statistical models.

24 In spite of time limitations, we include in our syllabus advanced topics such as orthogonal contrasts in analysis of variance, dummy variables in multiple regression models, and fractional factorial designs (factors at two or three levels). These subjects are scarcely taught in Spanish universities, and we want to emphasize that they are frequently requested by industry for inclusion in advanced statistical training.

25 Table 2 shows the relative importance of the different statistical methods included in our syllabus in comparison to the course proposed at the 1984 conference on the statistical education of engineers (Hogg 1985).

Table 2:  Relative Importance (Percentage of Assigned Time)
                 of Statistical Methods in Syllabus

  PUV:  Polytechnic University of Valencia
  Task Force:  "Statistical Education for Engineers:  
                An Initial Task Force Report" (Hogg 1985)

      Subject                 PUV  Task Force
      Descriptive Statistics   16      10
      Probability              16     17.5
      Stochastic Processes     16       0
      Statistical Inference    12     17.5
      Design of Experiments    32      25
      Regression Models        8       10
      Reliability              0       10
      Quality Control          0       10

26 The table shows that the course we are teaching is very similar to that recommended by the task force report. The only differences lie in quality control, reliability, and stochastic processes. Although we are aware of their importance in the training of engineers, we do not teach quality control and reliability. A time limitation has prevented us from including them in the statistics course until now. On the other hand, an introduction to stochastic processes is very important for computer science engineers as a prerequisite for other subjects in their curriculum.

3.4 Course Organization

27 Approximately 800 students are involved in this project per year; there are 90 students in each class. The working team consists of seven teachers (the authors of this paper) who are members of the Statistics and Operations Research Department of the Polytechnic University. Our backgrounds and research activities mainly concern statistics applied to engineering and consulting.

28 The student-to-teacher ratio in the project is 115 to 1. Teaching loads vary from six to twelve hours per week, although we have tried to give each member of the team an eight hour per week teaching load. We think that the optimum teaching load and student-to-teacher ratio are lower than the ones we have. Teaching load might have been a limiting factor in the project; a lower load allows more student contact, which increases students' motivation towards the subject and their active participation in the teaching/learning process.

29 In the Agricultural Engineering School the subject is taught five hours a week for one semester. In the Computer Science School (CSS) the subject is taught four hours a week for two consecutive semesters. In both cases, all class hours take place on the same day of the week and are divided into three types of sessions.

30 The first session lasts two and a half hours (two hours in the CSS) and consists of explanation by the teacher and individual study by the students. The teacher explains the basics of each educational unit, relating them to the acquired knowledge and motivating the need to learn new concepts.

31 The basic methodology used is the study of a real problem, drawn from the areas of the students' interest and the teacher's experience, which stimulates the active participation of the students. A personal survey filled in by the students on the first day of class provides a source of relevant data to be used in the introduction of basic statistical concepts.

32 We follow, as does Mosteller (1980), the Particular General Particular (PGP) strategy. According to this approach, the basics of each technique are illustrated using real problems (see Appendices 1 and 2). During this first session, students are arranged in groups of three to study the explained concepts. They use teaching materials that contain the educational units along with self-evaluation exercises and questions. This material has been prepared by some of the teachers involved in this project and has been published as a textbook by the Publications Service of our university (Romero and Zunica 1993).

33 The second session, lasting one hour, involves a discussion of actual problems introduced by the teacher using the STATGRAPHICS statistical package on a portable computer with a liquid crystal display screen. These are valuable tools since they easily display tables and graphs that help students to intuitively understand the theoretical concepts explained.

34 The third session lasts one and a half hours (one hour in the CSS) and takes place in a computer room with twenty PCs. (Each class is divided into two groups that occupy the laboratory during consecutive sessions.) In these laboratory classes the students work in teams of two or three. They carry out practical tasks using STATGRAPHICS to solve actual problems, some of which have already been explained in the classroom. Usually, a written report, using non-technical language, must be prepared at the end of this session. This report is evaluated and must contain the results and discussion of the analyses done to solve a problem proposed by the teacher.

35 In our opinion, more time in the computer room would be better. The number of hours devoted to this subject in the course program, the large number of students following the project (more than 800), and the available resources have forced us to limit time in the computer room.

36 We consider it extremely important to teach statistics using suitable statistical software. This reduces or even eliminates the time devoted to boring, irrelevant, and often practically impossible arithmetical calculations done by hand. Statistical software also allows students to focus on questions relevant to the exposition of a problem and on the interpretation and critical analysis of the results. Nowadays, the computer is an indispensable tool for dealing with real data and limited time. We use the software STATGRAPHICS because it is easy to use, it has very good quality graphs, and it has implemented the most common statistical methods taught during the course. In the course for the CSS we also use QSB+ (Quantitative Systems for Business Plus) to introduce Stochastic Processes.

37 To monitor and improve the quality of this project, we have formed a Quality Circle made up of the seven teachers and some of the students. The team identifies areas that affect the quality of teaching. Issues addressed have included the textbook, pace of the lectures, and laboratory classes.

3.5 Results

38 We have assessed the results obtained in the four and a half years of our experience as very positive. Four graduating classes have been trained in the most commonly applied statistical techniques in the industrial world.

39 The new teaching methodology has increased class attendance to 90%, or often even 100%, much higher than the average attendance for other subjects. These high rates are remarkable, given that the project has been introduced in two third-year classes in the School of Agriculture and seven fourth-year classes in the Computer Science School, with a total of 800 students per year. Academic results have also improved, in spite of the difficulty and complexity of the exam questions. More than 90% of the students attend the exams (65% before this project), and the pass rate is 85%.

40 The most positive result of the experience, however, is the change in student attitude towards the subject. At the end of the year the students complete a survey on every subject. Statistics obtains very good results in these opinion surveys and is considered one of the most useful subjects because of the interest it arouses and its usefulness in the engineers' future careers.

41 These improvements also increase the teacher's own motivation and satisfaction. Material resources (portable computers, LCD screens and PCs for the computer classroom) have increased.

42 New teaching materials, both for lectures in the classroom and for classes in the computer room, had to be prepared to reflect the new teaching methodology. A revised version of these materials which takes into account the experience acquired during the two first years of the project has been published as a textbook in Spanish by the Publications Service of our university. This textbook is a valuable tool in the teaching/learning process and contains the basics of the subjects included in the syllabus and the practical cases.

43 We are aware, however, that the final outcome of the teaching innovation project may not be known for ten years. Then we shall be able to verify whether our students have incorporated the statistical techniques into their knowledge and applied them to improve the quality and productivity of the processes for which they are responsible.

44 As suggested by the referees, we are planning to design a follow-up questionnaire to get results concerning student use of statistics in the work place. We believe that an assessment of this type would provide a powerful validation of these methods of teaching statistics.

4. Final Considerations

45 We realize that many difficulties may arise in implementing this new teaching approach. An important obstacle may be the extra work load for the teacher. This is especially acute during the first year, since self-teaching units and practical tasks must be prepared by the teacher in advance.

46 It is extremely important to stimulate the university-industry relationship. The consequences of this will not be merely economic, but, much more importantly, will lead teachers to get involved in real problems and gain practical experience to share with their students.

47 From the point of view of resources, it is absolutely necessary to have enough personal computers (PCs) in computer rooms where students can carry out practical tasks. We consider that these rooms must be designed to host at least twenty PCs, allowing sixty students to work at a time. With fewer computers, teaching hours increase dramatically because a large class must be split into many smaller groups.

48 We believe that the main difficulty in implementing these reforms is the lack of a suitably prepared and motivated teaching staff to promote this new methodological approach. To motivate teachers to get involved in improving the quality of the educational process, university management teams must promote a real cultural change that acknowledges and rewards efforts made toward such improvement. Unfortunately, this is neither the kind of atmosphere that academic authorities have encouraged in our country, nor what prevails in the majority of Spanish universities.

49 Finally, although the current results of our Educational Innovation Project for Statistics are highly satisfactory, the project is part of a continous quality improvement effort in the teaching/learning process. Given this, we consider that the following can be done:


We thank the editor and the three referees for helpful suggestions and comments, which led to a much improved presentation of this paper.

Appendix 1: Introducing 2^K Factorial Designs: An Example of a Practical Task

To illustrate the approach we follow in the laboratory classes, we describe an example of a real problem that the teachers have analyzed in their consulting work in a certain company. The students, working in groups, must solve this problem using STATGRAPHICS.

An experiment was done to improve the adhesive force obtained in the adhesive process of polyurethane sheets used in the inner lining of various types of equipment. The objective was to guarantee a minimum resistance of four newtons.

The two-level design factors were A, amount of glue; B, predrying temperature; C, tunnel temperature; and D, pressure. A reduction in the amount of glue, factor A, and in the tunnel temperature, factor C, would reduce costs, so those factors were economically critical. An unreplicated 2^4 full factorial design was chosen for this experiment.

Students are given the results obtained for the experiment and asked to complete the following assignment.

(a) Complete the analysis of variance including all main and interaction effects. Repeat the analysis applying the pooling technique.
(b) Interpret the results. What effects are significant at the 0.05 level? What levels of the factors maximize the mean adhesive force? What is the predicted mean adhesive force for these optimal levels of the factors? Try to find a technical interpretation of the significant interaction effect found.
(c) Determine whether there is any process variable affecting the variability of the adhesive force. Give a technical interpretation of the obtained results. What is the predicted variance of the adhesive force for the optimal levels of the factors?
(d) What is the probability that a polyurethane sheet made under the optimal conditions will have a resistance less than four newtons? If the objective is to guarantee a maximum probability of 1%, what operating conditions do you propose to make the process cheaper?

Appendix 2: Example of Multiple Linear Regression: Control of Energy Consumption in a Car Factory

To illustrate our teaching methodology, we describe the way multiple regression analysis is introduced to students. This is the last statistical technique taught in the course. At this point the students have already studied descriptive statistics, analysis of variance, and design of experiments.

In the section on descriptive statistics, the following topics (among others) have been introduced: bidimensional variables (marginal and conditional distributions), scatterplots, correlation, and simple linear regression. In this part of the course, students study multiple regression, emphasizing polynomial models, analysis considerations when using "dummy variables," and residual analysis techniques for model validation.

During the first hour of the session, the teacher presents a practical case from the teacher's consulting work: a car factory is interested in implementing a system to control daily energy consumption. Energy consumption and average temperature have been recorded daily over a period of time.

Once the regression equation of daily energy consumption on average temperature has been estimated using the statistical software STATGRAPHICS, the technical interpretation of each coefficient is addressed. Residual analysis is used to look for a non-linear relationship between these two variables. This leads to a multiple regression model (the response is curvilinear).

The students work on this new model, answering the following questions: What does the new regression function look like? What is the technical interpretation of the curvature? What is the practical meaning of the R-squared?

The next step in the analysis is to consider the effect of the day of the week (from Monday to Friday). When the model has been estimated, including "dummy variables" to account for the effect that day of the week may have on the response, the students interpret the coefficients of the model and make inferences about them using hypothesis testing.

Residual analysis is applied to detect departures from the underlying assumptions that have been made thus far in our study of regression analysis.

When the model's adequacy has been measured and validated, the students design a consumption control system. They construct a control chart for the consumption data, demonstrating the expected range of energy consumption (with 95% confidence) for a given day with a certain temperature.

Finally, the students account for an improvement in the system that is the consequence of a certain action performed on a given day. This improvement can be detected as a special cause of variability on a control chart for the residuals of the regression model. To model the effect of the action, a dummy variable is included in the regression model.


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ASA Section on Statistical Education Committee on Training of Statisticians for Industry (1980), "Preparing Statisticians for Careers in Industry," The American Statistician, 34, 65-75.

Box, G. E. P. (1976), "Science and Education," Journal of the American Statistical Association, 71, 791-799.

Garfield, J. (1993), "Teaching Statistics Using Small-Group Cooperative Learning," Journal of Statistics Education, v.1, n.1.

Godfrey, B. (1986), "Future Directions in Statistics," Report 10, Center for Quality and Productivity Improvement, University of Madison, WI, 34-39.

Hogg, R. V. (1985), "Statistical Education for Engineers: An Initial Task Force Report," The American Statistician, 39, 168-175.

Joiner, B. L. (1986), "Transformation of the American Style of Teaching Statistics," Report 10, Center for Quality and Productivity Improvement, University of Madison, WI, 30-33.

Mosteller, F. (1980), "Teaching of Statistics," The American Statistician, 34, 11-17.

Pena, D., Prat, A., and Romero, R. (1990), "La ensenanza de la Estadistica en las Escuelas Tecnicas," Estadistica Espanola, 32, 147-200.

Proyectos de Innovacion Docente (1993), Technical Report SPUPV-93.2018, Polytechnic University of Valencia, Spain.

Romero, R., Zunica, L. (1993), ESTADISTICA (Proyecto de Innovacion Educativa), SPUPV-93.637, Valencia, Spain: Polytechnic University of Valencia.

R. Romero
A. Ferrer
C. Capilla
L. Zunica
S. Balasch
V. Serra
R. Alcover

Department of Statistics
Polytechnic University of Valencia
Apartado 22012
46071 Valencia
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