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Technology in the classroom: Using PCs to teach business and economic statistics
Compurrrs Educ. Vol. 23. No 4. pp. 253-259. 1994
Pergamon
Copyright 0 1994 Elsevicr Sciena Ltd Primed in Grear &rain. All rights reserved 0360-1315194 $7.00 + 0.00
TECHNOLOGY IN THE CLASSROOM: USING PCs TO TEACH BUSINESS AND ECONOMIC STATISTICS JE~REY W. STEAGALI.and
PAUL
M.
MASON
Department of Economics, University of North Florida. 4567 St Johns Bluff Road, South. Jacksonville, FL 32221-X%5. U.S.A. [Fax: (904) 646-25941
(Received 7 March 1994: accepted 9 Seprrnrber 1994) Abstract-Rapid advances and declining prices in computer technology have made its use as a classroom tool atfordable. However, while it has been clear that diverse disciplines can eKectively utilize computer technology to improve instruction, the implementation of computer-intensive pedagogy has been hindered by the lack of knowledge about redesigning courses to employ computers electively. This paper offers insights learned in teaching business and economic statistics over a period of several years. Both tools and techniques are discussed in the hopes that the paper will serve as a blueprint for others who wish to incorporate computer use into their statistics courses.
The increased availability of inexpensive, high-quality hardware and software has already revolutionized the teaching of most academic subjects. allowing students and instructors to focus on concepts and methodologies rather than on computation and manual data manipulation. For instance, computer-based calculus classes are becoming the norm and word-processors have improved the writing-and-revision process in a variety of subjects, so that students find editing drafts of papers to be less typcwritcr-intensive. The literature concerning the USCof computers in the classroom is massive and reflects applications in business, sociology, education, engineering. psychology, mathematics, economics, and virtually every other discipline. However, specifics regarding the use of computers in statistics are not as plentiful, nor do the articics provide much in the way of distinctive applications throughout an entire course. Rather, they either present the advantages of interactive computer analysis as a substitute for or supplen~ent to classroom instruction or emphasize the use of computers primarily in regression analysis. An article by Hunka [I] and another by Leiblum rr ul. [2], among many others, concentrate on Computer Assisted Instruction (CAI) as an alternative to classroom instruction. They show how CAI applications can be adapted for different systems. but emphasize that doing so is difficult, and cannot completely replace interaction with the instructor. Edmond [3], Doornbos and Oijkstra [4], Denby and Pregibon [5], and a series of articles by Atkinson n al. 16-91 reflect on the motivational and clarification benefits of computer simulations in regression analysis, but only regression. Black [IO] emphasizes that students tend to pay better attention to computer analyses than blackboard examples, while Holland and Joliffe [l I] reinforce that retention is greatly enhanced by having the students apply computer-assisted regression to data they have collected, and through emphasis on correct statements of hypotheses and conclusions. However, none of these articles provides many concrete examples of how computers can be used in the classroom throughout a course in statistics. Nor do they describe the extent to which pedagogy and students’ retention can be improved by bringing the computer to class. For maximum benefit, not only must the computer be used in the existing course, but also the course itself must be redesigned around the technology. Fortunately, integration of the computer into the statistics classroom is not only beneficial, but also relatively easy for the instructor. In fact, after a small initial time investment, preparation time for each class should fall once the computer has been integrated into the professor’s pedagogical toolbox. For example, rather than trying to anticipate every possible student question and to have output available for addressing them, faculty can work through the question in front of the class. Moreover, students can collect data and bring it to class so that the entire class can analyze it together. A side benefit of this approach is that students tend to learn better when they have some connection to the data and when they perceive that the instructor is learning along with them.
JEFFREY W. STEAGALL
254
and
PAUL M. Masos
These are just a couple of the benefits of the integration of technology into the statistics classroom for both students and professors. Our goal in this paper is to share our experiences in integrating the computer into our teaching of business statistics, in order to make integration even easier for others. We begin by setting the stage for our course. CHARACTERISTICS
OF OUR
UNIVERSITY,
STUDENTS.
AND
COURSES
Our experiences with integrating computers into business statistics have occurred at the University of North Florida (UNF), an urban university in Jacksonville, Fla. The College of Business serves approx. 1500 undergraduate business majors and 500 MBA students. The lack of on-campus housing and the relatively remote location of the campus imply that most of our students commute. Moreover, a large portion of our students work part-time or full-time in addition to taking classes. Our students are also somewhat older than students at traditional universities. Despite these atypical characteristics, however, we believe that our students are no more or less accustomed to computers than those at most other colleges and universities, so that the lessons we have learned in integrating computer technology into the statistics classroom should generalize to most academic settings. The course described here is a second course in business and economic statistics for undergraduates, although most of the material applies equally well to either a first course in statistics or a statistics course in any discipline. Most of the comments also apply to the analogous MBA course. The prerequisite course for our students is likely typical of most universities. They must complete an introductory business statistics course in order to be accepted into the College of Business. The introductory course is taught by the Statistics Department. Unfortunately, due to the large number of students in that course, it is taught in large, Iccturc-hall sections. As a result. computer integration in that class has been relatively slow, although the faculty have recently made strides in expanding computer USilgC. The second course in business statistics is taught by Economics Dcpartmcnt faculty in classes of 40-50 students. Second-scmestcr statistics courses can be structured in a variety of ways, but WC begin with coverage of the x’ goodness-of-fit technique. This scrvcs two purposes. First, since a large percentage of our students do not take the second statistics course immediately after their first course, x’ analysis reintroduces students to inferential statistics. Second, the x’ test requires only simple calculations, so that we can assign both computer exercises and hand-calculations. We have found that requiring both types of problems early in the term enhances students’ appreciation of the computer instantaneously. After $, one- and two-factor ANOVA arc covered. once and for all convincing students that learning to use the software is preferable to doing hand calculations. The bulk of the remaining class time is spent on regression and its business and economic applications. Timc-scrics analysis and statistical process control are also taught. TECHNOLOGY:
HARDWARE
AND
SOFTWARE
The technology available to us is probably no more sophisticated than that available at most other institutions of higher learning. The students lab consists mainly of XT and 286 machines, although six 386 PCs were recently acquired. While a large fraction of undergraduates do not have access to off-campus PCs, approx. 80% of our MBA students do have access to non-university PCs. The antiquity of the hardware in the student lab limits the choice of software, in addition to making the software run at a snail’s pace. However, our situation demonstrates that substantial resource allocations are not required for integration of technology in teaching. Software options abound, but for thesake of concreteness, we will focus here on the use of the DOS-based MYSTAT software. MYSTAT tabulates data, conducts ANOVAs and regression analysis and has some time-series applications. Recently, we have also begun to use a sister program called QCTOOLS to generate basic quality control charts. One advantage of these packages is that they are relatively inexpensive, and are sometimes included free-of-charge with textbooks.
Technology
255
in the classroom
We have chosen DOS-based software because of hardware limitations in the student lab, faculty offices, and students’ homes. One drawback of DOS-based statistical applications is that they often fail to be user-friendly, requiring students to use the proper syntax to execute a command. However, with the rapid technoIogica1 advances and corresponding price decreases, Windows applications are becoming available. We will begin experimenting with their use in Fall. 1994, in the expectation that students will be able to move more quickly along the learning curve to proficiency, so that they can focus on learning statistics rather than on learning software.
INTEGRATION
VS ADDITION
OF TECHNOLOGY
TO THE TEACHING
PROCESS
One way to utilize computer technology in teaching statistics is simply to review computer output in class and assign a few computer-based homework problems. However, merely adding the computer to the existing course, rather than integrating it into the pedagogical fabric of the course, does a disservice both to students and to faculty. Students lose because integration of the computer into lectures can help them both to understand the process of analysis and to learn how to use the software. Faculty lose from just adding the computer instead of integrating it because integration can actually reduce preparation time. For instance, examples can be shown “live” in class, instead of preparing multiple overheads to cover probable student questions. True integration of technology into the classroom requires overcoming several hurdies. Most fundament~ll is the elimination of student (and in some cases ~culty!) computer phobia. Despite the wide-spread use of personal computers, many still do not understand that computers are not fragile. Large groups of students remain petrified that they will destroy the hardware or at least lose their own work, by touching the wrong key. Perhaps the most important reason that computer phobia remains prevalent is that so many students lack basic computer skills. This remains true even though our students are rcquircd to take a computer applications course, in which they ostensibly learn the basics of DOS, a word-processor and a spreadsheet. Having the computer in the classroom also incrcascs the flexibility of the locturc. When assigning complex problems, students often dcvclop novel ways of ruaching a decision. Since anticipation of all possibilities is beyond our reach. having the computer in the classroom allows the class to consider and discuss the suggested alternative approaches. The flexibility and willingness of the professor to examine alternative angles to a problem enhances the students’ view of statistics as a creative process, rather than as merely number-crunching (as we believe it has been perceived in the past). In addition to stirring students’ creative juices (always a desirable goal), this flexibility also encourages true class discussion, which has often been lacking in traditional statistics courses. One technique that we find useful for generating this type of behavior is to have a set of “class discussion problems”-exercises that students must complete before coming to class. The various approaches to these problems can then be analyzed, and the class can arrive at a consensus answer. Having the computer at hand also facilitates revirw. Students often ask questions about a problem covered a week earlier. Without the computer, the only way to answer would be to carry overhead transparencies to class. While this may be feasible, it is impossible to anticipate all possible questions and prepare appropriate transparencies. Moreover, the computer allows all previous questions to be “fair game”, improving students’ understanding of course material. The remainder of this paper cxposirs a detailed “how-to” program for integrating the computer into the classroom.
COMPUTERS
IN THE
STATISTICS
CLASSROOM:
GENERAL
BENEFITS
A critical feature of integrating the computer into the classroom is to convince students that you are serious about it. We accomplish this-by bringing the computer into the first or second class meeting in order to demonstrate the software. Instead of trying to demonstrate the computer with one monitor at the front of the room, we use an important piece of hardware: a computerscreen projection device that allows the information on the computer monitor to be projected onto the classroom’s screen using a standard overhead projector. We use Telex MagnaByte screen
JEFFREY W. STEAGALL and
2%
PAUL M. MASON
projectors, but several other models are available. Far better projection devices, such as threegun, ceiling-mounted projectors, exist. However, for much of the business statistics course, the simpler, far cheaper, device is adequate. Our unit is attached to an XT. which sometimes requires up to 30s to complete a complex problem. However, with a bit of planning by the professor, students hardly notice the delay. The use of the computer-screen projection device has greatly improved both the presentation and reception of our lectures. Students are always enthusiastically appreciative of that piece of equipment, and they generally make a point of mentioning its value in clarifying lectures. Once students realize that the computer will be an integral part of the course, most of their resistance to it dissipates. We have also noticed former students using the software (and the projection hardware-when they can get permission to use it) in applications in other business coursework, suggesting the all important transference of material from statistics to other fields. Another important skill that can perhaps best be demonstrated in a statistics class is the ability to share data (and text) among software applications. Almost all statistics packages include an ASCII interface for importing and exporting data. Because data are increasingly available in ASCII format from governmental and other databases, students must understand how to import them into their statistical packages. As educators with a vested interest in enhancing students’ appreciation of computer technology, we should also integrate these features into our courses. For example, many inexpensive, DOS-based statistics programs, including MYSTAT, have inferior graphing capabilities. Professors using such packages should encourage students to export data to a spreadsheet when graphs are desired. Students should also be encouraged to learn to export statistical output to their word-processors to avoid retyping, which requires time and can be inaccurate. Most programs can also save statistical output in a text file for dirsct importation into a word processor. Students must understand, though, that statistical output. which is typically designed to contain a lot of information in a concise format, should often bc edited for inclusion in a paper. Unnecessary information should bc edited out, a rcasonablc number of significant digits kept, and easy-to-read tables crcatcd. Direct transfer of results is dcsigncd to rcducc work; it cannot eliminate work. This raises the point of how much detail to cover in the course. Since we are educating future business persons in using statistics to make decisions, our prcfercnce is to minimize the formulas and calculations required, following the economic principle of specialization. The computer should bc used for graphing and calculation. Students should focus on understanding the statistical output and especially on making decisions from the information provided by the computer. For example, while we continue to explain and demonstrate the formulas for test statistics, we seldom require students to calculate the statistics by hand. That is the purview of the computer. By reducing the effort students must expend on calculations (and finding their errors), large blocks of time are freed up both in class and for doing homework problems. This time is more productively used in teaching students how to use statistics to make decisions. Finally, most students enter a statistics course warily. Much like in their math classes, students are unsure of their abilities to perform statistical tests, making failure a major concern. It puts students at ease to know that the computer will help them with the arithmetic, leaving interpretation as the primary goal.
COMPUTERS
IN THE
STATISTICS
CLASSROOM:
SPECIFIC
APPLICATIONS
As alluded to earlier, we begin with x2 analysis and hand calculations employing a simple mathematical formula to solve simple problems. However, as we proceed to problems like fitting a Normal or Poisson distribution, students realize that the process can be more complex. Typically, one homework assignment mandates that they perform calculations by hand. After reviewing what they did, and emphasizing all of the places they could go wrong with the calculations, we roll in the computer projection technology and solve these same problems in a matter of seconds. Students are generally thrilled to know that they can do the computational work so quickly, leaving much more time for the important interpretation. In addition to goodness-of-fit tests. we also investigate contingency tables. Once again, the software performs the test in the blink of an eye.
Technology
in the classroom
257
One-way ANOVA begins by hand, but quickly we return to the software, with two-factor ANOVA tables completed only by computer. By this time 100% of the students are convinced of the benefits of using the computer to do the grunt work. Unfortunately, ANOVA problems in textbooks are typically very mundane. The computer allows us to use outside data sets to spice up the analysis, e.g. does gender influence preferences for colors, shopping, sex? When we begin regression, the computer really takes over. Although we present the formulas for deriving the slope and intercept in bivariate regression, computations are primarily performed using the software. We both use data sets with many variables from which the students can construct models, right there in class. Repeated regressions performed in a matter of seconds allow the professor to emphasize how R’s, F-statistics, coefficients, and standard errors change as the independent variables change. Students also have the opportunity to analyze coefficients and econometric problems as the models change. For example, one of the authors uses data relative to the 1980 election, building an increasingly larger model regressing the percentage of state voters who voted for Ronald Reagan on independent variables like unemployment rates, the percentage of the population over 65, etc. The students pick the variables, and each additional independent variable can be analyzed, as well as the influences on the R’s, F-statistics, previous coefficient magnitudes, and economic indicators, e.g. the Durbin-Watson statistic, the Bartlett Chi-square, etc. Providing ail of these opportunities for interpretation also allows us to bring in regression results from our own research, and the time to introduce non-linear regression. and techniques for qualitative dependent variables, e.g. probit, logit, binomial regression, etc. Econometric problems seem considerably less overwhelming when the computer software can adjust for thcsc problems simply. Instead of fearing autocorrclation or hetcroscedasticity, or even forsaking proper mothodology to avoid them. our students arc considerably more likely to take these problems seriously, and correct for them properly. Both authors USC a data set rigged to imply hctcrosccdasticity which can bc manipulated in class to eliminate the problem. When the students XC that the problem can be easily eliminated in a short amount of time, they arc more prone to do so in other applications. In the time-series section. the computer is integrated once again, allowing consideration of linear trends, non-lincnritics, and the methods for linearizing. Computing scasonality index numbers. or adjusting for cyclicality is enhanced by using a sprcadshcct program in conjunction with the basic computer software. This, in particular, motivates the students to learn how to transfer data bctwcen software packages. Quality-control is also computer-intensive. The computer calculates control limits and capability indices, and draws the control charts. Again, students are able to focus on the interpretation of the control charts and capability indices, rather than having to waste time graphing by hand.
HOMEWORK
Homework problems in statistics have historically been pure drudgery. Students have traditionally spent hours calculating and then checking the outcomes of the assigned problems, after which they frequently forgot to interpret the results for all of the number-mashing. In our courses, the drudgery is left to the computer, so that students arc much more creative and conscientious with their homework. Instead of number-crunching, students spend their time interpreting the results and making the output concise and aesthetically pleasing. The use of the computer also allows students to analyze large. real-world data sets instead of fictitious ones. They can even collect their own information to analyze. We have found students much more interested in the outcome of such problems than they have been in purely academic exercises.
TESTING
Traditional in-class tests virtually require students to calculate statistics by hand. Unfortunately, such evaluation methods signal to students that hand calculations remain of paramount importance. For computers to be used properly in statistics courses, traditional testing must be foregone in
258
JEFFREY W. STEAGALL and PAUL .M. MASON
favor of methods consistent with the goal of encouraging computer use for calculation and brain use for decision-making. One possible solution is to integrate computer output into traditional, in-class tests. Computer output generated for a problem can be displayed, and the students asked to interpret it. While such a procedure accomplishes the goal of inducing students to take information from the computer and make decisions with it, this methodology also eliminates a critical step in the statistical decision-making process. Specifically, students are not required to demonstrate their ability to take a problem and a data set and generate the correct output with which to make the decision. Moreover, computers enable students to look at problems from more than one angle, but only if they have adequate time to do their own modefling. These inconsistencies between what we teach in the class and what we require in testing are serious, and undoubtedly confuse students about the value of computers for statistical analysis. Fortunately this can be remedied even with technological constraints. Another possible solution to the testing problem is to conduct exams in classrooms in which each student has his own PC with which to work. Unfortunately, such classrooms are few and far between, even when they are reliably operational. Moreover. testing in a timed setting precludes requiring data entry by students. Since the ability to enter data in the way that the statistical package understands is one area where our students have quite a bit of difficulty (especially early in the semester), the inability to test it is a drawback. Finally, one can pose only fairly straightforward questions on an in-class exam. It is unfair to ask students to read and to analyze immcdi~Itefy a compficatcd statistical problem. In practice, many insights appear only after the subconscious has had a chance to work on the problem. Inclass testing eliminates that aspect of analysis. Our solution to the testing dilemma is to distribute take-home exams to be completed over a 5-7-day period. During this time, some of us instruct students not to work togcthcr. Of course, under this requirement, WC arc compfctcly at the mercy of the students’ integrity, and WC realize that collusion occurs frequently. Others aitow collusion, arguing that the advantages from group learning outweigh the potential grade-inflation and free-rider problems. Under this paradigm, the instructor can distinguish student pcrlbrmancc by designing aftcrnativo evaluation instruments, such as graded homework and an in-class portion on exams. Rcgardfcss of the collusion decision WC believe that the amount of learning that occurs on takehome statistics exams far exceeds that of in-class exams. In part, this is due to the more realistic and more invofvcd questions that can be posed on take-home exams. Take-home exams also allow students to complete ail facets of statistical analysis, beginning with understanding the probfcm and entering data, through preliminary statistical analysis of the problem, and ending with statistically-based decision-making. in short, given computer availability, take-home tests arc superior to in-cfilSS exams in statistics.
CONCLUSlONS
AND
RECOMMENDATIONS
Proper use of technology to improve the teaching of business statistics requires a complete rethinking of the teaching process, from prerequisite skills to tecturc styles to examinations. Computer skiffs must be upgraded, and ail faculty must be involved in ensuring not only that the basic computer skills course is accomplishing its objectives (and that it has the resources to do SO), but also that computer skiffs are being emphasized across the curriculum. While this is relatively easy to do in our own courses, others should be encouraged to require computer use wherever it is appropriate. in the classroom, computers fundamentally after the emphasis of statistics courses. WC need no longer emphasize calculations at the expense of intuition and decision-making. The ~cxibility of having a computer at hand to help answer student questions and to examine alternative approaches improves the creativity, discussion, and learning in the course. We also advocate the predominance of take-home exams over in-class exams, since the former are more consistent with the philosophy of doing statistics in the information age and they allow more realistic questions to be asked. Take-home exams allow testing of the entire statistical process, including problem formulation, data entry. anafysis, and decision-making. Simply requiring
Technology
in the classroom
259
computer use of students is a disservice to the educational process. Integrating computer technology into statistics courses also permits carry avers to other economics and business course work. REFERENCES 1. Hunka 2. 3. 4. 5. 6. 7.
8. 9. IO. II.
S.. Sixteen years of teaching elementary applied statistics using CAI: a case study. J. &hx. Technol. Sysf. 19. 139-150 (1990). Leiblum M. D.. Derks K. and Hermans D., A decade of CA1 at a Dutch university. Compurers Educ. IO. 229-243 (1986). Emond W. J., Some benefits of micro-computers in teaching statistics. Compurers E&c. 6. 51-54 (1982). Doombos R. and Oijkstra J. B.. Teaching statistics using a computer. Eur J. Engng Educ. IO, 339-343 (1985). Denby L. and Pregibon D.. An example of the use of graphics in regression. Am. S~orisr. 41. 33-37 (1987). Atkinson M., Bajgier S. M. and Prybutok V. R.. Using microcomputer graphics to investigate the properties of visual fits of simple regression models, Decision Sciences fnsrifure: 18th Annual Meeting Proceedings. pp. 877-879 (1986). Atkinson M.. Bajgier S. M. and Prybutok V. R., Using microcomputer graphics and visual fits of simple regression models as a pedagogical tool for regression. Contpurrr Science cmJ Starisfics: Proceedings o/the 19th Symposium on rhe Inrerjke. pp. 308-3 I3 ( 1987). Bajgier S. M., Atkinson M. and Prybutok V. R.. Visual fits in the teaching of regression concepts. Am. Smfist. 43, 229-234 (1989). Prybutok V. R., Bajgier S. M. and Atkinson M.. Statistics instruction: the next generation. J. Compur. Murh. Sci. Teuch. 10. 15-27 (1991). Black K., Computer augmented teaching: the computer screen versus the chalkboard. Acod Contpur. May/June, 4649 (1988). Holland L. A. and Jolilfe F. R.. Computers, social surveys and teaching statistics. fnr. J. Compur. Atlulr Glut. Tiuin. I. 7-14 (1988).
Pergamon
Copyright 0 1994 Elsevicr Sciena Ltd Primed in Grear &rain. All rights reserved 0360-1315194 $7.00 + 0.00
TECHNOLOGY IN THE CLASSROOM: USING PCs TO TEACH BUSINESS AND ECONOMIC STATISTICS JE~REY W. STEAGALI.and
PAUL
M.
MASON
Department of Economics, University of North Florida. 4567 St Johns Bluff Road, South. Jacksonville, FL 32221-X%5. U.S.A. [Fax: (904) 646-25941
(Received 7 March 1994: accepted 9 Seprrnrber 1994) Abstract-Rapid advances and declining prices in computer technology have made its use as a classroom tool atfordable. However, while it has been clear that diverse disciplines can eKectively utilize computer technology to improve instruction, the implementation of computer-intensive pedagogy has been hindered by the lack of knowledge about redesigning courses to employ computers electively. This paper offers insights learned in teaching business and economic statistics over a period of several years. Both tools and techniques are discussed in the hopes that the paper will serve as a blueprint for others who wish to incorporate computer use into their statistics courses.
The increased availability of inexpensive, high-quality hardware and software has already revolutionized the teaching of most academic subjects. allowing students and instructors to focus on concepts and methodologies rather than on computation and manual data manipulation. For instance, computer-based calculus classes are becoming the norm and word-processors have improved the writing-and-revision process in a variety of subjects, so that students find editing drafts of papers to be less typcwritcr-intensive. The literature concerning the USCof computers in the classroom is massive and reflects applications in business, sociology, education, engineering. psychology, mathematics, economics, and virtually every other discipline. However, specifics regarding the use of computers in statistics are not as plentiful, nor do the articics provide much in the way of distinctive applications throughout an entire course. Rather, they either present the advantages of interactive computer analysis as a substitute for or supplen~ent to classroom instruction or emphasize the use of computers primarily in regression analysis. An article by Hunka [I] and another by Leiblum rr ul. [2], among many others, concentrate on Computer Assisted Instruction (CAI) as an alternative to classroom instruction. They show how CAI applications can be adapted for different systems. but emphasize that doing so is difficult, and cannot completely replace interaction with the instructor. Edmond [3], Doornbos and Oijkstra [4], Denby and Pregibon [5], and a series of articles by Atkinson n al. 16-91 reflect on the motivational and clarification benefits of computer simulations in regression analysis, but only regression. Black [IO] emphasizes that students tend to pay better attention to computer analyses than blackboard examples, while Holland and Joliffe [l I] reinforce that retention is greatly enhanced by having the students apply computer-assisted regression to data they have collected, and through emphasis on correct statements of hypotheses and conclusions. However, none of these articles provides many concrete examples of how computers can be used in the classroom throughout a course in statistics. Nor do they describe the extent to which pedagogy and students’ retention can be improved by bringing the computer to class. For maximum benefit, not only must the computer be used in the existing course, but also the course itself must be redesigned around the technology. Fortunately, integration of the computer into the statistics classroom is not only beneficial, but also relatively easy for the instructor. In fact, after a small initial time investment, preparation time for each class should fall once the computer has been integrated into the professor’s pedagogical toolbox. For example, rather than trying to anticipate every possible student question and to have output available for addressing them, faculty can work through the question in front of the class. Moreover, students can collect data and bring it to class so that the entire class can analyze it together. A side benefit of this approach is that students tend to learn better when they have some connection to the data and when they perceive that the instructor is learning along with them.
JEFFREY W. STEAGALL
254
and
PAUL M. Masos
These are just a couple of the benefits of the integration of technology into the statistics classroom for both students and professors. Our goal in this paper is to share our experiences in integrating the computer into our teaching of business statistics, in order to make integration even easier for others. We begin by setting the stage for our course. CHARACTERISTICS
OF OUR
UNIVERSITY,
STUDENTS.
AND
COURSES
Our experiences with integrating computers into business statistics have occurred at the University of North Florida (UNF), an urban university in Jacksonville, Fla. The College of Business serves approx. 1500 undergraduate business majors and 500 MBA students. The lack of on-campus housing and the relatively remote location of the campus imply that most of our students commute. Moreover, a large portion of our students work part-time or full-time in addition to taking classes. Our students are also somewhat older than students at traditional universities. Despite these atypical characteristics, however, we believe that our students are no more or less accustomed to computers than those at most other colleges and universities, so that the lessons we have learned in integrating computer technology into the statistics classroom should generalize to most academic settings. The course described here is a second course in business and economic statistics for undergraduates, although most of the material applies equally well to either a first course in statistics or a statistics course in any discipline. Most of the comments also apply to the analogous MBA course. The prerequisite course for our students is likely typical of most universities. They must complete an introductory business statistics course in order to be accepted into the College of Business. The introductory course is taught by the Statistics Department. Unfortunately, due to the large number of students in that course, it is taught in large, Iccturc-hall sections. As a result. computer integration in that class has been relatively slow, although the faculty have recently made strides in expanding computer USilgC. The second course in business statistics is taught by Economics Dcpartmcnt faculty in classes of 40-50 students. Second-scmestcr statistics courses can be structured in a variety of ways, but WC begin with coverage of the x’ goodness-of-fit technique. This scrvcs two purposes. First, since a large percentage of our students do not take the second statistics course immediately after their first course, x’ analysis reintroduces students to inferential statistics. Second, the x’ test requires only simple calculations, so that we can assign both computer exercises and hand-calculations. We have found that requiring both types of problems early in the term enhances students’ appreciation of the computer instantaneously. After $, one- and two-factor ANOVA arc covered. once and for all convincing students that learning to use the software is preferable to doing hand calculations. The bulk of the remaining class time is spent on regression and its business and economic applications. Timc-scrics analysis and statistical process control are also taught. TECHNOLOGY:
HARDWARE
AND
SOFTWARE
The technology available to us is probably no more sophisticated than that available at most other institutions of higher learning. The students lab consists mainly of XT and 286 machines, although six 386 PCs were recently acquired. While a large fraction of undergraduates do not have access to off-campus PCs, approx. 80% of our MBA students do have access to non-university PCs. The antiquity of the hardware in the student lab limits the choice of software, in addition to making the software run at a snail’s pace. However, our situation demonstrates that substantial resource allocations are not required for integration of technology in teaching. Software options abound, but for thesake of concreteness, we will focus here on the use of the DOS-based MYSTAT software. MYSTAT tabulates data, conducts ANOVAs and regression analysis and has some time-series applications. Recently, we have also begun to use a sister program called QCTOOLS to generate basic quality control charts. One advantage of these packages is that they are relatively inexpensive, and are sometimes included free-of-charge with textbooks.
Technology
255
in the classroom
We have chosen DOS-based software because of hardware limitations in the student lab, faculty offices, and students’ homes. One drawback of DOS-based statistical applications is that they often fail to be user-friendly, requiring students to use the proper syntax to execute a command. However, with the rapid technoIogica1 advances and corresponding price decreases, Windows applications are becoming available. We will begin experimenting with their use in Fall. 1994, in the expectation that students will be able to move more quickly along the learning curve to proficiency, so that they can focus on learning statistics rather than on learning software.
INTEGRATION
VS ADDITION
OF TECHNOLOGY
TO THE TEACHING
PROCESS
One way to utilize computer technology in teaching statistics is simply to review computer output in class and assign a few computer-based homework problems. However, merely adding the computer to the existing course, rather than integrating it into the pedagogical fabric of the course, does a disservice both to students and to faculty. Students lose because integration of the computer into lectures can help them both to understand the process of analysis and to learn how to use the software. Faculty lose from just adding the computer instead of integrating it because integration can actually reduce preparation time. For instance, examples can be shown “live” in class, instead of preparing multiple overheads to cover probable student questions. True integration of technology into the classroom requires overcoming several hurdies. Most fundament~ll is the elimination of student (and in some cases ~culty!) computer phobia. Despite the wide-spread use of personal computers, many still do not understand that computers are not fragile. Large groups of students remain petrified that they will destroy the hardware or at least lose their own work, by touching the wrong key. Perhaps the most important reason that computer phobia remains prevalent is that so many students lack basic computer skills. This remains true even though our students are rcquircd to take a computer applications course, in which they ostensibly learn the basics of DOS, a word-processor and a spreadsheet. Having the computer in the classroom also incrcascs the flexibility of the locturc. When assigning complex problems, students often dcvclop novel ways of ruaching a decision. Since anticipation of all possibilities is beyond our reach. having the computer in the classroom allows the class to consider and discuss the suggested alternative approaches. The flexibility and willingness of the professor to examine alternative angles to a problem enhances the students’ view of statistics as a creative process, rather than as merely number-crunching (as we believe it has been perceived in the past). In addition to stirring students’ creative juices (always a desirable goal), this flexibility also encourages true class discussion, which has often been lacking in traditional statistics courses. One technique that we find useful for generating this type of behavior is to have a set of “class discussion problems”-exercises that students must complete before coming to class. The various approaches to these problems can then be analyzed, and the class can arrive at a consensus answer. Having the computer at hand also facilitates revirw. Students often ask questions about a problem covered a week earlier. Without the computer, the only way to answer would be to carry overhead transparencies to class. While this may be feasible, it is impossible to anticipate all possible questions and prepare appropriate transparencies. Moreover, the computer allows all previous questions to be “fair game”, improving students’ understanding of course material. The remainder of this paper cxposirs a detailed “how-to” program for integrating the computer into the classroom.
COMPUTERS
IN THE
STATISTICS
CLASSROOM:
GENERAL
BENEFITS
A critical feature of integrating the computer into the classroom is to convince students that you are serious about it. We accomplish this-by bringing the computer into the first or second class meeting in order to demonstrate the software. Instead of trying to demonstrate the computer with one monitor at the front of the room, we use an important piece of hardware: a computerscreen projection device that allows the information on the computer monitor to be projected onto the classroom’s screen using a standard overhead projector. We use Telex MagnaByte screen
JEFFREY W. STEAGALL and
2%
PAUL M. MASON
projectors, but several other models are available. Far better projection devices, such as threegun, ceiling-mounted projectors, exist. However, for much of the business statistics course, the simpler, far cheaper, device is adequate. Our unit is attached to an XT. which sometimes requires up to 30s to complete a complex problem. However, with a bit of planning by the professor, students hardly notice the delay. The use of the computer-screen projection device has greatly improved both the presentation and reception of our lectures. Students are always enthusiastically appreciative of that piece of equipment, and they generally make a point of mentioning its value in clarifying lectures. Once students realize that the computer will be an integral part of the course, most of their resistance to it dissipates. We have also noticed former students using the software (and the projection hardware-when they can get permission to use it) in applications in other business coursework, suggesting the all important transference of material from statistics to other fields. Another important skill that can perhaps best be demonstrated in a statistics class is the ability to share data (and text) among software applications. Almost all statistics packages include an ASCII interface for importing and exporting data. Because data are increasingly available in ASCII format from governmental and other databases, students must understand how to import them into their statistical packages. As educators with a vested interest in enhancing students’ appreciation of computer technology, we should also integrate these features into our courses. For example, many inexpensive, DOS-based statistics programs, including MYSTAT, have inferior graphing capabilities. Professors using such packages should encourage students to export data to a spreadsheet when graphs are desired. Students should also be encouraged to learn to export statistical output to their word-processors to avoid retyping, which requires time and can be inaccurate. Most programs can also save statistical output in a text file for dirsct importation into a word processor. Students must understand, though, that statistical output. which is typically designed to contain a lot of information in a concise format, should often bc edited for inclusion in a paper. Unnecessary information should bc edited out, a rcasonablc number of significant digits kept, and easy-to-read tables crcatcd. Direct transfer of results is dcsigncd to rcducc work; it cannot eliminate work. This raises the point of how much detail to cover in the course. Since we are educating future business persons in using statistics to make decisions, our prcfercnce is to minimize the formulas and calculations required, following the economic principle of specialization. The computer should bc used for graphing and calculation. Students should focus on understanding the statistical output and especially on making decisions from the information provided by the computer. For example, while we continue to explain and demonstrate the formulas for test statistics, we seldom require students to calculate the statistics by hand. That is the purview of the computer. By reducing the effort students must expend on calculations (and finding their errors), large blocks of time are freed up both in class and for doing homework problems. This time is more productively used in teaching students how to use statistics to make decisions. Finally, most students enter a statistics course warily. Much like in their math classes, students are unsure of their abilities to perform statistical tests, making failure a major concern. It puts students at ease to know that the computer will help them with the arithmetic, leaving interpretation as the primary goal.
COMPUTERS
IN THE
STATISTICS
CLASSROOM:
SPECIFIC
APPLICATIONS
As alluded to earlier, we begin with x2 analysis and hand calculations employing a simple mathematical formula to solve simple problems. However, as we proceed to problems like fitting a Normal or Poisson distribution, students realize that the process can be more complex. Typically, one homework assignment mandates that they perform calculations by hand. After reviewing what they did, and emphasizing all of the places they could go wrong with the calculations, we roll in the computer projection technology and solve these same problems in a matter of seconds. Students are generally thrilled to know that they can do the computational work so quickly, leaving much more time for the important interpretation. In addition to goodness-of-fit tests. we also investigate contingency tables. Once again, the software performs the test in the blink of an eye.
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One-way ANOVA begins by hand, but quickly we return to the software, with two-factor ANOVA tables completed only by computer. By this time 100% of the students are convinced of the benefits of using the computer to do the grunt work. Unfortunately, ANOVA problems in textbooks are typically very mundane. The computer allows us to use outside data sets to spice up the analysis, e.g. does gender influence preferences for colors, shopping, sex? When we begin regression, the computer really takes over. Although we present the formulas for deriving the slope and intercept in bivariate regression, computations are primarily performed using the software. We both use data sets with many variables from which the students can construct models, right there in class. Repeated regressions performed in a matter of seconds allow the professor to emphasize how R’s, F-statistics, coefficients, and standard errors change as the independent variables change. Students also have the opportunity to analyze coefficients and econometric problems as the models change. For example, one of the authors uses data relative to the 1980 election, building an increasingly larger model regressing the percentage of state voters who voted for Ronald Reagan on independent variables like unemployment rates, the percentage of the population over 65, etc. The students pick the variables, and each additional independent variable can be analyzed, as well as the influences on the R’s, F-statistics, previous coefficient magnitudes, and economic indicators, e.g. the Durbin-Watson statistic, the Bartlett Chi-square, etc. Providing ail of these opportunities for interpretation also allows us to bring in regression results from our own research, and the time to introduce non-linear regression. and techniques for qualitative dependent variables, e.g. probit, logit, binomial regression, etc. Econometric problems seem considerably less overwhelming when the computer software can adjust for thcsc problems simply. Instead of fearing autocorrclation or hetcroscedasticity, or even forsaking proper mothodology to avoid them. our students arc considerably more likely to take these problems seriously, and correct for them properly. Both authors USC a data set rigged to imply hctcrosccdasticity which can bc manipulated in class to eliminate the problem. When the students XC that the problem can be easily eliminated in a short amount of time, they arc more prone to do so in other applications. In the time-series section. the computer is integrated once again, allowing consideration of linear trends, non-lincnritics, and the methods for linearizing. Computing scasonality index numbers. or adjusting for cyclicality is enhanced by using a sprcadshcct program in conjunction with the basic computer software. This, in particular, motivates the students to learn how to transfer data bctwcen software packages. Quality-control is also computer-intensive. The computer calculates control limits and capability indices, and draws the control charts. Again, students are able to focus on the interpretation of the control charts and capability indices, rather than having to waste time graphing by hand.
HOMEWORK
Homework problems in statistics have historically been pure drudgery. Students have traditionally spent hours calculating and then checking the outcomes of the assigned problems, after which they frequently forgot to interpret the results for all of the number-mashing. In our courses, the drudgery is left to the computer, so that students arc much more creative and conscientious with their homework. Instead of number-crunching, students spend their time interpreting the results and making the output concise and aesthetically pleasing. The use of the computer also allows students to analyze large. real-world data sets instead of fictitious ones. They can even collect their own information to analyze. We have found students much more interested in the outcome of such problems than they have been in purely academic exercises.
TESTING
Traditional in-class tests virtually require students to calculate statistics by hand. Unfortunately, such evaluation methods signal to students that hand calculations remain of paramount importance. For computers to be used properly in statistics courses, traditional testing must be foregone in
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JEFFREY W. STEAGALL and PAUL .M. MASON
favor of methods consistent with the goal of encouraging computer use for calculation and brain use for decision-making. One possible solution is to integrate computer output into traditional, in-class tests. Computer output generated for a problem can be displayed, and the students asked to interpret it. While such a procedure accomplishes the goal of inducing students to take information from the computer and make decisions with it, this methodology also eliminates a critical step in the statistical decision-making process. Specifically, students are not required to demonstrate their ability to take a problem and a data set and generate the correct output with which to make the decision. Moreover, computers enable students to look at problems from more than one angle, but only if they have adequate time to do their own modefling. These inconsistencies between what we teach in the class and what we require in testing are serious, and undoubtedly confuse students about the value of computers for statistical analysis. Fortunately this can be remedied even with technological constraints. Another possible solution to the testing problem is to conduct exams in classrooms in which each student has his own PC with which to work. Unfortunately, such classrooms are few and far between, even when they are reliably operational. Moreover. testing in a timed setting precludes requiring data entry by students. Since the ability to enter data in the way that the statistical package understands is one area where our students have quite a bit of difficulty (especially early in the semester), the inability to test it is a drawback. Finally, one can pose only fairly straightforward questions on an in-class exam. It is unfair to ask students to read and to analyze immcdi~Itefy a compficatcd statistical problem. In practice, many insights appear only after the subconscious has had a chance to work on the problem. Inclass testing eliminates that aspect of analysis. Our solution to the testing dilemma is to distribute take-home exams to be completed over a 5-7-day period. During this time, some of us instruct students not to work togcthcr. Of course, under this requirement, WC arc compfctcly at the mercy of the students’ integrity, and WC realize that collusion occurs frequently. Others aitow collusion, arguing that the advantages from group learning outweigh the potential grade-inflation and free-rider problems. Under this paradigm, the instructor can distinguish student pcrlbrmancc by designing aftcrnativo evaluation instruments, such as graded homework and an in-class portion on exams. Rcgardfcss of the collusion decision WC believe that the amount of learning that occurs on takehome statistics exams far exceeds that of in-class exams. In part, this is due to the more realistic and more invofvcd questions that can be posed on take-home exams. Take-home exams also allow students to complete ail facets of statistical analysis, beginning with understanding the probfcm and entering data, through preliminary statistical analysis of the problem, and ending with statistically-based decision-making. in short, given computer availability, take-home tests arc superior to in-cfilSS exams in statistics.
CONCLUSlONS
AND
RECOMMENDATIONS
Proper use of technology to improve the teaching of business statistics requires a complete rethinking of the teaching process, from prerequisite skills to tecturc styles to examinations. Computer skiffs must be upgraded, and ail faculty must be involved in ensuring not only that the basic computer skills course is accomplishing its objectives (and that it has the resources to do SO), but also that computer skiffs are being emphasized across the curriculum. While this is relatively easy to do in our own courses, others should be encouraged to require computer use wherever it is appropriate. in the classroom, computers fundamentally after the emphasis of statistics courses. WC need no longer emphasize calculations at the expense of intuition and decision-making. The ~cxibility of having a computer at hand to help answer student questions and to examine alternative approaches improves the creativity, discussion, and learning in the course. We also advocate the predominance of take-home exams over in-class exams, since the former are more consistent with the philosophy of doing statistics in the information age and they allow more realistic questions to be asked. Take-home exams allow testing of the entire statistical process, including problem formulation, data entry. anafysis, and decision-making. Simply requiring
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computer use of students is a disservice to the educational process. Integrating computer technology into statistics courses also permits carry avers to other economics and business course work. REFERENCES 1. Hunka 2. 3. 4. 5. 6. 7.
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