Abstracts and Short Presentations

Computer Aided Instruction for Statistics Courses

Noel Crockett - Sydney, Australia

Teaching an elementary statistics service course with an enrolment of over 3000 students each year presents difficulties with both instruction and assessment. A computer aided instruction program has been developed which is intended to provide hands-on instruction as well as assisting in the assessment of student performance. An additional benefit for teaching staff is the provision of immediate feedback on students' understanding of individual topics and techniques. The program is easily amended to include different topics and can thus be used in any slatistics course.

Objective-based Computerised Teaching and Testing in an Introductory Statistics Course

Robert J Cruise - Loma Linda, California, USA Jerome D Thayer - Berrien Springs, Michigan, USA

An elementary statistics course is described which is built around a large number of specific concept and problem objectives. An item bank of concept and problem items are organised according to these objectives. Each objective has items in the bank which are used in an instructional mode to teach the objective, and other similar items that measure achievement of the objective. The computer programs used were described, and examples were given of each teaching and testing mode used,

Session B3

ICOTS 3, 1990

Statistics made Enjoyable : Learning with Statgraphics

Neville Davies - Nottingham, England Andrew Tremayne - Sydney, Australia

It is of vital importance that any statistical package to be used in teaching statistics to nonspecialist students provides a congenial environment in which they can be convinced of the important role statistics can play in their other subjects of study.

The tremendous growth in business oriented packages for spreadsheet and data- base analysis has given rise to students and staff who require reports and projects presented in a professional and near publishable way. Reports in statistics using output from, say, Minitab, may have a somewhat less professional look because of the "line printer" appearance of the text and graphics. In addition, the feeling has developed that the command driven structures of Minitab and SAS, admirable packages though they are in many ways, were cumbersome, especially for beginners. They are also rather unforgiving with mistyped commands and it is arguable that the more forgiving menu driven structure of word processors and database systems is more appropriate in the business and management world.

When teaching nonspecialist students it seems necessary to have available a statistical package that (a) is easy to use; (b) motivates statistical concepts well; (c) is capable of high quality graphical output; and (d) provides facilities to easily customise graphs and to mesh them with word processors.

There are many alternative packages available, but many, with the notable exception of Statgraphics, seem to have some features of user unfriendliness and require varying amounts of time for familiarisation. As an aside, teachers who are users of statistical packages often believe the one they use themselves to be the best available; this is a prejudice that sometimes has to be overcome with regard to changing statistical packages.

In selecting a preferred package, it is important to constantly keep reminding oneself of the type of student who will be using the package, the need to stimulate and interest the client group of students, and the fact that nonspecialist students often wish to be consumers, rather than producers, of statistics. In addition, the package has to be able to cover material appropriate to an introductory course in statistics as typified by a text such as Newbold (1991). Without going into details, we simply report that, amongst PC-based packages (in our cases Macintosh-based packages were not considered because of institutional hardware configurations), we find Statgraphics comes closest to satisfying all our desiderata.

Statgraphics for teaching students of business, management and economics: At the beginning of an introductory course in statistics, it is important for students to be quickly able to do some practical work with a package and not have to spend too long mastering the system. The Statgraphics menu system provides very quick access to facilities for pie chart, barchart, boxplot, stem-and-leaf and scatterplot screen present- ations. These simple, yet very important, display techniques for data can be customised for professional quality hardcopy graphs. Furthermore all graphics screens can be exported and saved to files readable by word processors such as Word Perfect. We have

Session B3 235

ICOTS 3, 1990

found that students regard this initial graphical approach to be enjoyable and that they become enthusiastic about proceeding to use other sections of the menu. The environment is both appealing and motivating.

In this short article, space prevents us from giving detailed comments on many of the facilities available, but the graphics associated with regression analysis, statistical process control charts and forecasting are particularly strong. In addition, report writing can be a pleasurable exercise for students who link text and graphics output with a word processor.

The student view: It is unusual to be able to elicit the opinions of students on service courses with regard to competing statistical packages, since they are often only exposed to one. In 1989, the 80 students on the second year of their BA Business Studies degree at Nottingharn Polytechnic were taught using Statgraphics, having used Minitab in their fmt year. Remarkably, they were unanimous in their preference for the Statgraphics environment for analysing, presenting and reporting business data. At the University of Sydney, graduate students of management have taken well to undertaking statistical analysis with Statgraphics and first indications from the large Econometrics I course, only a limited number of the students from which will pursue econometrics beyond first year, are encouraging.

A guide to teaching statistics using Statgraphics: We have written a guide (Davies and Tremayne, 1991) that provides the student with a self-contained text for learning statistics that, inter alia, utilises the powerful graphics capabilities of Stat- graphics. Our approach is one which suppresses formulae and routine learning of techniques in favour of linking the software use with the exercise of data review, analysis and interpretation. We stress that, with Statgraphics, becoming a consumer of statistics appropriate in business, management and economics can actually be an enjoyable exercise.

References

Davies. N and Tremayne. A R (1991) Statistics Made Enjoyable : Learning with Statgraphics. Queensland University of Technology. Brisbane. Australia.

Newbold, P (1991) Statistics for Business and Economics (3rd ed). Prentice Hall.

GINNY : Nonlinear Regression via MINITAB

Murray Jorgensen - Hamilton, New Zealand

Statisticians are learning to take for granted the powerful facilities provided by modem statistical packages for fitting ANOVA and regression models to data, facilities which go beyond tests and estimates to include residual plots and diagnostic statistics for examining model assumptions and influential data. We are not satisfied as easily as we might have been with a standard set of outputs from a program, and are happiest when we can analyse a set of data interactively.

Session B3 236

ICOTS 3, 1990

With more complex procedures, however, there is a tendency to ask for less than our linear model packages give us. There is also a tendency for us to resort to a "black box" such as Genstat OPTIMIZE which hopefully will give us the "answers". In other words, when we leave the security of the linear model we turn the clock back 15 years and forsake interactive analysis for standard routines.

The GINNY macros allow MJNITAB to be used to fit a very broad class of nonlinear models in a manner that leaves the user very much in control of the process. If all goes well you will have the standard outputs and a wide range of diagnostics quite readily. If there are numerical problems with fitting the model (and no canned program can anticipate all that could go wrong), there are also tools for exploring the likelihood surface near the current parameter estimates and conducting on-the-& repairs.

There are teaching advantages to this approach as well: the student fitting a nonlinear model finds the task broken up into a number of steps each expressed in a =AB macro whose purpose is clear and conceptually simple. Furthermore, the interactive environment makes the inspection of intermediate steps easy.

More information about the GINNY macros can be found in Jorgensen (1989, 1990).

References

Jorgensen. M A (1989) Fitting non-linear models : keep it simple. New Zealand Statistician 24, 36-42.

Jorgensen, M A (1990) GINNY : A Collection of Macros for Nonlinear Regression. Research Report No 194, Department of Mathematics and Statistics. University of Waikato, Hamilton. New Zealand.

The Impact of Computers on Statistics Teaching at Computer Intensive Institutions

Richard S Lehman - Lancaster, Ohio, USA

In the past five or six years several colleges and universities in the United States have become "computer intensive". While the exact definition of "computer intensive" varies widely, it usually means that the institution has taken steps to see that all of its students and faculty have very easy access to computing facilities. In some cases, the institution provides a personal computer to all incoming students or requires them to purchase one. In other cases, the institution has negotiated favourable prices with computer vendors and students are encouraged to buy equipment. In most cases, the institutions have also established centralised laboratories so that students without computers will have easy access to equipment.

Faculty response to such a computer-rich environment varies from ignoring the new equipment to the total revision of existing courses and the development of entirely new ones. To investigate such faculty responses, I obtained a sample of 25 individuals

Session B3 237

ICOTS 3, 1990

at 16 institutions'. In order to qualify, the respondent's institution or department met the following requirements: (1) There is an institutional and/or departmental commit- ment to making computing facilities readily available to all students and faculty; (2) Thus there is an implicit understanding that students will have easy access to certain computational facilities, and that those facilities will be essentially identical for all students; (3) As a result, instructors have the freedom to assume that those common computer facilities are available to all students and may thus choose to build assign- ments and class presentations around them. While the number of respondents is small in absolute terms, the population that they represent is tiny. Because of this, the data are highly representative, since they include at least one response from a majority of the American institutions that describe themselves as computer intensive.

All of the respondents hold a PhD; most of the degrees are in mathematics or statistics, although several social science disciplines are represented. They have been teaching for between 3 and 33 years (median = 10.5 years). Most say that their teaching has been "computer intensive" for between 3-8 years (median = 5.5 years, but with a range of 2-25 years). Three indicated that, although they taught at an institution that met the definition of "computer intensive", they would not characterise their own teaching in that way.

Nearly all respondents indicated that their courses included descriptive statistics, estimation and hypothesis testing, correlation/regression, and probability. Most also taught graphing techniques, although the coverage here was less in "pure" mathematics courses (those intended primarily for mathematics majors) than in "service" courses (courses offered by a mathematics department as a service to other departments), or in "methods" courses (offered in a non-mathematics discipline for its majors). Analysis of variance and contingency table methods were also given most often in service and methods courses; factorial analysis of variance was never reported in a mathematics course but was often taught in methods courses.

While nearly all responding institutions offer extensive personal computer involvement, every respondent reported that a large central computer facility was also available that offered one or more standard statistical packages. Many also reported that computer labs or clusters of microcomputers were easily available. The labs were often networked together and to the central computer. Seventeen respondents reported that their students were encouraged (or forced) to purchase a personal computer. Of these, seven reported MS-DOS and 10 reported Mac purchases. Commercial software was generally used for personal computers or workstations, frequently listed software including MINITAB and SPSS, as well as Systat, DataDesk, Statview, S, GLIM, Mystat, CLR ANOVA, MAPLE, Solus, and Worrnstat. Only four instructors reported that their students used a home-grown statistics program.

Respondents described how the course content had changed with the advent of a computer-rich environment. Some reported that their courses now have less emphasis on arithmetic (11 respondents), concentrate more on concepts (lo), use larger and more realistic data sets (9), offer a larger range of topics, usually further development of ANOVA or the inclusion of multiple regression (8), and have an increased stress on interpreting and reporting results (8). A companion question asked how the course had NOT changed with the introduction of computing. Twenty-three individuals reported that the basic content of the course was completely or almost completely unchanged by the introduction of computing. Seven of these stressed that the focus remains heavily

Session B3 238

ICOTS 3, 1990

oriented toward fundamentals and statistical logic. For most respondents, the most important goal was teaching their students to

use hardware and software independently. Six said that they expected their students to do things that had been impossible without computing, citing such examples as fitting multiple models to data, extensive exploration of residuals, constructing normal probability plots, or carrying out simulations by using a statistical package.

Historically, some instructors have been reluctant to incorporate computing into their courses for fear of driving students away. Twenty of the respondents said that they had no evidence that students avoided the course because of its computer content; nine of these also commented that it was impossible to avoid their course. Five individuals reported that they had witnessed an increase in the demand for their courses since the advent of intensive computing.

Altogether, the results lead to two clear conclusions. First, instructors at computer intensive institutions have, by and large, incorporated computing into their statistics teaching without in any way "selling out". They are strong and nearly unanimous in their declaration that the fundamentals that they have always taught remain unchanged. These instructors view their courses as statistics courses first, emphasising logic and interpretation, and not as computing courses. Second, using computing has freed instructors to do other things in their courses. Most of the course enhancements seem to have been to add "applied" topics, though new material was added in some cases. No respondent complained that teaching how to use the computer had merely replaced teaching how to do the calculations. Perhaps this is a testament to the ease of use of many of the statistical packages available for teaching.

Individuals who advocate heavy computing in statistics instruction face a mixed audience of fellow instructors. Some in the audience resist the intrusion of computing, others remain of a mixed mind, and then there are those who are "the converted. This report could be dismissed as merely a survey of "the converted, since only instructors at computer intensive institutions were polled. While there's no debating the fact that the institutions represented are "converted", that fact is both a plus and a minus in interpreting the results.

On the negative side, it is true that few skeptics are represented here. Only two respondents described courses that had not incorporated computing at all, despite the computer intensive environment. And in fact, there were few real opportunities in the survey for the respondents to express negative opinions. On the positive side, the fact is that these data come from institutions that are highly representative of colleges and universities that have embraced computing throughout their cumcula. They thus constitute an important and informative sample of teaching in settings where computing is an assumed skill. M i l e the respondents here are clearly unrepresentative of statistics and methods instructors in general, they are probably quite representative of those who are able to freely incorporate computing in their teaching.

The debate over eliminating arithmetic from the statistics courses by using computers has been raging for years, and this survey will not resolve the controversy. It doesn't address the issue of whether hand calculation clarifies concepts. It is silent on the question of whether students can really uliderstand a data set if they are "distanced" from it by accessing it only with a computer. And there is no answer here to the question of carry-over - do students retain skills and understanding better after a hand- calculation course? The answers to those questions await additional data.

Session B3

ICOTS 3, 1990

It is informative to the argument, though, to note that no fundamental statistical content has been lost to computing in any course described here. -That fact alone should allay the fears of instructors womed about what they might have to eliminate. Not only has no statistical content been lost, but the courses seem to have been enhanced in important ways. The respondents are enthusiastic about computing in their courses. The content is still there (and often enhanced), the time spent on teaching computing appears to be less than that previously devoted to teaching arithmetic, and there is some evidence that students like the courses better.

Footnote

1. The schools represented are Allegheny College, Colby College. Cornell University, Dartmouth College, Drew University, Drexel University, Franklin & Marshall College, Grinnell College, Mt Holyoke College, Oberlin College, Purdue University, Reed College, St Lawrence University, University of Indiana, the University of Georgia, and the United States Military Academy at West Point.

Using Workstations in Undergraduate Statistics Education

Michael Meyer - Pittsburgh, Pennsylvania, USA

Over the past five years Carnegie-Mellon University has actively deployed modern workstations in public clusters.

Undergraduate students have essentially unlimited access to these computers and are encouraged (and often expected) to use the machines for all of their courses. In this talk I discussed our experiences in adapting our undergraduate statistics courses to this rich computing environment. In many courses we have attempted to use commercial (or at least widely available) software. Even when the students use simple software such as MINITAB, we find that the computing environment encourages them to explore the data and to document the analyses. With more sophisticated software, such as S, we see students really exploring data, changing assumptions, and postulating new models. For us, the era of interactive computing is finally having an impact on the art of undergraduate data analysis.

Insights from Sampling

Clifford H Wagner - Middletown, Pennsylvania, USA

Computer generated sampling provides an efficient and effective means of

Session B3 240

ICOTS 3, 1990

developing some of the insights which students need in order to understand statistical reasoning &d calculation. This article describes some graphical computer generated examples that illustrate population characteristics, sample characteristics, distributions of sample statistics, and reliabilities of statistical inferences. The advantage of a graphical computer generated approach is that estimates and impressions can be made quickly and easily without the need of numerical precision and without the necessity of specifying the density function for the underlying population. The examples are offered and d e s c r i i in the style of a classroom presentation. The reader should be able to offer additional observations and leading questions for each example. The examples and figures below were generated on a Macintosh computer using software developed by the author.

Example 1: The continuous distribution in Figure 1 was sketched by hand (and mouse) on a computer screen and scaled so as to assure that the area under the curve is 1.0. What is your estimate of the mean and standard deviation? The important idea here is to start with an arbitrary population so that when the Central Limit Theorem is subsequently introduced it is obvious that the theorem applies to all distributions.

FIGURE 1 An arbitrary continuous population

Example 2: The histograms in Figure 2 summarise three random samples of sue 35 selected from the previous population. For each sample, note the values and estimate the range, mean, and standard devktion. What similarities or differences do you see between these samples and the underlying population? (In the classroom, I would discuss a few histograms in detail and then quickly show a sequence of histograms from additional samples in order to demonstrate the variety among different samples.)

FIGURE 2 Histograms for three random samples of size 35 from the previous continuous population

Example 3: One hundred samples of size 35 were selected from the previous population. Their sample means are summarised in the histogram of Figure 3. Given that each histogram rectangle has a width of five units, what is your estimate of the

Session B3 241

ICOTS 3, 1990

probability that a sample of size 35 would have a sample mean that differs from the population mean by more than 5?, by more than lo? How accurate are your estimates of these probabilities?

FIGURE 3 The previous population and a histogram for 100 sample means

from random samples of size 35

Example 4: The hypotheses Ho : p = 50, Ha : p ;t 50, are to be tested using a single random sample of size 35 selected from the underlying population. The null hypothesis (which is true) is to be rejected whenever the sample mean is iess than 45 or greater than 55. Based on Figure 3, what is your estimate of the probability of making an error with this particular test?

I would use these four examples on four different occasions, reviewing the previous examples before introducing the current example. I would also be careful to repeat each example with discrete as weII as continuous populations and with a variety of shapes for the population distributions.

Session B3

ICOTS 3, 1990