Revising a Basic Statistics Course

William C. Rinaman
Le Moyne College

Journal of Statistics Education v.6, n.2 (1998)

Copyright (c) 1998 by William C. Rinaman, 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 author and advance notification of the editor.

Key Words: Collaboration; Group work; Laboratory; Minitab; Service course.


Members of the faculty of Le Moyne College made sweeping changes in the basic statistics course provided for the social and life sciences by the Department of Mathematics. The departments involved undertook an intensive collaboration. Intense scrutiny was given to the purpose and goals of the course. The result is a course that is significantly different from its predecessor. It places more emphasis on concepts and technology. A laboratory component was added to give students experience with Minitab and messy datasets. The implementation of the course had the expected problems. These are documented along with what was done to improve the course the second time it was offered.

1. Introduction

1 Le Moyne College is a small comprehensive college in the Jesuit tradition. The full-time undergraduate population is slightly less than 2000. Approximately three-fourths of the students major in the liberal arts, social sciences, and physical sciences. The remaining students major in business, accounting, or industrial relations.

2 The Department of Mathematics offers a service course sequence in introductory statistics. It provides basic statistical training for students in biology, economics, industrial relations, political science, psychology, and sociology. Statistics for business and accounting majors is taught by members of the faculty of the Department of Business Administration. Depending on a student's major, this is a one-semester or a two-semester sequence. Until recently, the course used traditional texts. The last three texts we used were Anderson, Sweeney, and Williams (1994), McGhee (1985), and Sincich (1990). The course introduced Minitab to illustrate the capabilities of statistical computer programs. It was not, however, an integral part of the course.

3 The first-semester course, depending on the text used, typically consisted of descriptive statistics, probability, the binomial and normal distributions, sampling distributions, one sample confidence intervals and tests on the mean, and two sample tests on means. The second semester covered inference on proportions, contingency tables, regression, and analysis of variance. The order followed that of the text being used.

4 Students move on to research methods, econometrics, or genetics courses in their own departments. These courses expose them to the particular statistical methods that are commonly used in their disciplines. There was considerable overlap in topics covered by the courses offered by the Department of Mathematics and these research methods courses.

5 Until recently, collaboration with the departments served by our course was minimal. The Chair of the Department of Mathematics met irregularly with the chairs of the client departments to ascertain whether they wanted any changes in the content of the course. They rarely asked for changes. As a result, the Department of Mathematics let the course stagnate. Students disliked the course. They had a hard time seeing the relevance of statistics. The course became one of matching this formula with that type of problem. Understanding of statistical ideas and statistical thinking were, for the most part, lacking. Students felt that the computer was another burden being forced on them, rather than being a useful tool. The client departments saw students come into their research methods courses with some mechanical skill at running numbers through a formula and using the tables in the back of the book, but with little ability to intelligently interpret what they were doing.

6 Preliminary discussions with members of the social science departments showed that both we and they wanted to make substantial changes in the content and emphasis of the introductory statistics courses. Over the course of two years we engaged in intense dialogue regarding the content and goals of a basic statistics course. This resulted in a course that is much different from the one of the past. This new course was given for the first time in the fall semester of 1996.

7 We feel that an exposition of what took place at Le Moyne might help those in similar situations. Section 2 of this paper will describe the process we used to develop the new course. Section 3 will describe the course that resulted. Section 4 will give the results of an evaluation of the course by students, the experience of a member of the Sociology Department who sat in on the course, and the reactions of the faculty who taught it. Section 5 discusses changes we made when teaching the course for the second time. It also includes student reactions to the second running of the course.

2. The Development of a New Course

8 In January 1994, the College adopted a Social Science Area Plan. A major component was the planned creation of a computer laboratory to provide statistical help for students and faculty doing research. This prompted the faculty of the social science departments (i.e., economics, political science, psychology, and sociology) to reassess statistical training in general. They held meetings where the main topic of discussion was the possibility of a new social statistics course. Each department provided a list of the topics covered in their research methods and econometrics courses. They also provided lists of material they considered to be essential prerequisites to their courses. The meetings produced a draft document to serve as a basis for subsequent meetings with the Department of Mathematics. This draft set forth the following goals for the proposed new course.

  1. The Applications Goal: Students completing the course should be prepared to perform basic analysis of social, economic, and demographic data from sources such as agency caseload files, surveys and polls, and public-use datasets. They should be able to use standard statistical software on these data.

  2. The Statistical Knowledge Goal: Students should be sufficiently prepared to pursue subsequent study of statistical methods.

  3. The Evaluation Goal: Students should be able to review statistical analyses in applied settings. They should be able to identify major problems of logic and violations of the assumptions required for basic techniques.

  4. The Communication/Visualization Goal: Students should be able to intelligently present statistical analyses to audiences with diverse levels of statistical understanding.

9 Implicit in these goals was the addition of a computer laboratory component to the course. There, students should gain experience working with actual data using statistical software. The laboratory would also emphasize and expand on the material covered in the classroom. The laboratory component necessitated that the course be changed from three credit hours to four.

10 Members of the client departments felt that it was extremely important that they should take a more active role in the conduct of the course. In particular, they would supply datasets to the Department of Mathematics. In addition, they would work closely with the mathematicians in the development of exercises, laboratory work, and classroom examples. Some even suggested that members of these departments might serve in the classroom from time to time to give illustrations of the applications of the material being covered to their fields of interest. They hoped that this would make statistics seem more relevant to the students.

11 Next, members of the client department faculty met with mathematics faculty. These meetings accomplished the following. The client departments not in the social sciences agreed to the goals set forth by the social sciences. The members of the Department of Mathematics felt that the goals of the social science departments could be incorporated into a revised course. The members of the client departments indicated that the Department of Mathematics should have the final say in matters of pedagogy.

12 We discussed a general outline for the content of the course. Everyone generally felt that there should be a lessening of the traditional emphasis on probability. Instead, the necessary concepts would be presented at a time when they were needed in the context of a discussion of statistical ideas. For example, if students do not really need to be able to compute conditional probabilities, then we should de-emphasize or eliminate them. Both parties agreed that we should use technology (i.e., computers and graphing calculators) in a way that allows students to concentrate more on the ideas being discussed than on the mechanics of a particular calculation. Also, the laboratory component should use computers to give students experience in handling complex datasets. The particular statistical software to be used would be chosen by the Department of Mathematics based on pedagogical considerations. We also agreed that the breadth of topics covered in the first course was not as important as having students master the basic concepts of sampling, confidence, and significance.

13 The Department of Mathematics then devised a course. We wanted to accommodate the goals of the client departments while keeping the content of the course at a level appropriate for a college-level statistics course. The chair of the department, in collaboration with the statisticians in the department, did most of the work for next phase. The following set of working assumptions drove the development.

  1. The new course should concentrate on summarizing data and making inferences and decisions from data. Issues of data collection should largely be left to the methods courses in the client departments.

  2. Virtually all computation should be left to technology. Formulas should not be emphasized in the classroom.

  3. The course should make heavy use of real data provided by members of the client departments.

  4. Topics should be motivated, as much as possible, by practical questions based on real data.

  5. Less can be more. It is better that students be exposed to a single type of test or confidence interval and really understand what is going on, rather than be shown a wide variety of tests and confidence intervals and not have the slightest idea of what they mean.

  6. The course should give students an appreciation not only of what statistics can do, but also what it cannot do.

14 There is a conflict between Assumption 1 and Assumption 6. Issues of data collection need to be mentioned when discussing the limitations of statistics. Consequently, we decided to cover the basic ideas behind simple random sampling and the problems associated with not doing random sampling.

15 The Department of Mathematics used these assumptions to develop a revised basic statistics course. We then presented it to the client departments. The proposed course was overwhelmingly approved. One department had minor misgivings about increasing the course from three to four credits. After the course proposal was approved by the Curriculum Committee of the Faculty Senate, we began work on preparing the manual for the laboratory component. This author wrote the manual. Members of the client departments prepared datasets. They also prepared lists of questions that members of their discipline would ask of the data. We offered the new course for the first time in the fall semester of 1996.

16 The process of developing the new course went very smoothly. The fact that the social science departments developed a commonly accepted set of goals eliminated many potential problems. Another important feature is that the client departments accepted our set of working assumptions. Members of the Department of Mathematics met frequently with a committee of members of the client departments. These meetings assured that everyone was involved with all steps of the development process. We feel this continual dialogue was a major factor in preventing conflicts between us and the client departments. We also cannot discount the fact that Le Moyne is a small college, and members of all departments see each other on a regular, informal, basis.

3. The New Course

17 The course that finally resulted is a four-credit-hour course. There are five contact hours consisting of three hours of lecture/classroom and a two-hour computer laboratory. Each component will be discussed separately.

18 The laboratory phase uses Minitab for the analysis. We chose Minitab because we felt that it is more accessible than other programs to students with little computer experience. In addition, the macro capability meant that students could be eased into the more complex tasks that some of the activities would require.

19 The laboratory activities draw heavily on datasets provided to us by the client departments. The Sociology Department provided a subset of the National Survey of Families and Housing (NSFH). This dataset consists of results on 36 items from 2000 randomly selected respondents. It is described in Appendix A. That appendix also gives some sample activities that students were asked to do in the laboratory. The Economics Department provided six sets of data from the CITIBASE archive. These sets are 50-year time series of national economic data. The sets covered time series on construction, labor, industry, finance, manufacturing, and prices. Finally, the Psychology Department provided the raw data from two experiments done by members of the department. One experiment compares response times using visual and auditory stimuli. The other compares methods of memorization. In addition to these data, the departments also supplied lists of questions that persons in their disciplines would answer using those data. The datasets kept the original variable-naming conventions and form. This gave students an appreciation of how members of their professions actually do their work.

20 The only processing the data received was conversion into Minitab worksheets. This author developed the laboratory manual (Rinaman 1997). The data sets and macros are available from him. The laboratory sessions were keyed to the pace and order of development of topics in the text chosen for the classroom part of the course. The laboratory sessions were planned so that the statistical techniques used in lab would be covered first in class. Appendix B gives an outline of the laboratory manual.

21 We chose the Rossman (1996) text for use in the classroom part of the course. It recently received a good review in The American Statistician (Cryer 1997). Although this book is probably best used in a computer-equipped classroom, we felt we could adapt it successfully to an ordinary classroom with the help of graphing calculators. A graphing calculator version of this text is now available. The book covers an adequate number of topics for a first course. The most important feature, from our perspective, is the philosophy of having students learn the concepts by working on activities in class. The activities are arranged so that the concepts are motivated by questions arising from real data. The book asks the students to run a number of simulations in order to motivate ideas such as confidence and significance. Since the students would not have access to computers in the classroom, the instructors handed out copies of the relevant Minitab results in class. Students worked from these.

22 For the graphing calculator, the department members teaching the course opted to recommend that students buy TI-83 calculators. We chose this calculator because of its wide range of statistical capabilities. This calculator can be used in a traditional classroom to perform the in-class activities in the Rossman (1996) text that do not require simulations. Simulations can also be done if the students are provided with the necessary calculator programs. The calculator was recommended, rather than required, because of reluctance on the part of some faculty members. One faculty member was concerned about how much students would have to spend for the course. Another felt his lack of familiarity with the calculator would be a detriment. Yet another was not convinced that graphing calculators were necessary. The decision not to require that all students have a TI-83 turned out to be a mistake.

23 The method of instruction varied among the instructors. In all cases the classroom activities were done by students working in groups. Some professors, however, used permanent groups and cooperative learning methods. In this approach, students form permanent groups that work together both inside and outside of class. Articles in this journal, such as those by Garfield (1993) and Keeler and Steinhorst (1995) discuss this approach to learning. Other faculty members had students work in non-permanent groups in class with no requirements for working together outside the classroom.

24 The laboratories and classroom sections were scheduled separately. We wanted to give students greater flexibility in organizing their schedules. Students received a single grade for the course rather than one grade for the laboratory and another one for the classroom part. Laboratory sessions were graded on a satisfactory/unsatisfactory basis. A student receiving more than one unsatisfactory score incurred a one letter decrease in his/her course grade. In addition, students could correct and resubmit unsatisfactory laboratory reports. We did this because we wanted to encourage students to relax in lab and concentrate on the goals of the session. Questions related to laboratory work were included on classroom examinations. This served as a check to insure that students actually did the laboratory work.

4. Evaluation of the Course

25 Near the end of the first running of the course, students filled out a course evaluation questionnaire. A copy of the questionnaire codebook is given in Appendix C. Since the College conducts separate teacher evaluations, we asked students to concentrate on the course and, insofar as possible, not on their instructor. A number of the questions were aimed at the materials used in the course. We wanted to know how the Rossman (1996) text was received. We also wanted to determine how the laboratory manual needed to be revised.

26 As far as the Rossman (1996) text is concerned, students seemed to enjoy the in-class activities. About 55% cited this way of presenting the material as the best quality of the text. In addition, they liked the accessibility of the material and the interesting datasets. Interestingly, but not necessarily surprisingly, students felt that replacing worked-out examples with the in-class activities was the worst feature of the book. This resulted in about 61% of the students indicating that they felt the presentation was the worst quality of the text. Students told us that they tend to rely on examples to serve as templates for working on problems in mathematics courses. They found the removal of such support unsettling.

27 The philosophy of the laboratory manual was to present the new Minitab tools that would be needed for the session. They were described in a general sense and followed by an example of their use. The discussions and examples were not intended to serve as detailed descriptions of what was to be done in that particular lab session. This was because the techniques, such as stacking and recoding data, learned in one session would be used in later sessions. We hoped that students would get enough information from the discussion to figure out how to apply the new commands to the task at hand. This was somewhat optimistic. Approximately 52% of the students said that they wanted the discussion to be more closely related to the precise things they were being asked to do that week. In addition, about 50% of the students felt that the laboratory did not contribute to the course. This was, apparently, mainly due to frustrations with the manual.

28 The classroom instructors were interested in the responses to the questions regarding the best and worst aspects of the classroom sessions. About 87% of the students indicated that they really enjoyed working on the activities in a group environment. On the other hand, about 50% of the students said that they wanted the instructor to lecture more. Apparently, we needed to strike a balance between having students directly observe statistical concepts and using lecture to guide them through the material. Students seem to be less comfortable with less structured learning environments in mathematics courses than in other subjects.

29 We had the luxury of having a member of the faculty of our Sociology Department sit in on the course. He provided insight by experiencing the course from the perspective of a student. About half-way through the semester, his classroom section moved from a traditional classroom to one equipped with computers. He thought the course went much more smoothly once the computer classroom was used. He noted that, prior to moving, there appeared to be something of a "haves" versus "have nots" atmosphere in class depending on whether or not a student had a TI-83 calculator. This tension disappeared once the classroom change took place. It would have been better if we had either required each student to have that calculator or had not mentioned its existence. He felt that every section should use a computer classroom. In this way, the Minitab experience in lab and class could complement each other. He also remarked on the need for an increase in the amount of time spent lecturing.

30 The instructors who taught the sections of the new course were fairly uniform in recommending that the course be taught in a classroom equipped with computers. The approaches to using the text varied from a pure workshop approach to a mixture of in-class group work on the activities and formal lecture. Not surprisingly, student reactions were more positive in the latter setting. It is not clear how many of the problems in using the workshop approach can be attributed to the lack of experience on the part of the instructors with that method of conducting a class. Most instructors, however, felt that the course should be successful once we gained more experience in implementing it.

5. Changes Made

31 The lack of structure in the classroom part of the course was one of the main problems noted in the first teaching of the course. Students were uncomfortable working on the in-class activities without more frequent feedback from the instructor that they were doing the right things. In addition, faculty were dissatisfied with the slow pace of progress in the course. The Rossman (1996) text is designed to cover about two topics per week. With one exception, we covered only about three-fourths of that. Each faculty member learned what he/she needed to do differently to improve the pace of the course and to insure that students were learning what they needed from each topic. For the most part, this meant that we needed to hold students to more strict deadlines for completion of topics. Also we needed to be more diligent about giving each topic an introduction and a wrap-up. An introduction would help students understand the goals of the in-class activities. They would also be shown what to do to complete each activity. A wrap-up would reassure them that they had accomplished those goals. In addition, we tried to get as many sections as possible scheduled in computer-equipped classrooms.

32 In the laboratory part of the course, it was clear that the laboratory manual needed some revisions. The laboratory manual was rewritten in a couple of ways. Examples in the text were more clearly spelled out. Also, the laboratory activities gave more details on how to use Minitab tools to accomplish the necessary tasks. The first iteration of the laboratory manual was produced by the on-campus print shop. It was photocopied and bound. A number of students indicated that they felt the manual was a "rush job." In order to have a more professional-looking product, we used a textbook publisher to produce the revised manual. Also, some students disliked the fact that they did not receive a letter grade for all the effort they were putting into lab. We decided to give students grades for each session and to include these grades as part of the overall course grade.

33 The changes were implemented in the fall semester of 1997. We administered the same questionnaire near the end of the semester. The results for the two years are shown in Table 1.

Table 1: Comparison of Course Evaluations

Topic 1996 1997
Best quality of the Rossman text
Presentation 55% 56%
Activities 43% 41%
Other 2% 3%
Worst quality of the Rossman text
Presentation 61% 60%
Activities 35% 25%
Other 4% 15%
Lab did not contribute to course 50% 21%
Lab manual should relate more to text 52% 29%
Professor should lecture more 50% 14%
Liked working in groups 87% 84%

34 The results regarding the Rossman (1996) text remained relatively unchanged. The comments on the classroom sessions were, however, quite different. This time only 14% wanted the instructor to lecture more, while 84% still felt that group work was effective. Only 21% felt that the labs did not contribute to the course. In addition, only 29% wanted the explanations to be more closely related to that week's activities. This time there were no comments about the manual being a "rush job." With one exception, every instructor was able to cover about two topics per week. The exception was a faculty member who was teaching the course for the first time.

6. Summary

35 Members of the faculty of the College made sweeping changes in the basic statistics course provided for the social and life sciences by the Department of Mathematics. The departments involved engaged in an intensive collaboration. Previously, discussions regarding the course revolved around the list of topics to be covered. This time we gave intense scrutiny to the goals and purpose of the course. The result is a course that is significantly different from its predecessor not only in content, but in emphasis. The course attempts to give students an appreciation of how professionals in their major departments need and use statistics. We also give students a thorough grounding in statistical concepts. These goals are accomplished at the expense of breadth of topic coverage. We feel that the degree of interaction between the Department of Mathematics and the client departments was crucial in creating an approach to statistics instruction that gives the students an improved introduction to statistics.

36 The implementation of the new course was not without the expected problems. It was a learning experience for everyone involved in the course. The second teaching of the course went much more smoothly than the first. We have laid out our experiences in the hope that they will be of service to those who are in the process of revising their own curricula. The reactions of both students and faculty in the course indicate that, despite the rough edges, the new course is a distinct improvement over the more traditional one we used to teach.

Appendix A: The NSFH Dataset

The National Survey of Families and Households (NSFH) is a cross-sectional national probability dataset of 13,008 cases centered on family and household issues. The University of Wisconsin's Demography and Ecology Center collected the data in 1987-88. The survey includes a main sample of the non-institutionalized population of the US, 19 years of age and older, and oversamples (Stark and Roberts 1996) of Blacks, Puerto Ricans, Chicanos, single parents, persons with stepchildren, cohabiting persons, and persons recently married. Within households, one adult was randomly selected as the primary respondent. There is a main face-to-face interview with the primary respondent as well as a self-administered questionnaire covering sensitive topics. There is also a self-administered questionnaire completed by the primary respondent's spouse or partner when appropriate.

The NSFH data described below are a simple random sample of 2000 cases drawn from the full sample of 13,008 on 36 variables. The following list gives the variable names and a brief description of what each represents.