St. Joseph's University

Journal of Statistics Education v.2, n.2 (1994)

Copyright (c) 1994 by Sandra Fillebrown, 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**: Problem-based learning; Student-generated data;
Experiments; Surveys.

Two of the most common suggestions for improving statistics education are using substantial open-ended projects and using real data sets for statistical analysis. Both recommendations have been incorporated successfully into an elementary statistics class for non-science majors by having the students design, implement, and analyze the data from their own statistical study over the course of a semester. Details of how this implementation was organized as well as a partial list of the students' projects are included.

1 Recent articles (Hoaglin and Moore 1992; Moore and Witmer 1991) have encouraged mathematics departments to reevaluate their offerings in statistics. In response to these recommendations, the Department of Mathematics and Computer Science at St. Joseph's University now teaches an elementary statistics course for liberal arts and social science majors as one of their two required mathematics courses. The course stresses data analysis and presentation, sampling, and experimental design. Emphasis is on working with data rather than with formulas. (We use the book Concepts and Controversies by David S. Moore and cover chapters 1 through 5 and 7.) Almost all sections of the course use a spreadsheet or statistical package as an integral part of the course.

2 The current reform movement has encouraged faculty to consider new ways of actively involving students and new methods of evaluating student performance (Maher 1990; National Research Council 1991). In response to these suggestions, I decided to have my students do semester-long projects. I wanted them to have an immediate application for what they were learning in class, and I also wanted them to walk away from the course with an "end product." The students were required to design and carry out a statistical study and then present their data with a brief analysis in a report.

3 Having students do projects in a statistics course is not a new idea; descriptions of two successful implementations, one for engineering students and one for MBA students, can be found in Hunter (1977) and Roberts (1992). At St. Joseph's University, students (usually math majors) in our calculus-based statistics course are routinely required to do projects at the end of the semester. Students majoring in sociology and psychology take a research methods course in their major departments, in which they must complete a project. It seemed that requiring projects in an elementary statistics course would be just as valuable an experience, even if the projects were somewhat limited in scope.

4 One topic in this course is the effective presentation of data. For their projects, students had to include tables and graphs done with a spreadsheet. They were also encouraged to use the spreadsheet to do their statistical analysis. In many sections of this course, instructors (myself included) spend a significant amount of class time teaching the students to use a spreadsheet. The department has debated the advantages of spreadsheets versus statistical packages and for the moment has decided on spreadsheets. For many students taking the course, this is their only exposure to computer applications and a spreadsheet was seen as more useful. In addition, many faculty believe that having the students compute means, variances, correlations, etc. in a spreadsheet without using built-in formulas (at least at first) is important pedagogically.

5 The first day of class, students were told that they would be required to do a project. They were encouraged to work in pairs, as this has been shown to be a valuable learning experience. They would be turning in preliminary material and rough drafts throughout the semester that would be critiqued but not graded. There would be several deadlines during the semester, and although they might not understand everything that would be in the finished project as they were working during the semester, we would be covering topics in class well before they would be needed for a deadline. Many opportunities for feedback were built into the semester to help reduce the anxiety of the students and to make sure they were making steady progress. The students were also told that the final report was to look professional and must be done using a wordprocessor as well as the spreadsheet.

6 The guidelines given for the projects were purposely vague at the outset, but we discussed the projects and the students' progress regularly in class. As a result, none of the students complained about not knowing what was expected of them. They first had to choose a topic and whether they would do a survey, an experiment, or a study based on available data. Examples were given in each category, but the students were urged to choose a topic that truly interested them. They were told that they needed to get information about several different factors concerning their topic since they would be required to explore how the factors were related. Eventually they would examine associations between their variables by constructing tables of cross-classified data or computing correlation coefficients; however, it was difficult to make these requirements precise early on. The report was to consist of a detailed explanation of how or where they got their data, a display of their data in tabular and graphical form using the spreadsheet, and a brief summary of any interesting information they found. Because this course is an introductory course (we do not cover hypothesis testing, for example), the students were told that the analysis should simply be a reporting of facts and that they should not try to draw precise conclusions. The students were to summarize their data and provide any statistics that would help describe their data. They were to discuss any patterns or relationships they found, but they were warned to avoid making generalizations or cause and effect type statements.

7 The following is a summary of the timetable used, the requirements at each stage, and roughly what had been covered in class at each point:

- I. Description of Topic
- Deadline: week 4

Coverage: sampling and sampling design, experiments - The students were asked to choose a topic but very little detail was required at this point. They were asked to choose between a survey, an experiment, and a study based on available data and to describe in general what they wanted to explore. This first step allowed me to quickly weed out those projects that might have been too ambitious or too simple and those projects that would not meet the strict guidelines of the Committee on Human Subjects, the campus committee that must approve any research that uses students in any way. Since this was my first attempt using projects and I wanted things to go as smoothly as possible, I also vetoed any project that had the potential for controversy.
- II. Method of collecting data
- Deadline: week 5

Coverage: experimental design - The main purpose of this step was to have students give a more detailed description of their project. Students doing a study based on available data were to cite references and describe specifically what variables they would examine. Students doing an experiment were to describe in detail the design of their experiment and what provisions were made for reducing confounding and bias. Students doing a survey had to turn in their questionnaire, which was then submitted to the Committee on Human Subjects. They also had to describe how they intended to select their sample. At this step I was able to tell students whether their proposal met my guidelines for including variables that could be examined for possible relationships. Many students needed a great deal of feedback at this step to focus their ideas.
- III. Data in rough form
- Deadline: week 8

Coverage: measurement, reliability, validity, displaying data, graphs, histograms - At this stage students had to demonstrate that they had performed their survey or experiment or had located appropriate resources by submitting their data in some form. Students who did surveys and experiments turned in their tabulated data. Students who did studies based on available data turned in copies of their data. Many students turned in their data already in the spreadsheet, as we had by this time spent several class periods working with Quattro Pro.
- IV. Data in spreadsheet form
- Deadline: week 9

Coverage: mean, variation, normal distribution - Students had to turn in their data in a spreadsheet. They were encouraged to begin summarizing their data; displaying their data in charts, graphs, and tables; and looking for interesting relationships in their data. They were told that they could turn in their work for feedback as often as they liked. Most students took advantage of this option since they were unsure about what they could do with their data besides reporting the basics. We were about to begin the sections in the text on cross-classified data, linear regression, and correlation coefficients; as we covered these topics, many students turned in new tables and graphs for further comments.
- V. Rough draft
- Deadline: week 11

Coverage: cross-classified data, scatterplots, correlation, linear regression - At this point in the course we had finished the sections on linear regression and correlation, so students had all the information needed to finish the projects. They were given the opportunity to turn in more than one rough draft for comments.
- VI. Final drafts
- Deadline: week 13

Coverage: simple probability and simulation

8 The students' projects were on the whole very good. They were not advanced statistical studies, but good presentations of information. For each of the three types of studies, I was looking for different things to see whether the students had understood the basic underlying principles. Students who did surveys needed to describe how they chose their samples and how confident they were about whether it was a random sample. I also looked for statements about the populations they were trying to investigate and whether they thought they had been successful. Students doing experiments needed to describe their experimental design and the reasons for choosing the particular design. Students working with available data needed to carefully describe the variables and relationships they were investigating. I also looked for substantially more data description on these types of projects. Most of the final projects met these criteria successfully. A partial list of the projects is included as an appendix.

9 One recommendation I have to anyone considering assigning
projects is to spend some class time doing "sample projects."
After collecting their data, many students did not know what to do
next. Most class work involving data sets was an explanation of
**how** to do something with the data, not so much
**what** would make
sense to do, and this was the sticking point for most students.
Sometime around week 9, a good class exercise would be to either
provide data sets that might be appropriate for projects or
actually have a few students present the data from their projects.
Then the class, as a whole or in groups, could suggest what
should be done - what tables should be constructed, what graphs
would help illustrate the data, what comparisons would be
appropriate, what statistics should be computed, etc. This
exercise would have made my review of the rough drafts considerably
easier and reduced the number of office visits the preceding week.

10 My section of the course had 30 students. Although I encouraged students to work in groups, not many did, and there were 27 different projects. In terms of the amount of time required from me, it was a reasonable number. In a larger class, however, small groups would have to be mandatory. Although somewhat time-consuming, I feel that the continuous review process was extremely important. Most of the students in my class were freshmen and they found the periodic deadlines and feedback very reassuring. It also helped them regard the projects as a learning experience and not focus on the grade. Although I stated that I would look over their work before each deadline as many times as they liked, only a handful (3-4) asked me to do so. Most students found the written comments they received at each stage sufficient.

11 At the end of the semester the students were asked to critique the course including the project component. Of the 21 questionnaires completed, only three had negative responses to the project-related questions and these were complaints about the amount of time and effort the project and the computer work required. The rest of the comments were positive, indicating that the students thought the projects were a worthwhile part of the course and that they had learned something from doing it. Some of the more specific comments included the following:

- "The project was a good way to tie the course together."
- "The deadlines were reasonable and I did actually enjoy seeing the project go from its early stages to the final completed report."
- "It brought all the material together well."
- "The project was interesting because it was a topic of our choice."
- "[The project] made you look at statistics in a hands on way."

12 From my point of view, the projects made the course much more enjoyable to teach. It required more than the usual effort on my part as well as the students', but it was well worth the time. As the semester progressed, I found I was interested in the results the students were getting and looked forward to reading their reports. The next time I teach this course, I will definitely require projects again.

Some Projects Done by the Students

- Favorite color jelly beans; a survey was taken of a random sample of the student body as to their favorite color jelly bean and then separated by gender.
- Candidate preferences; a survey was taken of a random sample of the student body as to which presidential candidate they had favored before the November 1992 election and which candidate they thought would be doing the best job in the spring of 1993. Relationships between initial candidate preference, likelihood of change and party affiliation were examined.
- Weight room facilities; a survey was taken of a random sample of users of the new campus weight room as to their satisfaction level. Users were categorized by the extent of their use of the facilities, by gender and by whether they were varsity or non-varsity athletes.
- Changes in physical condition, eating habits and exercise habits; a random sample of freshmen were surveyed to see if their physical condition or eating and exercising habits had changed from high school to college. Results were tabulated for all freshmen and by gender.

- Economy vs. name brand laundry detergent; two different laundry detergents were compared as to their effectiveness in removing stains. An unbiased judge ranked the cleanliness of socks, stained with four different types of stains and then washed in one of the two types of detergents.
- Mailing times; the length of time letters took to arrive at several different destinations, with and without zipcodes, was measured (this was a suggestion from the textbook). Letters were sent to six different towns in different regions of the country, two with and two without zipcodes.
- Car manufacturers; the number of foreign and domestic cars passing a given location during a specified time period were recorded. Several similar intersections in different neighborhoods near Philadelphia were observed to see if the geographic location affected the ratio.

- Church attendance; the attendance records at a particular church were examined for Sundays when Holy Communion was offered and for Sundays when Holy Communion was not offered to see if this had any effect.
- Fraternity GPAs; the average grade point averages of all the students in a fraternity were compiled by semester and then grouped depending on the semester during which the student pledged. The GPAs were then compared with the average GPA of the general student population.
- Temperature and homicides; the average high temperature by month for Philadelphia (compiled from newspapers) and the number of homicides per month (obtained from the District Attorney's office) for a three year period were examined to see if there was a correlation between temperature and the number of homicides.
- Motor vehicle accidents, fatalities and DWI arrests; data from the _Statistical Abstract of the United States_ were used to examine the numbers of registered drivers and the rate of motor vehicle accidents, fatalities, and driving while under the influence arrests in the United States. The data were given for all drivers and then broken down by gender and by different age groups. The data were examined for several different years to see if there were any trends.

Hoaglin, D. C. and Moore, D. S. (eds.) (1992), Perspectives on Contemporary Statistics, MAA Notes No. 21, Washington, DC: Mathematical Association of America.

Hunter, W. G. (1977), "Some Ideas About Teaching Design of Experiments, with 2^5 Examples of Experiments Conducted by Students," The American Statistician, 31, 12-17.

Maher, R. J. (1990), "Mathematics Reform: Some Short Term Suggestions," Notices of the American Mathematical Society, 37, 1013-1015.

Moore, T. L. and Witmer, J. A. (1991), "Statistics Within Departments of Mathematics at Liberal Arts Colleges," American Mathematical Monthly, 98, 431-436.

National Research Council (1991), Moving Beyond Myths: Revitalizing Undergraduate Mathematics, Washington, DC: National Academy Press.

Roberts, H. V. (1992), "Student-Conducted Projects in Introductory Statistics Courses," in Statistics for the Twenty-First Century, eds. Florence Gordon and Sheldon Gordon, MAA Notes No. 26, Washington, DC: Mathematical Association of America, 109-121.

Sandra Fillebrown

Department of Mathematics and Computer Science

St. Joseph's University

Philadelphia, PA 19131

sfillebr@sju.edu

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