Teaching Statistics Visually: A Quasi‐Experimental Evaluation of Teaching Chi‐Square through Computer Tutorials¹

1. An earlier draft of this paper was presented at the 2005 Annual Meeting of the American Society of Criminology in Toronto, Canada.

Abstract

This paper examines the effectiveness of computer graphic tutorials in explaining statistical concepts to undergraduates enrolled in two sections of criminal justice research methods. We demonstrated key concepts to a treatment group through a Microsoft Excel spreadsheet and Macromedia Flash movies. The students’ statistical skills were measured through a test on mathematical calculation and multiple‐choice questions about chi‐square concepts. Both sections scored similarly on the skills test; however, the treatment group performed better on the conceptual questions. We discuss the implications for teaching methods and statistics and offer several resources that instructors can use in their courses.

1. An earlier draft of this paper was presented at the 2005 Annual Meeting of the American Society of Criminology in Toronto, Canada.

Acknowledgments

The authors thank Natalie Metz for her help with data collection and Thomas Mitchell from SIU’s Department of Economics for inspiration. We also thank the anonymous reviewers. Finally, we thank our good cousins of the Carbonari for their helpful comments on an earlier draft.

Notes

1. An earlier draft of this paper was presented at the 2005 Annual Meeting of the American Society of Criminology in Toronto, Canada.

2. A free on‐line version of Felder and Solomon’s instrument and documentation is available at http://www.engr.ncsu.edu/learningstyles/ilsweb.html. In addition to an on‐line survey, the authors provide tips for learning for each of the styles.

3. The authors thank Dr. Richard Felder for providing us with this example.

4. The motivation for creating the tutorials began when the first author of this study began using color‐coded handouts that would match formula symbols with numbers in the calculation. In the standard deviation formula, for example, the symbol for the mean () was colored blue as well as the value of the mean in the computation; the symbol for the sample size (n) was colored red. Thus, students could match the symbol with its value through color. Given the anecdotal success with this color‐coding scheme in an undergraduate statistics course, the handouts were converted into interactive tutorials. Students could “point and click” on various parts of a formula to activate an informational popup box.

5. In this last step, the instructor discussed how to evaluate the hypothesis overall based on the calculations obtained in steps 7 and 8.

6. The figures presented in this paper are limited in demonstrating the utility of the Excel and Flash tutorials, especially since we can only present single frame instances in black and white. We therefore encourage the reader to examine each of the tutorials to get an appreciation for the interactivity. For some of the tutorials, we changed the color scheme to create the appropriate contrast in black and white. All the tutorials are available at http://mypage.siu.edu/gburruss/tutorials.

7. A copy of the Excel file is available at http://mypage.siu.edu/gburruss/tutorials/chisquare_calculator.xls. To open the excel file from your web browser, you will need to allow the macros to run; they do not contain any viruses. If you do not have a registered copy of Microsoft Excel, you may download a free viewer at http://www.microsoft.com/downloads/.

8. Both groups had permission to use a calculator during the lecture, on their homework assignment, and during the test. This is a common practice and tends to reduce math anxiety.

9. This tutorial is not shown here but is available at http://mypage.siu.edu/gburruss/tutorials/contingency.swf.

10. The Flash viewer can be obtained free of charge from Adobe (http://www.adobe.com).

11. The distribution tutorial is available at http://mypage.siu.edu/gburruss/tutorials/distribution.swf.

12. In addition to the visual appeal of the Flash tutorial, we also added a bit of humor: the rider screams when he fails to clear the hurdles and is swarmed by flies as the dust settles from his fall. A reviewer raised the concern that the horse‐and‐rider analogy can be misleading: failing to reject the null hypothesis is a literal failure and therefore bad. We weighted this concern against the benefit of getting students, especially undergraduates, to make the correct decision about rejecting the null hypothesis when comparing the chi‐square obtained to the chi‐square critical. We feel this benefit outweighs any shortcoming. Nevertheless, instructors may wish to use our analogy to discuss this issue and point out the analogy’s limitations.

13. The significance tutorial is available at http://mypage.siu.edu/gburruss/tutorials/significance.swf.

14. The phi tutorial is available at http://mypage.siu.edu/gburruss/tutorials.phi.swf.

15. A factor analysis of the chi‐square test showed that the calculation questions loaded on two factors‐one for calculating column percentages and one for the chi‐square statistic and expected values. The definitional and interpretation questions loaded on separate factors.

16. Because the test is several pages long, we do not include a copy here; however, a copy is available from the first author.

17. A reviewer raised the issue of external validity because we did not give partial credit on calculations. Since many statistics instructors give partial credit, our scheme for grading may invalidate test comparisons. However, we felt that subjectively giving partial credit would cause reliability problems with the grading scheme. Moreover, we were not evaluating the effectiveness of the statistics test itself; thus, external validity was not an issue for the results of the study.

18. The scale is as follows: 0 or 1 is a strong verbal preference, 2 or 3 is a moderate verbal preference, 4 or 5 is a mild verbal preference, 6 or 7 is a mild visual preference, 8 or 9 is a moderate visual preference, and 10 or 11 is a strong visual preference (Felder and Spurlin 2005). We contemplated measuring the other dimensions of learning styles, sensing/intuitive, active/reflexive, and sequential/global; however, we wanted to keep the survey manageable.

19. The MERLOT website can be accessed at http://taste.merlot.org/catalog/.

20. The Educause can be accessed here: http://www.educause.edu/

21. The Just in Time Teaching website can be accessed here: http://www.jitt.org/