Research

This paper describes an interactive Web-based tutorial that supplements instruction on statistical power. This freely available tutorial provides several interactive exercises that guide students as they draw multiple samples from various populations and compare results for populations with differing parameters (for example, small standard deviation versus large standard deviation). The tutorial assignment includes diagnostic multiple-choice questions with feedback addressing misconceptions, and follow-up questions suitable for grading. The sampling exercises utilize an interactive Java applet that graphically demonstrates relationships between statistical power and effect size, null and alternative populations and sampling distributions, and Type I and II error rates. The applet allows students to manipulate the mean and standard deviation of populations, sample sizes, and Type I error rate. Students (n = 84) enrolled in introductory and intermediate statistics courses overwhelmingly rated the tutorial as clear, useful, easy to use, and they reported increased comfort with the topic of statistical power after using the tutorial. Students who used the tutorial outperformed those who did not use the tutorial on a final exam question measuring knowledge of the factors influencing statistical power.

Researchers and educators have found that statistical ideas are often misunderstood by students and professionals. In order to develop better statistical reasoning, students need to first construct a deeper understanding of fundamental concepts. The Sampling Distributions program and ancillary instructional materials were developed to guide student exploration and discovery. The program allows students to specify and change the shape of a population, choose different sample sizes, and simulate sampling distributions by randomly drawing large numbers of samples. The program provides graphical, visual feedback that allows students to construct their own understanding of sampling distribution behavior. To capture changes in students' conceptual understanding we developed diagnostic, graphics-based test items that were administered before and after students used the program. An activity that asked students to test their predictions and confront their misconceptions was found to be more effective than one based on guided discovery. Our findings demonstrate that while software can provide the means for a rich classroom experience, computer simulations alone do not guarantee conceptual change.

This study examined the relative effects of cooperative vs. lecture methods of instruction. Two sections of an undergraduate statistics course were studied. Test scores were dependent variables. Students in one section were randomly assigned to cooperative groups. Students in both sections completed assignments and practice problems -- in the cooperative class in groups during class, and in the lecture class individually, outside of class. Students in the cooperative learning class achieved higher test scores. Implications of the study and resulting questions are discussed.

Using data from the 1997 Digest of Education Statistics, this teaching case addresses the relationship between public school expenditures and academic performance, as measured by the SAT. While an initial scatterplot shows that SAT performance is lower, on average, in high-spending states than in low-spending states, this statistical relationship is misleading because of an omitted variable. Once the percentage of students taking the exam is controlled for, the relationship between spending and performance reverses to become both positive and statistically significant. This exercise is ideally suited for classroom discussion in an elementary statistics or research methods course, giving students an opportunity to test common assumptions made in the news media regarding equity in public school expenditures.