An International Journal on the Teaching and Learning of Statistics

## JSE Volume 10, Number 1 Abstracts

#### Ann A. O'Connell Student Perceptions of Assessment Strategies in a Multivariate Statistics Course

The purpose of this paper is to illustrate the use of several assessment strategies in an advanced course in statistics, and present the results of student ratings for each assessment strategy in terms of difficulty, appropriateness, level of learning achieved, and preference. The assessment strategies used include structured data analysis assignments, open-ended data analysis assignments, reviews of applied research articles, and annotating computer output of multivariate procedures. Findings indicate that students "prefer" instructor-directed or structured assignments overall, but feel they learn the most when the assessment is unstructured and requires greater self-direction. Suggestions for incorporating these assessment strategies into the multivariate classroom, as well as examples of each strategy, are included in this study.

Key Words: Classroom activity; Instruction; Multivariate analysis; Student perceptions.

#### Chong Ho Yu, Sandra Andrews, David Winograd, Angel Jannasch-Pennell, and Samuel A. DiGangi Teaching Factor Analysis in Terms of Variable Space and Subject Space Using Multimedia Visualization

There are many common misconceptions regarding factor analysis. For example, students do not know that vectors representing latent factors rotate in subject space, rather than in variable space. Consequently, eigenvectors are misunderstood as regression lines, and data points representing variables are misperceived as data points depicting observations. The topic of subject space is omitted by many statistics textbooks, and indeed it is a very difficult concept to illustrate. An animated tutorial was developed in attempt to alleviate this problem. Since the target audience is intermediate statistics students who are familiar with regression, regression in variable space is used as an analogy to lead learners into factor analysis in subject space. At the end we apply the Gabriel biplot to combine the two spaces. Findings from textbook review, survey and the "think aloud" protocol were taken into account during the program development and are discussed here.

Key Words: Biplot; Eigenvector; Hypermedia; Vector space.

#### Peter E. Kennedy More on Venn Diagrams for Regression

A Venn diagram capable of expositing results relating to bias and variance of coefficient estimates in multiple regression analysis is presented, along with suggestions for how it can be used in teaching. In contrast to similar Venn diagrams used for portraying results associated with the coefficient of determination, its pedagogical value is not compromised in the presence of suppressor variables.

Key Words: Detrending; Multicollinearity; Omitted regressor; Regression graphics; Teaching statistics.

#### Jamie D. Mills Using Computer Simulation Methods to Teach Statistics: A Review of the Literature

The teaching and learning of statistics has impacted the curriculum in elementary, secondary, and post-secondary education. Because of this growing movement to expand and include statistics into all levels of education, there is also a considerable interest in employing effective instructional methods, especially for statistics concepts that tend to be very difficult or abstract. Researchers have recommended using computer simulation methods (CSMs) to teach these concepts; however, a review of the literature reveals very little empirical research to support the recommendations. The purpose of this paper is to summarize and critically evaluate the literature on how CSMs are used in the statistics classroom and its potential impact on student achievement. The recommendation is that more empirically and theoretically grounded research studies are needed to determine if these methods improve student learning.

Key Words: Education research; Innovative instruction; Learning methods.

#### Teaching Bits: A Resource for Teachers of Statistics

This department features information sampled from a variety of sources that may be of interest to teachers of statistics. Deb Rumsey abstracts information from the literature on teaching and learning statistics, while Bill Peterson summarizes articles from the news and other media that may be used with students to provoke discussions or serve as a basis for classroom activities or student projects.

#### LeRoy A. Franklin and Belva J. Cooley An Experiential Approach to Integrating ANOVA Concepts

This paper presents a data set based on an industrial case study using design of experiments. The data set is pedagogically rich because it has a rather large total sample size from an industrial setting that naturally yields a large third order interaction term. The experiment is a 23 design and is initially presented with no replications. The sample size of the data is then doubled and the analysis repeated, comparing these results with previous results. The process is repeated until eight replications are available for each combination of factors and all parameters are estimated. With eight replications, the analysis shows all main effects and all interactions are statistically significant at the a = 0.05 level. With smaller sample sizes, various main effects and interactions are not found to be statistically significant. Through this presentation the instructor can lead students in discussions about the effect of increased sample sizes, power, statistical significance (or insignificance), interaction terms, Type I and Type II errors as well as the importance and the role of the error term. In addition, students can manipulate the data set in a computer laboratory setting to illustrate many of the concepts inherent in the design of experiments and analysis of variance.

Key Words: Cell means; Interaction; Parameter estimation; Power; Replication; Sample size.