Teaching Factor Analysis in Terms of Variable Space and Subject Space Using Multimedia Visualization

Abstract

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 an 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 the subject space. At the end we apply the Gabriel biplot to combine the two spaces. Findings from a textbook review, a survey, and a “think aloud” protocol were taken into account during the program development and are discussed here.

• Biplot
• Eigenvector
• Hypermedia
• Vector space

Acknowledgements

Special thanks to Eldon Norton and Robert Sookvong for reviewing this paper. Also, special thanks to Natalie Schroeder and Gregory Van Eekhout for enhancing the multimedia program.