First presenter Co-presenter(s)
Name :  Jaime Curts * Name:   
E-mail: E-mail:  
Affiliation: University of Texas Pan American Name:   
Department: Quantitative Research Methods  E-mail:    
City: Name:   
State/Province:   E-mail:    
Country: USA Name:   
01-09  E-mail:    
Session: 1- Computer Algebra in Education Schedule:
Thursday, 16:00
Related website:  
Title of
Teaching Principal Component Analysis in Minitab®
Slides of talk (PDF, 1595 Kb)

Slides of talk (PDF, 1595 Kb)

The purpose of this paper is to introduce the logical and arithmetic operators and simple matrix functions of Minitab® –a well-known software package for teaching statistics- as a computer-aid to teach Principal Components Analysis (PCA) to graduate students in the field of Education.

PCA, originally proposed by Pearson (1901) is a mathematical technique –a vector space transform- that has its roots in linear algebra and in statistics. Its main purpose is to reduce a correlated multidimensional data set to an uncorrelated lower dimensional space with maximum variance. PCA concepts can be a roadblock for non-mathematical oriented students, since statistical definitions (i.e., variance-covariance, correlation) need to be connected to matrix algebra (eigenvectors of a variance-covariance matrix) and to graphical vector representation (including matrix rotation).

Effective teaching of PCA requires students to develop a “feeling” for the intuitive sense of eigenvalues and eigenvectors and Minitab® provides a flexible vector-based environment and tools which students can use for meaningful learning of such concepts.

Though MINITAB by no means falls under the definition of a computer algebra system (CAS), it is well suited –among other functions- to manipulate, calculate, transform, and save data or matrices (transpose, inverse, eigen-analysis and matrix arithmetic) and has been reported to be successful teaching linear algebra (Greenwell, 1985). Following Güyer’s general taxonomy of computer aided mathematics education software (Güyer, 2008), Minitab® is here considered as a general purpose software that can efficiently be used as a teaching tool and may interact with other CAS. It is not as sophisticated as Maple® or Mathematica®, but the purpose here is to illustrate how to teach PCA by manipulating data sets and taking advantage of the software editing facilities (Bassett, Brooks, & Morgan, 1995).

This presentation will also show how to use the graphical capabilities of Minitab® and illustrate the bi-plot graphic display of matrices with application to PCA (Gabriel, 1971). Bi-plots can be used to support students’ conceptual and cognitive difficulties with the geometrical interpretation of eigenvectors and eigenvalues. Earlier, Gould (1967) suggested to consider a matrix of coordinates of points in space and interpret the eigenvalues and associated functions as geometric properties of the arrangements of these points.

Finally this paper wants to illustrate Minitab® as a learning tool to support graduate students in the field of Education in their conceptual understanding of reducing data dimensionality and other multivariate methods. These students are commonly introduced to PCA as one of the most commonly used exploratory data reduction procedure used in educational research at the same time they experience the analysis and computation of large number of variables. For such purpose ample examples of PCA guides to educational research exist (ex., Osborne & Costello, 2004; Pohlmann, 2004) and its application is evidenced by the wide range of educational research studies as exemplified by numerous perceived self-efficacy beliefs studies (e.g. Curts, Tanguma, & Peña, 2008; Dellinger, Bobbett, Oliver, & Ellet, 2008).