An Introduction to the Analysis of Variance

An Introduction to the Analysis of Variance

An Introduction to the Analysis of Variance

An Introduction to the Analysis of Variance

Synopsis

This book is for students taking either a first-year graduate statistics course or an advanced undergraduate statistics course in Psychology. Enough introductory statistics is briefly reviewed to bring everyone up to speed. The book is highly user-friendly without sacrificing rigor, not only in anticipating students' questions, but also in paying attention to the introduction of new methods and notation. In addition, many topics given only casual or superficial treatment are elaborated here, such as: the nature of interaction and its interpretation, in terms of theory and response scale transformations; generalized forms of analysis of covariance; extensive coverage of multiple comparison methods; coverage of nonorthogonal designs; and discussion of functional measurement. The text is structured for reading in multiple passes of increasing depth; for the student who desires deeper understanding, there are optional sections; for the student who is or becomes proficient in matrix algebra, there arestill deeper optional sections. The book is also equipped with an excellent set of class-tested exercises and answers.

Excerpt

In teaching the statistics course for first-year psychology graduate students, both in the past at the University of Illinois, Champaign-Urbana, and now at the University of Massachusetts, Amherst, I have encountered each year a group of students diverse in both their backgrounds and their objectives. Students continue to range from those with more than enough mathematical background to understand everything that is going on to those who have avoided things mathematical whenever they could. For some, the course contains information that they know they will need in order to do the work they have chosen. For others, the same course at first glance seems an obstacle to their getting down to the real work for which they came to graduate school. Fortunately, in almost every case the students have been highly motivated self-starters who have risen to the challenges the course offered.

Teaching in the face of this diversity has been my challenge, requiring that the basic statistical ideas be reviewed, the foundational concepts be provided, the tools of the trade be made available to those who will need them, and enough of the depth and the beauty of the formal structures involved be presented to interest and excite those who are capable of going beneath the surface. I have tried to do this in my teaching, and I have tried to do it in this book.

The material covered here, emphasizing the analysis of variance, has been presented in the second semester after a thorough grounding in probability and the logic of inferential statistics has been presented in the first semester. Both the geometric and the algebraic representations of analysis of variance and the general linear model are given because many students get the big ideas from the geometric representations when those ideas seem to be obscured by the algebraic equations. I have stressed the model equation as the basis of all that follows and have shown in detail how degrees of freedom, sums of squares, and expected values of mean squares are interrelated, and all flow from the formulation of the . . .

Search by... Author
Show... All Results Primary Sources Peer-reviewed

Oops!

An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.