The Geometry of Multivariate Statistics

by Thomas D. Wickens (Author)

7 customer reviews

ISBN-13: 978-0805816563

ISBN-10: 9780805816563

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A traditional approach to developing multivariate statistical theory is algebraic. Sets of observations are represented by matrices, linear combinations are formed from these matrices by multiplying them by coefficient matrices, and useful statistics are found by imposing various criteria of optimization on these combinations. Matrix algebra is the vehicle for these calculations. A second approach is computational. Since many users find that they do not need to know the mathematical basis of the techniques as long as they have a way to transform data into results, the computation can be done by a package of computer programs that somebody else has written. An approach from this perspective emphasizes how the computer packages are used, and is usually coupled with rules that allow one to extract the most important numbers from the output and interpret them. Useful as both approaches are--particularly when combined--they can overlook an important aspect of multivariate analysis. To apply it correctly, one needs a way to conceptualize the multivariate relationships that exist among variables.

This book is designed to help the reader develop a way of thinking about multivariate statistics, as well as to understand in a broader and more intuitive sense what the procedures do and how their results are interpreted. Presenting important procedures of multivariate statistical theory geometrically, the author hopes that this emphasis on the geometry will give the reader a coherent picture into which all the multivariate techniques fit.

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Editorial Reviews

Review

A very valuable addition to the literature.
—CHOICE

The book is nicely written and proceeds step by step from bivariate regression to more complicated multivariate methods.
—Zentralblatt MATH

Hardcover: 174 pages
Publisher: Psychology Press (December 1, 1994)
Language: English
ISBN-10: 9780805816563
ISBN-13: 978-0805816563
ASIN: 0805816569
Product Dimensions: 6.2 x 0.8 x 9.5 inches
Shipping Weight: 13.6 ounces (View shipping rates and policies)
Average Customer Review: 7 customer reviews
Amazon Best Sellers Rank: #1,190,610 in Books (See Top 100 in Books)
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David Collins

Makes sense out of regression analysis

November 2, 2003

Format: HardcoverVerified Purchase

Well, actually, this book is applicable to much more than regression analysis, e.g., ANOVA and "general linear statistical models". It also helps make sense of univariate statistics, not just multivariate. Regression analysis, though, is the main application of the methods in this book. It will not substitute for Neter, et al. or any of the numerous texts on techniques of regression analysis; what it does is provide a simple geometric model for understanding regression. A couple of teasers: why does SSTO = SSR + SSE work in terms of degrees of freedom as well as the actual sums of squares? Where does that term, "degrees of freedom," come from anyway? The DF is the dimension of a vector subspace, as Wickens explains. What does the correlation coefficient really mean? Dig into that old linear algebra text, and you'll notice that it has the mathematical form of the cosine of the angle between two vectors in n-space - no coincidence. This geometric viewpoint was the basis for much or R. A. Fisher's early work, and has been unfortunately obscured since then. If you have a modicum of familiarity with vector spaces, and the ability to visualize, this book is an epiphany!

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Gary Wong

Great help for conceptual understanding, but better use with or after matrix.

June 15, 2015

Format: Kindle EditionVerified Purchase

A clear presentation of multivariate statistics (MS) from the geometric perspective. You will come across matrix in your learning journey of MS, and I bet you will be confused, if not desperately frustrated, by all those matrix notations and operations somewhere somehow. You realise that these are inevitable as matrix is the tools to get to the answers but somehow you will wonder why bother as all the calculations are done by the computer. The geometric presentation arrives as help at these moments: they probably have no use in calculation but are great for conceptual understanding.
But, be cautious that I don't mean you can throw away those matrix or standard MS textbooks: from my own experience, you get most from this book AFTER you had taken on, successfully or not, those thick and hard matrix stuff first.

4 people found this helpful

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March 31, 2012

Format: HardcoverVerified Purchase

There is a time when anyone seriously studying a subject has their 'a-ha' moment, and for me this came when I read this exquisitely simple but elegant explanation of 'statistics in pictures'. It is now just so easy to visualise all of those statistics that are typically rote learnt and understand how they fit together. This book is a masterpiece and should be introduced early into any budding statistician's toolkit. The only prerequisite is an introductory knowledge of the geometry of linear algebra; the rest follows naturally.

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June 3, 2018

Format: Paperback

Excellent linear algebra approach to basic regression. I took an intro regression course in college and many concepts were either poorly explained using calculus or taken for granted (which is bad considering I'm a maths major!). If you have studied linear algebra and have an affinity for vectors I recommend this book! It extremely easy to read, moves at a perfect pace, is easily understood, and is truly a beautiful piece to have in your collection.

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February 3, 2011

Format: Hardcover

Terrific book. As a previous review said, this is the only book I came across which uses geometrical intuition to build concepts in statistics. Its explanation of PCA was the cleanest I have come across.
Strongly recommended.

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Jump

not as hard as it looks

December 19, 2005

Format: Hardcover

The only book multivariate stats books Ive found that bases its approach on a geometrical interpretation of what is being done. It succeeds in imparting an intuitive picture of the ideas behind the math - very clearly written, and informative.

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Enkidum

Best stats text I've read

January 1, 2011

Format: Hardcover

I'm far from an expert in stats, indeed this was one of the texts for the third stats class I've ever taken. But I think that for anyone who can visualize vector spaces, as the previous reviewer said, it's certain to provide a powerful way of thinking about stats in general. It is broader than its title, as it gives a coherent account of univariate stats geometrically too, which really changed my understanding of the whole enterprise.

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