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Siegel&Morgan review
Posted:
Apr 26, 1996 1:30 PM
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Book Review
> Statistics and Data Analysis: An Introduction (2nd ed.)
> Andrew F. Siegel and Charles J. Morgan
> Wiley, 1995, $68, ISBN 0471574244
>
> This book is the second edition of an underground classic first
> published in 1988. The first edition (by Siegel alone) was
> reviewed for Volume 26 of STN (December 1990) by Joan Garfield.
> She used it for many years at the University of Minnesota, and
> colleagues and I used it at Plymouth State College until last
> summer. It recently showed up as one of the seven textbooks the
> College Board is recommending for the new Advanced Placement Test
> in Statistics. Even so, it is no secret that the book was not a
> great success in the marketplace. The second edition attempts to
> broaden the book's appeal. I think it succeeds, but sometimes at
> the expense of muting a few of the virtues that made the first
> edition so outstanding.
>
> One of those virtues is the writing. The first edition was by
> far the most readable introductory statistics text I have ever
> used. It was also written in a warm and friendly tone that
> remains unusual in statistics textbooks. The second edition
> maintains a high level of readability. The warmth is somewhat
> diluted.
>
> Another thing that set the book apart was its content. Although
> the NCTM Standards suggest big changes in how mathematics is
> taught, and smaller changes in what mathematics is taught, the
> underlying mathematics has not changed much. One and one still
> is two, and has been for quite some time. Statistics, on the
> other hand, underwent a great revolution in the 1960's, a
> revolution often linked with the name of John Tukey. One of the
> first things I look for in a statistics textbook is whether there
> is any sign that the author has heard about this revolution yet.
> Because so many statistics textbooks are written by
> non-statisticians, the news has spread very slowly. Andrew
> Siegel was part of the Tukey revolution, and I think that is one
> reason why the first edition was ahead of its time. All the good
> K-12 statistics materials from NCTM and QLP are definitely
> post-Tukey, but many college textbooks still are not. Caveat emptor.
>
> One sign of Tukey's influence is the use of stem (and leaf) plots
> and box (and whisker) plots. These are a necessary condition
> for textbook adoption these days, but alas not a sufficient one.
> A few of you may remember the "new math" era, when set ideas were
> supposed to unify all of mathematics. We then saw textbooks that
> sprouted an obligatory "Chapter 0" where set notation (not ideas)
> was introduced, and then forgotten, and certainly never used to
> unify the rest of the content. Similarly, we have reached the
> point where most textbooks now mention the stem and leaf or
> boxplot, but many really don't know what they are for, and so
> never use them for anything.
>
> Another way people characterize the Tukey revolution is in terms
> of the "three R's" of post-Tukey statistics
>
> residuals
> reexpression
> robustness
>
> Residuals are usually first encountered in the context of fitting
> lines to data. There they are the (signed) distances between the
> points and the fitted line. Analyzing them helps us to evaluate
> how well our straight line model fits the data. Siegel and
> Morgan introduce residuals very early -- the deviations from the
> mean that figure in the computation of variance and standard
> deviation are presented as residuals. Toward the end of the book
> there is a masterful example of the use of residuals in
> regression analysis. Data is presented on the average heights of
> girls for ages 2-11. Height versus age looks like a nearly
> perfect straight line, and the correlation is 0.997. Yet a graph
> of the residuals shows pronounced curvature in the relationship,
> something you would never see without examining the residuals!
> (Although the book does not mention it, fitting a quadratic to
> the data gives a residual plot that clearly indicates a cubic
> component!) This is an example of one of the great strengths of
> this book -- it not only shows you the latest techniques, it shows
> them to you in examples that indicate what the technique does for
> you and why it is important, rather than with examples that merely
> show you the mechanics of carrying out the technique. Without
> the "why", the "how" is useless.
>
> Reexpression is more often called "transformation". Perhaps the
> most traditional example of that is the fact that some
> relationships are better plotted on logarithmic or
> semilogarithmic graph paper. The TI-82 calculator uses such
> transformations (taking logs of x or y or both) to fit a variety
> of models to two-variable data. The first edition of Siegel
> contains the best elementary introduction to the use of
> transformations in statistics. They are introduced early in the
> book and used in both the analysis of variance and regression
> chapters. The second edition contains the second-best elementary
> introduction to the use of transformations in statistics. The
> initial coverage is cut about in half, and the applications to
> regression have disappeared. This is especially unfortunate for
> use in the high schools, where the logarithmic and exponential
> curve fitting features have found many uses in mathematics and
> science classes, and raised a lot of questions and confusion
> among teachers about what is going on there. In this instance, I
> think Wiley has stepped backward too far. While the first
> edition may have been (too far?) ahead of its time, much has
> changed since 1988, and in this area the second edition is behind
> the times -- though still ahead of most other textbooks!
>
> The third R, robustness, refers to the the ability of a statistical
> measure or technique to resist the effects of errors and outliers
> in the data, or violations of the assumptions underlying the
> technique. The traditional mean and standard deviation are not
> very robust to outliers, and so the more robust median and
> interquartile range are preferred in many situations. (Note that
> the boxplot is based on them.) Siegel and Morgan introduce these
> robust measures first, and present them as the standard tools.
> The mean and standard deviation are then introduced as
> specialized tools particularly appropriate to normally
> distributed data. This makes it clear that the Tukey revolution
> really was a revolution -- it not only introduced additional
> techniques, but changed the way statisticians regard the older
> techniques. Siegel and Morgan understand this, but many other
> textbook authors do not.
>
> The new edition extends the coverage of nonparametric techniques.
> These are techniques that make fewer assumptions than the
> traditional techniques, and generally handle outliers better.
> They may be less efficient if your data really are drawn from a
> normal distribution, but safer if they are not, or if you cannot
> tell, as with small samples.
>
> One serious flaw in the first edition was the very small number
> of problems for students. I would estimate that the new edition
> has three to five times as many. There are answers to about half
> of these, and the answers contain more words than numbers. The
> words deal with interpretation of the data, which, after all, is
> what statistics is all about. There is also an Instructor's
> Solution Manual in the works with more detailed solutions. (I
> put it on reserve in the library for student use.)
>
> Another criticism of the first edition was that it contained
> hardly any formulas. Calculations were explained in a manner
> resembling instructions for filling out your income tax forms.
> Personally, I saw this as an asset. I teach a general education
> statistics course to first and second year students at a small
> former state teachers' college. For most of these students,
> formulas would be a barrier to understanding rather than a path
> to understanding. However, if you are a high school teacher
> trying to show students the use of algebra in statistics, you
> will want to see formulas. If you are a high school teacher
> doing an AP Statistics course, you will want to keep your
> students' algebra skills reasonably fresh for when they take the
> SAT and go on to college. Indeed, the sample questions
> distributed for AP Statistics require much more algebraic
> facility than most of my college students have. For those who
> like a little algebra in their statistics, the second edition of
> this book is now bilingual.
>
> Indeed, the second edition is trilingual. The steps of carrying
> out a procedure are given in words, in formulas, and in commands
> for the Minitab statistical software. The computer examples do
> not replace a manual for the software; often you see just the
> final steps of an analysis, without any explanation of how they
> set up the database or how they got to the last step. At least
> the examples get you started and provide some experience in
> interpreting computer printout in situations where no computer is
> available. I think the choice of the Minitab software package is
> a good one. There are versions of Minitab for DOS, Windows,
> and the Macintosh. The software was originally designed for
> educational purposes, and is probably the most widely used
> software in college statistics courses, yet it is also used by a
> majority of the Fortune Top 50 companies in the US. It was also
> one of the first packages to reflect the Tukey revolution. A
> disk containing most of the data sets from the book is promised.
> The draft disk I examined had some bugs in it but there were
> about 100 data sets, some of them definitely too large to ask
> students to type in.
>
> There is no mention of calculators in either edition of the book.
> That does not bother me, since a computer is a much more
> appropriate tool for statistics, but it may bother some high
> school teachers for whom graphing calculators are more familiar
> and accessible to both themselves and their students. While we
> all have to do the best we can with what we have, I hope prior
> comfort levels with calculators will not divert teachers from
> pressing for more appropriate technology.
>
> One of the limitations of calculators in statistics is their
> limited data storage capacity. This book "recycles" many of its
> data sets over and over, using them to illustrate a number of
> different points. Sometimes a question raised in one chapter is
> not fully answered until a later chapter when the same data is
> examined again. I think this is a good technique, but I would
> hate to have to constantly be retyping or reloading the data into
> a calculator.
>
> My biggest disappointment with this text is that it does not do a
> very good job of convincing the student that statistics is
> important. There are many real data sets, and they are often
> extremely well chosen to illustrate the techniques, but the
> techniques are not often used to answer any real question of
> interest. For example, the areas of important islands in the
> Atlantic Ocean are used as an example of transforming data. It
> is a wonderful example for that purpose. If you plot the data on
> a linear scale you get Greenland at one end of the graph and a
> big smudge including all the other islands at the other end. You
> can not even get a legible graph without transforming this data.
> However, no reason is ever given as to why we might want to study
> the areas of these islands. We come away from the example
> knowing more about statistics, but we do not know any more about
> islands. This is sad, because statistics is primarily a tool to
> answer real questions in areas outside of statistics. I should
> make it clear that the present book is not outstandingly bad in
> this regard. It is actually somewhat above average. However, it
> is a failing of most textbooks that has come to bother me more
> and more each year. You will need to supplement this one (and
> most others) with some more motivating and realistic examples.
>
> One potential supplement would be _Statistics by Example_ by
> Sincich (Dellen). This book contains a huge number of problems
> based on real studies. Often the background is too sketchy or
> too technical, and sometimes we get only summary statistics
> rather than raw data, but there are so many problems that it is
> still a worthwhile resource. (The book is pretty ordinary
> otherwise, with only slight signs of Tukey-awareness.)
>
> My colleague Bill Roberts and I are currently half way through an
> introductory statistics course using the Siegel and Morgan text,
> and we are quite happy with it. I urge anyone looking for a
> textbook to adopt to look at it. Those wanting to learn more
> about statistics themselves might want to try to dig up a copy of
> the first edition.
>
>
> Reviewed by Robert Hayden
> Plymouth State College
> Plymouth, New Hampshire
>
> *********************************************************
>
--
_
| | Robert W. Hayden
| | Department of Mathematics
/ | Plymouth State College
| | Plymouth, New Hampshire 03264 USA
| * | Rural Route 1, Box 10
/ | Ashland, NH 03217-9702
| ) (603) 968-9914 (home)
L_____/ hayden@oz.plymouth.edu
fax (603) 535-2943 (work)
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