The Political Methodologist vol no Book Review Review of by erinbeno


									16                                                                              The Political Methodologist, vol. 14, no. 2

                                                        Book Review

Review of Essential Mathematics for Political and Social Research, by Jeff Gill
 Ryan T. Moore
 Harvard University

Introduction                                                      and to remain relevant beyond the first week of everyone’s
        Jeff Gill’s new Essential Mathematics for Political        graduate career. empsr achieves both, by starting with
and Social Research (empsr) is one of few texts developed         extremely elementary material, incorporating over 100 ex-
for political scientists, by a political scientist, that moti-    amples (most drawn from actual, published social research),
vates the range of topics taught during a typical first gradu-     and still touching on topics that may not resurface until the
ate course in quantitative methods. Different programs in-         third or fourth graduate course in statistical methods.
volve different first courses – semester courses may focus on               The numerous examples provide instructors with a
probability and mathematical statistics, data analysis and        ready-made answer to a common question of new graduate
regression, or research methods broadly construed; one- or        students: “Why am I starting political science grad school
two-week pre-semester “math camps” also abound. empsr             with pure math?” Namely, “To learn useful tools for answer-
speaks to all of these settings, but focuses on short pre-        ing interesting substantive questions in politics.” Although
fresher courses. After some general comments about usage          the title suggests that empsr might be purely a primer in
in various settings, I trace empsr’s contents more system-        basic mathematics, the text highlights social science appli-
atically, and compare empsr to other popular introductory         cations. Prominent examples follow in the next section.
materials.                                                                New graduate students and those anticipating grad-
        empsr could serve as the primary or secondary text        uate study should find comfort in empsr’s approachable
in many introductory settings. The range of topics suf-           style, its warnings of common confusions, and in the con-
fices to fill a semester-long course on prerequisite mathe-         nections it draws between the mathematics and the sub-
matics, especially in departments where new graduate stu-         stantive questions of interest. empsr’s chapters begin with
dents may arrive with little quantitative background. De-         explicitly-stated objectives, helping to socialize new politi-
partments that begin graduate training with data analysis         cal scientists into the academic discipline. Reference tables,
and regression could view the text as a prerequisite to pro-      intuitive explanations, chapter lists of new terminology, and
gram entry, and encourage summer study by their incoming          the relevance and volume of the topics all imply that empsr
classes. The wealth of applied examples could inform dis-         will be helpful in the early days, but also a well-worn text
cussion in courses on general social science research meth-       by the time students finish their degrees.
ods, either at the graduate or undergraduate level. Given
their breadth, however, such courses may not invest the time      Concepts and Examples
required for mastery of most mathematical skills empsr ad-               empsr begins with the most elementary mathemat-
dresses. Math camp courses should seriously consider using        ical topics required for quantitative research: arithmetic,
empsr as their primary text, and Gill offers several tem-          notation, and functions. However, by page 5 students have
plates for doing so. My experience with empsr is largely          already encountered something that political scientists will
as an instructor of one such course; thus, although empsr         recognize as being of significant value: Riker and Ordeshook
can contribute in several settings, a math camp perspective       (1968)s model for voter utility, R = P B − C. Although
dominates this review.                                            simple, this model is still widely discussed; in 2006 alone
        The students’ diverse set of backgrounds, aptitudes,      it has appeared in the apsr, ajps, bjps, and jop. The
and interests creates much of the difficulty in teaching a          second chapter covers analytic geometry and includes the
successful first methods course in political science. In many      most relevant topics from a high school trigonometry course.
programs, future philosophers sit next to future statisti-        Political-scientific examples include parabolic presidential
cians. This diversity particularly complicates a math camp        approval and elliptical voting preference models.
textbook’s two-fold charge: to enable all students to feel rea-          Chapters 3 and 4 straightforwardly introduce linear
sonably well-prepared on the first day of a term-time course,
The Political Methodologist, vol. 14, no. 2                                                                                  17

algebra. Chapter 3 defines vectors, matrices, operations,         ity, reversibility) and state characteristics (recurrent, ab-
and related properties. Central topics in Chapter 4 in-          sorbing, transient, closed). Gill demonstrates the utility of
clude the geometry of matrices, the determinant, eigenval-       Markov chains as descriptive of social processes in their own
ues, quadratic forms, and inverses. Example 4.6, a two-page      right, but the underlying motivation may be to lay founda-
exercise in estimating ols regression parameters, provides       tions for future Bayesian work.
an introduction to a ubiquitous application of matrix alge-
bra to political science data.                                   Comparisons and Conclusions
        Scalar and vector calculus fill Chapters 5 and 6,                  There are many candidate materials for political sci-
which include traditional definitions and applications of lim-    ence math camps. Instructor’s notes, Simon and Blume
its, derivatives, and integrals. Example 5.9 applies scalar      (1994), Morgan (1997), and Hagle (1996) appear particu-
calculus to another mainstay of political science, the Median    larly common. empsr contrasts with Hagle and Morgan in
Voter Theorem of Black (1958). empsr highlights often-           two primary ways. First, empsr’s scope is broader. The
used skills such as extrema- and root-finding, multiple inte-     last third of empsr covers probability and statistics mate-
gration, and vector differentiation. Foundations such as the      rial omitted from the other two texts, for example. Second,
gradient and Hessian, Lagrange multipliers, and constrained      the exercises and examples in empsr are significantly more
optimization appear.                                             applied than those of Hagle or Morgan.
        The pre-statistics section of empsr begins with prob-             One’s preference for adopting empsr may hinge on
ability theory in Chapter 7. True to his Bayesian roots, Gill    whether one prefers the clear lines of fundamental skills
opens the chapter with a discussion of subjective versus ob-     repetition or the more thought-provoking and interpretive
jective probability. This chapter includes set-theoretic def-    fuzziness of examples of political science research. To illus-
initions and properties, probability functions, conditional      trate the difference, consider the problem sets on differentia-
probability, Bayes’ rule, Simpson’s paradox, and indepen-        tion. Hagle’s includes six consecutive questions instructing
dence. empsr also demonstrates odds, a topic that political      simply, “Find the derivatives of the following functions.”
scientists often encounter, but may have less prior exposure     Meanwhile, empsr sandwiches its one such question be-
to than some other social researchers (like epidemiologists).    tween exercises using published political research on subur-
        Chapter 8 covers random variables, and includes a 4-     ban demographics and the siting of US county seats. Exer-
page discussion of levels of measurement. empsr introduces       cises in Hagle, Morgan, and Simon and Blume are also split
familiar distributional families as models for social data-      into relatively small, homogeneous sections, while those of
generating processes: Bernoulli and binomial data, Pois-         empsr are collected at chapters’ ends. The former design
son counts, and uniform, exponential, gamma, and normal          encourages rote repetition, while the latter can obscure basic
Gaussian phenomena all appear. This chapter’s wealth of          skills, but more accurately reflects the problems and choices
applied modeling examples includes Supreme Court deci-           students of methodology will face.
sions, legislative bill passage, strategic alliance formation,            In my view, occasional over-complexity is the weak-
incidence of war, income distributions, probit analysis of       ness of empsr. While the variety of examples is generally a
vote choice, and the presence of women in US state legis-        strength of empsr, sometimes there is too much of a good
latures. The last of these features a quantile-quantile plot,    thing. For example, in demonstrating inner products and
thus giving a welcome introduction to model fit diagnostics.      cross products, Examples 3.6 and 3.8 use the same defi-
        Only after these examples does empsr cover mea-          nitions for 1 × 3 vectors u and v, but Example 3.7 uses
sures of central tendency and spread. This ordering is con-      different ones. Using consistent definitions would simplify
sistent with texts like Rice (1995), but can lead to discus-     the matter and allow readers to focus on understanding the
sion of these measures that precedes their formal definition.     algebra. For a math camp, empsr’s problem sets are long
empsr succeeds more than Rice in minimizing such discus-         and include some potentially intimidating problems. Select-
sion, but does not avoid it entirely as do treatments like       ing exercises to assign will require judicious consideration of
Purves (1991). Other topics include summary statistics’          one’s audience. Also, at this time, an answer key is still in
breakdown points, correlation, expected value inequalities,      development. Until its release, instructors may have to sup-
and distributions’ moments and central moments. A die-           ply their own solutions.
rolling example illustrates expected value, as does an ex-                On the whole, empsr succeeds. Its range and depth
tended sequence of calculations derived from craps bets.         of topics form appropriate standards for incoming and con-
        The last chapter is somewhat unexpected. Here,           tinuing political science graduate students. Its constant at-
Gill introduces Markov chains, a topic that most political       tention to published research introduces budding profession-
scientists might not encounter until they take a course in       als to exactly how and why learning mathematics is an im-
Bayesian modeling or data analysis. The chapter elucidates       portant first step.
major chain concepts (periodicity, homogeneity, irreducibil-
18                                                                            The Political Methodologist, vol. 14, no. 2

                       References                                    A.K. Peters.

     Black, Duncan. 1958. Theory of Committees and                Rice, John A. 1995. Mathematical Statistics and Data
        Elections. Cambridge: Cambridge U Press.                     Analysis. Belmont, CA: Duxbury Press.

     Freedman, David, Robert Pisani and Roger Purves.             Riker, William H. and P.C. Ordeshook. 1968. “A
        1991. Statistics. New York: Norton.                          Theory of the Calculus of Voting.” American
     Hagle, Timothy M. 1996. Basic Math for Social                   Political Science Review 62 (1):2542.
       Scientists. Thousand Oaks: Sage.
                                                                  Simon, Carl P. and Lawrence Blume. 1994. Mathematics
     Morgan, Frank. 1997. Calculus Lite. Wellesley, MA:              for Economists. New York: W.W. Norton.

                                                   Section Activities

A note from our Section President                               plications are available at:
                                                                methods2007/register/. We thank the program commit-
I would like to offer a hardy thank you to Adam Berinsky,        tee, Rebecca Morton (chair), Suzanna DeBoef, Burt Mon-
Michael Herron, and Jeff Lewis for their hard work and ded-      roe, Kevin Quinn, and Jake Bowers for their hard work and
ication in producing The Political Methodologist for the past   dedication in bringing together the meeting. The National
three years! It is an invaluable communication tool for the     Science Foundation, in conjunction with Penn State Univer-
section. Please join me in welcoming the new TPM editors,       sity, will continue to support 35 graduate students through
Paul Kellstedt, David Peterson, and Guy Whitten. We look        a competitive process. We thank the Graduate Student Se-
forward to continued success of TPM under the guidance of       lection Committee for their work as well. The committee
the new Texas A&M editors.                                      includes Dan Wood (chair), Michele Claiborne, David Dar-
        Nominations for the second annual John T. Williams      mofal, and Kevin Clarke.
Dissertation Prize are being solicited. The prize is given              We now have over sixteen active committees. A full
in recognition of John T. Williams’ contribution to gradu-      listing of all the committee members and a list of their
ate training and is for the best dissertation proposal in the   charges is available on the Political Methodology website:
area of political methodology. Proposals using quantitative We thank for
or qualitative methods are welcomed and should follow the       Andrew Martin and Stephen Haptonstahl at Washington
National Science Foundation length and format guidelines.       University for their work on the website. They provide
Members of the committee are John Aldrich (chair), Tse-         ths excellent service for the section gratis. I want to high-
Min Lin, and Michael Colaresi. Materials should be sent to      light one new committee, the Undergraduate and Graduate
the John Aldrich at                           Methodology Committee, which is chaired by Lonna Atke-
        The 24th Annual Summer Meeting of the Society for       son. Other committee members include Garrett Glasgow,
Political Methodology will be held at Pennsylvania State        Paul Gronke, Dean Lacy, and Alan Zuckerman. Agenda
University, July 19-21. The hosts, Suzanna DeBoef and           items include: 1) developing best practices for departments
Burt Monroe, have information about the conference avail-       and students in order to be prepared for graduate school
able on the conference website at: http://polmeth.psu.          in political science; 2) increase the availability of methods
edu/. The past success and popularity of the meetings have      syllabi; 3) sponsor panels at the APSA Teaching and Learn-
led the Society’s membership to support the recommenda-         ing Conference on undergraduate and graduate methods;
tion of the Long Range Planning Committee by implement-         4) brainstorm about what the section should be doing for
ing an alternative model for the meeting to accommodate         it’s members who are at schools where there is significant
increased demand. In an effort to extend participation, the      emphasis on undergraduates and teaching; 5) explore best
meeting size is growing substantially. With increased size,     practices for interdisciplinary methods training for graduate
however, come some inevitable changes. The basic program        students. Please contact them if you want to get involved
format and the venerated graduate student poster session        or have an idea to share with them.
will remain. The host institution will be providing break-              Best wishes,
fast and lunch for the participants throughout the confer-
ence and will host a dinner and a reception in 2007. All                                             Jan Box-Steffensmeier
other expenses (notably, hotel accommodations and remain-                                        The Ohio State University
ing dinners) will be covered by attendees. Registration ap-

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