THE CHICAGO GUIDE TO WRITING ABOUT MULTIVARIATE ANALYSIS

THE UNIVERSITY OF CHICAGO PRESS

Contents

CHAPTER 1

Introduction

Writing about multivariate analyses is a surprisingly common task. Resultsof ordinary least squares (OLS), logistic, and other kinds of multivariateregression models inform decisions of government agencies, businesses,and individuals. In everyday life, you encounter forecasts aboutinflation, unemployment, and interest rates in the newspaper, predictionsof hurricanes' timing and location in television weather reports, andadvice about behaviors and medications to reduce heart disease risk inmagazines and health pamphlets. In many professional fields, multivariateanalyses are included in research papers, grant proposals, policy briefs,and consultant's reports. Economists and meteorologists, health researchersand college professors, graduate students and policy analysts all needto write about multivariate models for both statistical and nonstatisticalaudiences. In each of these situations, writers must succinctly and clearlyconvey quantitative concepts and facts.

Despite this apparently widespread need, few people are formallytrained to write about numbers, let alone multivariate analyses. Communicationsspecialists learn to write for varied audiences, but rarely aretaught specifically to deal with statistical analyses. Statisticians and researcherslearn to estimate regression models and interpret the findings,but rarely are taught to describe them in ways that are comprehensible toreaders with different levels of quantitative expertise or interest. I haveseen poor communication of statistical findings at all levels of trainingand experience, from papers by students who were stymied about how toput numbers into sentences, to presentations by consultants, policy analysts,and applied scientists, to publications by experienced researchersin elite peer-reviewed journals. This book is intended to bridge the gapbetween correct multivariate analysis and good expository writing, takinginto account your intended audience and objective.

Audiences for Multivariate Analyses

Results of multivariate analyses are of interest to a spectrum of audiences,including:

• legislators, members of nonprofit organizations, the general public,and other "applied audiences" who may have little statistical trainingbut want to understand and apply results of multivariate analysesabout issues that matter to them;

• readers of a professional journal in your field who oft en vary substantiallyin their familiarity with multivariate models;

• reviewers for a grant proposal or article involving a multivariateanalysis, some of whom are experts on your topic but not the methods,others of whom are experts in advanced statistical methods butnot your topic;

• an audience at an academic seminar or workshop where everyoneworks with various regression methods and delights in debating statisticalassumptions and dissecting equations.

Clearly, these audiences require very different approaches to writing aboutmultivariate analyses.

Writing for a Statistical Audience

When writing for statistically trained readers, explain not only the methodsand findings but also the reasons a multivariate model is needed foryour particular study and how the findings add to the body of knowledgeon the topic. I have read many papers and sat through many presentationsabout statistical analyses that focused almost solely on equations andcomputer output full of acronyms and statistical jargon. Even if your audienceis well versed in multivariate techniques, do not assume that theyunderstand why those methods are appropriate for your research questionand data. And it behooves you to make it as easy as possible for reviewersof your paper or grant proposal to understand the point of your analysisand how it advances previous research.

Another important objective is to avoid a "teaching" style as you writeabout multivariate analyses. Although professional journals usually requirethat you report the detailed statistical results to show the basis foryour conclusions, reading your paper should not feel like a refresher coursein regression analysis. Do not make your readers slog through every logicalstep of the statistical tests or leave it to them to interpret every numberfor themselves. Instead, ask and answer the research question, using theresults of your analysis as quantitative evidence in your overall narrative.

Writing for a Nonstatistical Audience

Although researchers typically learn to explain multivariate models toother people with training equivalent to their own, those who write forapplied or lay audiences must also learn to convey the findings to folkswho have little if any statistical training. Such readers want to know theresults and how to interpret and apply them without being asked to understandthe technical details of model specification, coefficients, and inferentialstatistics. Just as most drivers don't have the faintest idea whatgoes on under the hood of a car, many people interested in multivariatestatistical findings don't have a clue about the technical processes behindthose findings. They don't need to, any more than you need to understandyour car's engineering to be able to drive it.

When writing for an applied audience, make it easy for them to graspthe questions, answers, and applications of your study, just as car manufacturersmake it easy for you to operate your car. Translating your findingsin that way forces you to really understand and explain what yourmultivariate model means "in English" and as it relates to the conceptsunder study, which ultimately are important messages for any audience.Throughout this book I point out ways to explain various aspects of multivariateanalyses to applied audiences, with all of chapter 20 devoted to thattype of communication.

Objectives of Multivariate Analyses

Multivariate models can be estimated with any of several objectives inmind. A few examples:

• To provide information to an applied audience for a debate aboutthe issue you are analyzing. For example, findings about whetherchanging class size, teachers' qualifications, or curriculum yields thegreatest improvement in math skills are relevant to education policymakers, teachers, and voters.

• To test hypotheses about relationships among several variables. Forinstance, the net effects of exercise, diet, and other characteristics onheart disease risk are of interest to the general public, professionals inthe food and exercise industries, and health care providers.

• To generate projections of expected economic performance or populationsize over the next few years or decades. For example, forecastedemployment and interest rates are widely used by businesses andgovernment agencies in planning for the future.

• To advance statistical methods such as testing new computationalalgorithms or alternative functional forms. Information on the statisticalderivation, soft ware, and guidelines on how to interpret andpresent such findings will be useful to statisticians as well as researcherswho later apply those techniques to topics in other fields.

The audience and objective together determine many aspects of how youwill write about your multivariate analysis. Hence, a critical first step is toidentify your audiences, what they need to know about your models, andtheir level of statistical training. That information along with the principlesand tools described throughout this book will allow you to tailoryour approach to suit your audience, choosing terminology, analogies,table and chart formats, and a level of detail that best convey the purpose,findings, and implications of your study to the people who will read it.

If you are writing for several audiences, expect to write several versions.For example, unless your next-door neighbor has a doctorate in statistics,chances are he will not want to see the derivation of the equationsyou used to estimate a multilevel discrete-time hazards model of whichschools satisfy the No Child Left Behind regulations. He might, however,want to know what your results mean for your school district—instraightforward language, sans Greek symbols, standard errors, or jargon.On the other hand, if the National Science Foundation funded your research,they will want a report with all the gory statistical details and yourrecommendations about research extensions as well as illustrative caseexamples based on the results.

Writing about Multivariate Analyses

To write effectively about multivariate models, first you must master abasic set of concepts and skills for writing about numbers. As you write,you will incorporate numbers in several different ways: a few carefullychosen facts in an abstract or the introduction to a journal article; a tableand description of model estimates in the analytic section of a scientificreport; a chart of projected patterns in the slides for a speech or poster; ora statistic about the overall impact of a proposed policy in an issue briefor grant proposal. In each of these contexts, the numbers support otheraspects of the written work. They are not taken in isolation, as in a simplearithmetic problem. Rather, they are applied to some larger objective, asin a math "word problem" where the results of the calculations are used toanswer some real-world question. Instead of merely estimating a model ofout-of-pocket costs of prescription medications under the 2003 MedicarePrescription Drug, Improvement, and Modernization Act, for instance,the results of that analysis would be included in an article or policy statementabout insurance coverage for prescription medications. Used in thatway, the numbers generate interest in the topic or provide evidence for adebate on the issue.

In many ways, writing about multivariate analyses is similar to otherkinds of expository writing. It should be clear, concise, and written in alogical order. It should start by stating a hypothesis, then provide evidenceto test it. It should include examples that the expected audience can followand descriptive language that enhances their understanding of how theevidence relates to the question. It should be written at a level of detailthat is consistent with its expected use. It should set the context and defineterms the audience might not be expected to know, but do so in ways thatdistract as little as possible from the main thrust of the work. In short, itwill follow many of the principles of good writing, but with the additionof quantitative information.

When I refer to writing about numbers, I mean "writing" in a broadsense: preparation of materials for oral or visual presentation as well asmaterials to be read. Most of the principles outlined in this book applyequally to creating slides for a speech or a research poster. Other principlesapply specifically to either oral or visual presentations.

Writing effectively about numbers also involves reading effectivelyabout numbers. To select and explain pertinent numbers for your work,you must understand what those numbers mean and how they were measuredor calculated. The first few chapters provide guidance on importantfeatures such as units and context to watch for as you garner numeric factsfrom other sources.

A Writer's Toolkit

Writing about numbers is more than simply plunking a number or twointo the middle of a sentence. You may want to provide a general imageof a pattern or you may need specific, detailed information. Sometimesyou will be reporting a single number, other times many numbers. Justas a carpenter selects among different tools depending on the job, peoplewho write about numbers have an array of tools and techniques to use fordifferent purposes. Some approaches do not suit certain jobs, whether incarpentry (e.g., welding is not used to join pieces of wood), or in writingabout numbers (e.g., a pie chart cannot be used to show trends). And justas there may be several appropriate tools for a task in carpentry (e.g., nails,screws, glue, or dowels to fasten together wooden components), in manyinstances any of several tools could be used to present numbers.

There are three basic tools in a writer's toolkit for presenting quantitativeinformation: prose, tables, and charts.

Prose

Numbers can be presented as a couple of facts or as part of a detaileddescription of findings. A handful of numbers can be described in a sentenceor two, whereas a complex statistical analysis can require a pageor more. In the body of a paper or book, numbers are incorporated intofull sentences. In slides, the executive summary of a report, or a researchposter, numbers may be reported in a bulleted list, with short phrasesused in place of complete sentences. Detailed background information isoft en given in footnotes (for a sentence or two) or appendixes (for longerdescriptions).

Tables

Tables use a grid to present numbers in a predictable way, guided by labelsand notes within the table. A simple table might present high schoolgraduation rates in each of several cities. A more complicated table mightshow relationships among three or more variables such as graduationrates by city over a 20-year period, or results of statistical models analyzinggraduation rates. Tables are oft en used to organize a detailed set ofnumbers in appendixes, to supplement the information in the main bodyof the work.

Charts

There are pie charts, bar charts, line charts, scatter charts, and the manyvariants of each. Like tables, charts organize information into a predictableformat: the axes, legend, and labels of a well-designed chart lead theaudience through a systematic understanding of the patterns being presented.Charts can be simple and focused, such as a pie chart showing theracial composition of your study sample. Or they can be complex, such ascharts showing cross-level interactions from a multilevel model or confidenceintervals around estimated coefficients.

As an experienced carpenter knows, even when any of several toolscould be used for a job, oft en one of those options will work better in aspecific situation. If there will be a lot of sideways force on a joint, glue willnot hold well. If your listening audience has only 30 seconds to grasp a numericalrelationship, a complicated table showing results of five regressionmodels with up to 20 variables apiece will be overwhelming. If kids will beplaying floor hockey in your family room, heavy-duty laminated flooringwill hold up better than parquet. If your audience needs many detailednumbers, a table will organize those numbers better than sentences.

With experience, you will learn to identify which tools are suited todifferent aspects of writing about numbers, and to choose among theworkable options. Those of you who are new to writing about multivariateanalysis can consider this book an introduction to carpentry—a wayto familiarize yourself with the names and operations of each of the toolsand the principles that guide their use. Those of you who have experiencewriting about such models can consider this a course in advancedtechniques, with suggestions for refining your approach and skills to communicatereasons for and results of multivariate analyses more clearly andsystematically.

Identifying the Role of the Numbers You Use

When writing about numbers, help your readers see where those numbersfit into the story you are telling—how they answer some question youhave raised. A naked number sitting alone and uninterpreted is unlikelyto accomplish its purpose. Start each paragraph with a topic sentence orthesis statement, then provide evidence that supports or refutes that statement.An issue brief about wages might report an average wage and astatistic on how many people earn the minimum wage. Longer, more analyticpieces might have several paragraphs or sections, each addressing adifferent question related to the main topic. An article on wage patternsmight present overall wage levels, then describe a model of how they varyby educational attainment, work experience, and other factors. Structureyour paragraphs so your audience can follow how each section and eachnumber contribute to the overall scheme.
(Continues...)Excerpted from THE CHICAGO GUIDE TO WRITING ABOUT MULTIVARIATE ANALYSIS by Jane E. Miller. Copyright © 2013 The University of Chicago. Excerpted by permission of THE UNIVERSITY OF CHICAGO PRESS.
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