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Writing about multivariate analyses is a surprisingly common task. Results of ordinary least squares (OLS) and logistic regression models inform decisions of government agencies, businesses, and individuals. In everyday life, you encounter forecasts about inflation, unemployment, and interest rates in the newspaper, predictions of hurricanes' timing and location in television weather reports, and advice about behaviors and medications to reduce heart disease risk in magazines and health pamphlets. In many professional fields, multivariate analyses are included in research papers, grant proposals, policy briefs, and consultant's reports. Economists and meteorologists, health researchers and college professors, graduate students and policy analysts all need to write about multivariate models for both statistical and nonstatistical audiences. In each of these situations, writers must succinctly and clearly convey quantitative concepts and facts.
Despite this apparently widespread need, few people are formally trained to write about numbers, let alone multivariate analyses. Communications specialists learn to write for varied audiences, but rarely are taught specifically to deal with statistical analyses. Statisticians and researchers learn to estimate regression models and interpret the findings, but rarely are taught to describe them in ways that are comprehensible to readers with different levels of quantitative expertise or interest. I have seen poor communication of statistical findings at all levels of training and experience, from papers by students who were stymied about how to put numbers into sentences, to presentations by consultants, policy analysts, and applied scientists, to publications by experienced researchers in elite peer-reviewed journals. This book is intended to bridge the gap between correct multivariate analysis and good expository writing, taking into 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 training but want to understand and apply results of multivariate analyses about issues that matter to them;
readers of a professional journal in your field who often vary substantially in their familiarity with multivariate models;
reviewers for a grant proposal or article involving a multivariate analysis, some of whom are experts on your topic but not the methods, others of whom are experts in advanced statistical methods but not your topic;
an audience at an academic seminar or workshop where everyone works with various regression methods and delights in debating statistical assumptions and dissecting equations.
Clearly, these audiences require very different approaches to writing about multivariate analyses.
Writing for a Statistical Audience
When writing for statistically trained readers, explain not only the methods and findings but also the reasons a multivariate model is needed for your particular study and how the findings add to the body of knowledge on the topic. I have read many papers and sat through many presentations about statistical analyses that focused almost solely on equations and computer output full of acronyms and statistical jargon. Even if your audience is well versed in multivariate techniques, do not assume that they understand why those methods are appropriate for your research question and data. And it behooves you to make it as easy as possible for reviewers of your paper or grant proposal to understand the point of your analysis and how it advances previous research.
Another important objective is to avoid a "teaching" style as you write about multivariate analyses. Although professional journals usually require that you report the detailed statistical results to show the basis for your conclusions, reading your paper should not feel like a refresher course in regression analysis. Do not make your readers slog through every logical step of the statistical tests or leave it to them to interpret every number for themselves. Instead, ask and answer the research question, using the results of your analysis as quantitative evidence in your overall narrative.
Writing for a Nonstatistical Audience
Although researchers typically learn to explain multivariate models to other people with training equivalent to their own, those who write for applied or lay audiences must also learn to convey the findings to folks who have little if any statistical training. Such readers want to know the results and how to interpret and apply them without being asked to understand the technical details of model specification, coefficients, and inferential statistics. Just as most drivers don't have the faintest idea what goes on under the hood of a car, many people interested in multivariate statistical findings don't have a clue about the technical processes behind those findings. They don't need to, any more than you need to understand your car's engineering to be able to drive it.
When writing for an applied audience, make it easy for them to grasp the questions, answers, and applications of your study, just as car manufacturers make it easy for you to operate your car. Translating your findings in that way forces you to really understand and explain what your multivariate model means "in English" and as it relates to the concepts under study, which ultimately are important messages for any audience. Throughout this book I point out ways to explain various aspects of multivariate analyses to applied audiences, with all of chapter 16 devoted to that type of communication.
* OBJECTIVES OF MULTIVARIATE ANALYSES
Multivariate models can be estimated with any of several objectives in mind. A few examples:
To provide information to an applied audience for a debate about the issue you are analyzing. For example, findings about whether changing class size, teachers' qualifications, or curriculum yields the greatest improvement in math skills are relevant to education policy makers, teachers, and voters.
To test hypotheses about relationships among several variables. For instance, the net effects of exercise, diet, and other characteristics on heart disease risk are of interest to the general public, professionals in the food and exercise industries, and health care providers.
To generate projections of expected economic performance or population size over the next few years or decades. For example, forecasted employment and interest rates are widely used by businesses and government agencies in planning for the future.
To advance statistical methods such as testing new computational algorithms or alternative functional forms. Information on the statistical derivation, software, and guidelines on how to interpret and present such findings will be useful to statisticians as well as researchers who later apply those techniques to topics in other fields.
The audience and objective together determine many aspects of how you will write about your multivariate analysis. Hence, a critical first step is to identify your audiences, what they need to know about your models, and their level of statistical training. That information along with the principles and tools described throughout this book will allow you to tailor your 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 equations you used to estimate a multilevel discrete-time hazards model of which schools satisfy the No Child Left Behind regulations. He might, however, want to know what your results mean for your school district-in straightforward 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 your recommendations about research extensions as well as illustrative case examples based on the results.
* WRITING ABOUT MULTIVARIATE ANALYSES
To write effectively about multivariate models, first you must master a basic set of concepts and skills for writing about numbers. As you write, you will incorporate numbers in several different ways: a few carefully chosen facts in an abstract or the introduction to a journal article; a table and description of model estimates in the analytic section of a scientific report; a chart of projected patterns in the slides for a speech or poster; or a statistic about the overall impact of a proposed policy in an issue brief or grant proposal. In each of these contexts, the numbers support other aspects of the written work. They are not taken in isolation, as in a simple arithmetic problem. Rather, they are applied to some larger objective, as in a math "word problem" where the results of the calculations are used to answer some real-world question. Instead of merely estimating a model of out-of-pocket costs of prescription medications under the 2003 Medicare prescription drug act, for instance, the results of that analysis would be included in an article or policy statement about insurance coverage for prescription medications. Used in that way, the numbers generate interest in the topic or provide evidence for a debate on the issue.
In many ways, writing about multivariate analyses is similar to other kinds of expository writing. It should be clear, concise, and written in a logical order. It should start by stating a hypothesis, then provide evidence to test it. It should include examples that the expected audience can follow and descriptive language that enhances their understanding of how the evidence relates to the question. It should be written at a level of detail that is consistent with its expected use. It should set the context and define terms the audience might not be expected to know, but do so in ways that distract as little as possible from the main thrust of the work. In short, it will follow many of the principles of good writing, but with the addition of quantitative information.
When I refer to writing about numbers, I mean "writing" in a broad sense: preparation of materials for oral or visual presentation as well as materials to be read. Most of the principles outlined in this book apply equally to creating slides for a speech or a research poster. Other principles apply specifically to either oral or visual presentations.
Writing effectively about numbers also involves reading effectively about numbers. To select and explain pertinent numbers for your work, you must understand what those numbers mean and how they were measured or calculated. The first few chapters provide guidance on important features such as units and context to watch for as you garner numeric facts from other sources.
* A WRITER'S TOOLKIT
Writing about numbers is more than simply plunking a number or two into the middle of a sentence. You may want to provide a general image of a pattern or you may need specific, detailed information. Sometimes you will be reporting a single number, other times many numbers. Just as a carpenter selects among different tools depending on the job, people who write about numbers have an array of tools and techniques to use for different purposes. Some approaches do not suit certain jobs, whether in carpentry (e.g., welding is not used to join pieces of wood), or in writing about numbers (e.g., a pie chart cannot be used to show trends). And just as there may be several appropriate tools for a task in carpentry (e.g., nails, screws, glue, or dowels to fasten together wooden components), in many instances any of several tools could be used to present numbers.
There are three basic tools in a writer's toolkit for presenting quantitative information: prose, tables, and charts.
Numbers can be presented as a couple of facts or as part of a detailed description of findings. A handful of numbers can be described in a sentence or two, whereas a complex statistical analysis can require a page or more. In the body of a paper or book, numbers are incorporated into full sentences. In slides, the executive summary of a report, or a research poster, numbers may be reported in a bulleted list, with short phrases used in place of complete sentences. Detailed background information is often given in footnotes (for a sentence or two) or appendixes (for longer descriptions).
Tables use a grid to present numbers in a predictable way, guided by labels and notes within the table. A simple table might present high school graduation rates in each of several cities. A more complicated table might show relationships among three or more variables such as graduation rates by city over a 20-year period, or results of statistical models analyzing graduation rates. Tables are often used to organize a detailed set of numbers in appendixes, to supplement the information in the main body of the work.
There are pie charts, bar charts, line charts, scatter charts, and the many variants of each. Like tables, charts organize information into a predictable format: the axes, legend, and labels of a well-designed chart lead the audience through a systematic understanding of the patterns being presented. Charts can be simple and focused, such as a pie chart showing the racial composition of your study sample. Or they can be complex, such as charts showing confidence intervals around estimated coefficients or projected patterns based on a multivariate model.
As an experienced carpenter knows, even when any of several tools could be used for a job, often one of those options will work better in a specific situation. If there will be a lot of sideways force on a joint, glue will not hold well. If your listening audience has only 30 seconds to grasp a numerical relationship, a complicated table showing results of five regression models with up to 20 variables apiece will be overwhelming. If kids will be playing floor hockey in your family room, heavy-duty laminated flooring will hold up better than parquet. If your audience needs many detailed numbers, a table will organize those numbers better than sentences.
With experience, you will learn to identify which tools are suited to different aspects of writing about numbers, and to choose among the workable options. Those of you who are new to writing about multivariate analysis can consider this book an introduction to carpentry-a way to familiarize yourself with the names and operations of each of the tools and the principles that guide their use. Those of you who have experience writing about such models can consider this a course in advanced techniques, with suggestions for refining your approach and skills to communicate reasons for and results of multivariate analyses more clearly and systematically.
* IDENTIFYING THE ROLE OF THE NUMBERS YOU USE
When writing about numbers, help your readers see where those numbers fit into the story you are telling-how they answer some question you have raised. A naked number sitting alone and uninterpreted is unlikely to accomplish its purpose. Start each paragraph with a topic sentence or thesis statement, then provide evidence that supports or refutes that statement. An issue brief about wages might report an average wage and a statistic on how many people earn the minimum wage. Longer, more analytic pieces might have several paragraphs or sections, each addressing a different question related to the main topic. An article on wage patterns might present overall wage levels, then describe a model of how they vary by educational attainment, work experience, and other factors. Structure your paragraphs so your audience can follow how each section and each number contribute to the overall scheme.
To tell your story well, you, the writer, need to know why you are including a given fact or set of facts in your work. Think of the numbers as the answer to a word problem, then step back and identify (for yourself) and explain (to your readers) both the question and the answer. This approach is much more informative for readers than encountering a number without knowing why it is there. Once you have identified the objective and chosen the numbers, convey their purpose to your readers. Provide a context for the numbers by relating them to the issue at hand. Does a given statistic show how large or common something is? How small or infrequent? Do trend data illustrate stability or change? Do those numbers represent typical or unusual values? Often, numerical benchmarks such as thresholds, historical averages, highs, or lows can serve as useful contrasts to help your readers grasp your point more effectively: compare current average wages with the living wage needed to exceed the poverty level, for example.
Excerpted from The Chicago Guide to Writing about Multivariate Analysis by JANE E. MILLER Copyright © 2005 by The University of Chicago. Excerpted by permission.
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|2||Seven basic principles||13|
|3||Causality, statistical significance, and substantive significance||34|
|4||Five more technical principles||50|
|5||Creating effective tables||81|
|6||Creating effective charts||120|
|7||Choosing effective examples and analogies||167|
|8||Basic types of quantitative comparisons||184|
|9||Quantitative comparisons for multivariate models||207|
|10||Choosing how to present statistical test results||231|
|Pt. III||Pulling it all together|
|11||Writing introductions, conclusions, and abstracts||257|
|12||Writing about data and methods||272|
|13||Writing about distributions and associations||301|
|14||Writing about multivariate models||317|
|15||Speaking about multivariate analyses||349|
|16||Writing for applied audiences||380|
|App. A||Implementing "generalization, example, exceptions" (GEE)||407|
|App. B||Translating statistical output into table and text||417|
|App. C||Terminology for ordinary least squares (OLS) at logistic models||423|
|App. D||Using a spreadsheet for calculations||433|