From Numbers to Words

Reporting Statistical Results for the Social Sciences

Susan Morgan, Tom Reichert, Tyler R. Harrison

• Publisher: Routledge
• Year: 2016
• ISBN:
  9781317269755
• Edition: 1
• Topic: Sciences sociales
• Subtopic: Recherche scientifique et méthodologie

This invaluable resource guides readers through the process of creating scholarly, publishable prose from the results of quantitative experiments and investigations. It delves into the issues commonly encountered when reporting the results of statistical experiments and investigations, and provides instruction re the representation of these results in text and visual formats. This unique research companion serves as a must-have reference for advanced students doing quantitative research and working with statistics, with the goal of writing up and publishing their findings; it also serves as a useful refresher for experienced researchers.

Chapter 1
How to Use This Book

Even scholars who entered the social sciences with the knowledge that they would have to become astute in the use of statistics have had to wrestle with the issue of how to present the results of their research. After struggling to learn statistical programs, such as SAS, SPSS, or Minitab (among others), and finally receiving the prized, newly analyzed data, many researchers must now confront the puzzling task of how to write up the results of their hard work. Even after scholars interpret the results of a statistical analysis, they must still make these results comprehensible to others. These others may include reviewers for journals or academic conferences, colleagues who are interested in the researcher’s work, or (if these scholars are also students) their professors. Those who are interested in the statistical results of research need certain pieces of information so that they can obtain a clear picture of the data that have been collected. A well-written results section also will give readers clear answers to the hypotheses or research questions that were advanced prior to the collection of the data.

Unfortunately, it is very difficult to know how to write up the results of statistical analyses. Very little work has been done in this area, and even less is easy to use. An occasional textbook offers a few examples of a results section using a featured statistic, but it is usually unclear exactly what is required for a complete, well-written results section.

What This Book Is … and Is Not

The objective of this manual is to provide clear guidelines and examples for reporting the results of statistical analyses. In the following pages, we cover what information to present in a results section, including the statistical information needed for commonly used statistics, and the format for presenting this information through the use of examples. However, this is not a statistics textbook. As such, it will not help you decide what statistical procedures to use to analyze your data nor how to interpret the results you receive from those analyses. The following examples will, however, give you some clear guidelines for what to report in a results section and possible formats for the presentation of these results.

Because this book is the first of its kind, there has been little agreement on what should be included or how elements such as significance level should be reported. Therefore, you will note that a number of the examples deviate from some of our recommendations. Generally, these differences are not of central importance; some authors or editors may report that “p < .0005” instead of simply “p < .001,” but this does not alter the meaning or usefulness of the report. This book offers a complete list of all elements for each statistical test that needs to be reported in a results section. The examples that follow each list are designed to demonstrate how all of those numbers can be strung together with words to create a coherent report. Whenever the examples lack a necessary element, we have provided information about what else should have been included. Because clear standards for reporting results have not been adhered to, complete examples for all statistics from the existing literature are remarkably difficult to come by. We sincerely hope that we have achieved a balance of information that will lead to complete and accurate reporting with real-life examples of the statistics in action.

Overview of the Book

We have divided this book into several sections. First, in Chapter 2 we provide an overview of the elements that you will need to include in your results section. We cover some basic and not-so-basic issues, such as reporting the effect sizes of your findings and the reliabilities of the instruments you use, as well as manipulation checks. We also provide a reference chart on Greek symbols and tips on how to create them in Word and WordPerfect. In Chapter 3, we cover the reporting of descriptive statistics, including frequencies, percentages, means, and standard deviations. These are the basic elements of statistical reporting. In addition, we provide guidelines for incorporating written text with tables. Cronbach’s alpha for interitem reliabilities and Cohen’s kappa and Scott’s pi for interrater reliabilities are covered in Chapter 4. Correlation and measures of association appear in Chapter 5. These include commonly used correlation statistics such as Pearson’s r. In Chapter 6, we show how to report non-parametric statistics, including the ubiquitous chi-square family of statistics as well as rank tests, among others. Parametrics tests are covered in Chapter 7, and include both the basics, such as t tests and ANOVA, as well as more advanced procedures, such as trend analysis and logistic regression. Finally, we have included a chapter on how to present results visually (Chapter 8). Although we provide many examples of tables throughout the individual sections on many of the statistics, we have created a number of guidelines to help you construct clear and effective tables and figures. These guidelines are followed by a number of examples of different types of tables and figures.

What You Should Do if a Statistic of Interest Is Not Included

These chapters should help you report the results of many statistical analyses. However, if the statistic that you are using in your study does not appear in this book, you have a couple of options. First, if your statistic is closely related to one of those represented in this book, it is likely that the pattern of reporting will be very similar. Second, you may want to use this manual for some aspects of reporting (such as the section on presenting your results in a visual format) and then do a search of the literature for other studies that use a similar statistic. Be sure to compare the results section that you locate with the information provided in Chapter 2 (the overview of conventional elements included in a results section), because journals may vary in terms of what elements or style they require.

Writing for Publication

When you are reporting the results of your study for publication, please consult the individual journal for specific guidelines on how information should be presented. For example, should you use a % symbol, or should you write out the word percentage? Fortunately, many of these differences are stylistic, not substantive in nature. What’s more, if you report an element that we recommend but a journal deems unnecessary, it is easier to drop something than to go back to your computer program, rerun the analysis, and then figure out how to incorporate that information into your existing results section. The journal (or if you are a student, the professor) you submit your manuscript to will be the final arbiter of what should appear in the finished product; however, we believe that if you follow the guidelines presented in this book, your readers or reviewers will be pleased with the completeness of your report.

Chapter 2
Frequently Asked Questions about Reporting Statistics

”Results should be the payoff, the bottom line, the climax of the research report”

—(Shontz, 1986, p. 61).

Writing a good results section is not always simply an issue of formatting statistical results and choosing the right words. We’ve compiled a list of issues revisited frequently by most researchers, whether they are students or scholars. Some of these issues are basic whereas others are more advanced. These issues include

• What is a research report?
• What is a results section?
• What should I include in a results section?
• What are developing trends in reporting results?
• What is a manipulation check and how should I report it?
• How should I report the results of the tests of my hypotheses?
• What exactly should I report in my results section?
• What format should I use to report significance levels (p value)?
• What if my test is not significant?
• Are or were my results significant?
• What is an effect size (ES) indicator?
• Do I have to report the effect size?
• How do I report effect size?
• How do I use Greek symbols?
• Should I use tables?
• If I use tables, where do I put them?

As you use this book, you will notice that some of these issues are addressed in other chapters in more detail. However, this chapter should provide a brief overview of most of the important issues in constructing a solid results section.

What Is a Research Report?

Those new to the research process sometimes complain that journal articles are boring, no fun to read, and hence, deserving of their small readership. However, research reports aren’t written to be appealing to the masses. Although entertainment is not a primary goal of journals within the social science domain, the straightforward communication of information is. Simply put, the primary purpose of journal articles is the dissemination of knowledge. Knowledge, according to mass communication researchers Stempel and Westley (1989), “can progress only as rapidly and as effectively as we can communicate our findings” (p. 388). It is, they say, the journal article, convention paper, or book that is the conduit for bringing new ideas and introducing significant findings into the field. Therefore, the transmission of information is vital to progress and is especially important to those who may benefit from research.

The communication of knowledge, via research reports, is purposely constructed with several goals in mind. First, reports are written so that the logic, method, procedure, and analysis of the project are open to inspection. Skepticism and critical judgment are highly valued in science. The constant questioning and detailed inquiry of research may seem overdone by people not familiar to the process, but it is only by this method that knowledge in our respective fields is advanced. Similarly, research must be replicable. Providing the opportunity for other researchers to replicate the study to confirm the conclusions and assumptions is another important value of science. For this reason, readers must be provided with the necessary detail to replicate the procedures and variables under study via the research report.

Research reports convey information in a specialized way. For example, most reports are organized in a sequential format that contains, in this order, a statement of the problem (review of literature and hypotheses), method, results, and conclusion. Because the outlets for this knowledge (i.e., journals) are limited, as is journal space, the report must communicate these elements as efficiently as possible. This means utilizing certain conventions and employing an economy of words with precise meaning. This allows readers of research to be able to dissect the report and access pertinent information quickly. The outline and style of writing are illustrative of the systematization of the scientific approach.

What Is a Results Section?

An important component of a methodological report is the results section. Results, as the section is typically labeled, contains a description of the results of statistical analyses as they relate to the hypotheses and research questions in the study. A primary goal of this section, according to the American Psychological Association manual (1994), is the summarization of data collected and the statistical treatment of that data. Williams (1979) defines the results component of the report more generally as a precise statement of the knowledge gained in the study. Suffice it to say, the results section is the portion of the report devoted to summarizing the data and describing the outcomes of various analytical procedures applied to that data.

What Should I Include in a Results Section?

There are certain types of information typically found in the results section. This section, as mentioned earlier, is stylized, which means it should be written according to a template common to research reports. Remember that some researchers may seek this information out first if they are interested in the analysis plan or the strength and/or magnitude of the findings. The results section is generally guided by the statements of hypotheses generated in the first part of the research report. As such, certain types of information should be included in a quantitative research report. However, because not every study has the same goals, you will have to decide what is most appropriate to include. Understanding the basic elements contained in a results section should be helpful. These include

• Manipulation checks
• Results of hypothesis testing
• Results summarized in tables and figures (typically placed a...