1. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Numbers as evidence: Applying expository writing techniques to writing about numbers Jane E. Miller, PhD

2. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Overview Numbers as evidence Expository writing skills for writing about numbers – Structure of overall paper – Paragraph structure – Use of topic, evidentiary, and transition sentences

3. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Writing about numbers: Word problems Real-world questions that involve numbers – Social science, e.g., How does video game playing affect time spent reading? How did the subprime mortgage crisis affect the economy? – Biological or physical science, e.g., How do exercise and body weight affect mortality? How have ozone levels affected weather patterns? Numbers are evidence for – Describing a trend or cross-sectional difference – Testing a hypothesis

4. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Expository writing skills Many general expository writing skills carry over to writing about numbers. – Structure of a research paper – Use of paragraphs to organize ideas – Sentences to present evidence – Approaches to comparing facts and summarize patterns

5. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Numbers as evidence When writing an essay about a literary work, quotations are the evidence. – Used to document some thesis proposed at the beginning of the work. – A quote out of context is meaningless. When writing a paper for science, history, or other fields, numbers are often the evidence. – A number in isolation doesn’t answer the underlying substantive question.

6. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Structuring an essay with numbers as evidence Introduce the big picture – What is the substantive question the numbers are intended to answer? Present the numeric evidence – Report and interpret values – Specify direction and magnitude Conclude by returning to the big picture – Relate the body of evidence back to the original question.

7. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Structure of a legal argument Opening statement – Raises major questions to be addressed during the trial. – Introduces characters and events in question. Evidence portion of trial – Describes and justifies investigative methods. – Cites previous cases and whether they apply to current case. – Presents individual facts, ties them to other evidence to demonstrate patterns or themes. – Submits exhibits such as diagrams or physical evidence. Closing statement – Summarizes conclusions based on complete body of evidence, restating critical points but with less detail than in the evidence portion of trial.

8. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Structure of an academic paper Introduction – Parallels opening argument. – Introduces the overarching questions. Data and methods and results – Mirrors evidence portion of trial. – Explains why your methods are needed for your data and research question. – Systematically introduces and explains evidence from tables, charts, maps, or other diagrams. Discussion and conclusion – Parallels closing argument. – Summarizes findings and connects them back to initial questions and previous studies of related topics.

9. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Use “the W’s” to organize a paper Introduction – What is the topic and why is it important? – Frame overall topic, naming concepts involved. – Discuss previous literature to convey what is known. Data and methods – Who, when, where? (data source) – Two “how’s”? Data collection Analytic (statistical) techniques – What? (variables)

10. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Use “the W’s” to organize a paper Results – What were the detailed findings? Conclusions – So what? Summary of findings Tie results back to – Original research question – Previous studies Implications of findings for research and policy or practice

11. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Using paragraphs to organize evidence One major topic or set of related topics per paragraph – Topic sentence introduces the relationships to be discussed. – Evidentiary sentences follow principles for: Reporting and interpreting numbers Specifying direction and magnitude of associations Summarizing complex patterns – Transition sentences tie together paragraphs: Show how evidence in one paragraph leads or relates to topic and evidence in next paragraph Logical sequence of evidence

12. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Conveying the purpose of a number Write a good topic sentence to introduce each fact or comparison. Always include the level (value) for each group being compared. – Can put it in a table or chart if not the text. Interpret one or more type of numeric comparison. – Calculate, report and interpret the comparison. – A “naked number” is hard to interpret. – Give your audience enough information to See the point you are trying to make. Help them understand it in the context of their own experience.

13. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition.

14. Poor topic sentence Poor: [No introductory sentence.] “In 2000, there were 11,280 gun-related homicides (figure 1).” – This version refers to a figure and starts presenting data without orienting the audience to the topic and objectives. – Does not convey either the purpose or interpretation of those numbers.

15. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Better topic sentence Better: “What factors explain the observed rise and fall in the number of homicides in the United States in the 1990’s (figure 1)?” – This version uses a rhetorical question to introduce The context (where and when) Pattern to be investigated (time trend in homicides). – Does not specify which variables will be considered as possible explanatory factors.

16. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Best topic sentence Best: “Was the substantial rise and subsequent fall in the number of homicides in the 1990’s in the United States (figure 1) observed across all age groups and types of weapons?” – Sets the context (when, where) – Mentions the dependent (homicide) and independent variables (age and type of weapon) – Conveys the purpose of the numeric evidence to follow later in the paragraph

17. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Poor evidentiary sentence Poor: “In 1985, there were 12,263 gun-related homicides (figure 1).” – Doesn’t convey whether that number was high or low changing or stable – Fails to place the number in context by reporting and interpreting results of numeric comparisons against number of homicides committed with other weapons in other time periods

18. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Better evidentiary sentence Better: “Throughout the period shown, homicides were most often committed with guns. In 1985, for example, roughly 1.5 times as many homicides were committed with guns as with other types of weapons (12,263 versus 8,107; figure 1).” – The first sentence reports which type of weapon is most commonly used to commit homicide. – The second compares the number of homicides by type of weapon for one year, and refers to the associated chart. – Subsequent sentences [not shown] would describe Time trends in homicides by type of weapon How the ratio of gun to non-gun homicides changed across time.

19. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition.

20. Example transition sentence Transition sentence from a paragraph describing figure 1 to a second paragraph about figure 2: – “As shown in figure 1, the increase and subsequent decrease in homicides were driven entirely by trends in gun-related homicides. Figure 2 examines whether gun-related homicides exhibited the same time trend among all age groups of offenders.”

21. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Elements of the transition “As shown in figure 1, the increase and subsequent decrease in homicides were driven entirely by trends in gun-related homicides. Figure 2 examines whether gun- related homicides exhibited the same time trend among all age groups of offenders.” – Signals a second step in the analysis by starting a new paragraph about homicide patterns by age of offender,. – The first sentence summarizes the conclusions of the preceding section (on trends in homicide by type of weapon). – The second sentence introduces another angle to be considered in a further dissection of those time trends.

22. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Subheadings Subheadings can be used to provide further guidance through the different parts of a long results section that addresses several different topics or subtopics. – E.g., for homicide analysis “Homicide trends by type of weapon” “Homicide trends by age of offender”

23. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Writing a good numeric comparison Don’t write the problem set… Write the answer! – Don’t leave it to readers to do the calculations or comparisons. Not just a list of numeric values… An explanation of the patterns. – Use the numbers as evidence to answer the question.

24. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Discussion and conclusions In the concluding section: – Write a summary paragraph, show how the findings answer the original research. Bring the analysis full circle – Remind readers what the numbers mean in the substantive context of that research question.

25. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Poor summary Poor: “In the two youngest groups of offenders, gun- related homicides increased two-fold to four-fold between 1985 and 1994, then decreased until 2000. In contrast, the number of gun-related homicides committed by offenders aged 25 and older decreased slowly throughout the time period shown. Homicides committed with other weapons remained relatively steady over the entire period.” – Restates statistics from the results section. Adds nothing to what has already been demonstrated Fails to put the evidence back in the “big picture” of the main research question.

26. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Better summary Better: “The rise in the total number of homicides in the early 1990’s was due to increases only in gun- related homicides – increases that were concentrated largely among perpetrators in their teens and early 20’s.” – Brings the analysis full circle, relating the statistical evidence back to the original question about the roles of weapon type and age of offender in the overall time trend in homicides. – The conclusion could then be fleshed out with possible explanations for this pattern such as availability of guns, penalties associated with gun-related homicide, or factors that explain age patterns of violent criminal behavior.

27. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Summary Write a logical narrative with a – Beginning: Ask the question in plain English, mentioning the specific concepts under study – Middle: Systematically review the numeric evidence to answer that “word problem,” organized into one paragraph per major topic. – End: Answer the question in plain English, referring back to the original question. Use principles for reporting, comparing, and summarizing numbers to present evidence.

28. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Suggested resources Chapter 15 in Miller, J. E. 2013. The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition. Miller, J. E. 2006. “How to Communicate Statistical Findings: An Expository Writing Approach.” Chance 19 (4): 43–49. Miller, J. E. 2010. “Quantitative Literacy across the Curriculum: Integrating Skills from English Composition, Mathematics, and the Substantive Disciplines.” The Educational Forum 74 (4): 334–46.

29. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Suggested online resources Podcasts on – Reporting one number – Comparing two numbers or series of numbers – Summarizing a pattern with many numbers

30. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Suggested practice exercises Study guide to The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition. – Reviewing exercise #2 in the suggested course extensions for chapter 1 – Questions #1 and #2 in the problem set for chapter 12

31. The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Contact information Jane E. Miller, PhD jmiller@ifh.rutgers.edu Online materials available at http://press.uchicago.edu/books/miller/multivariate/index.html