Numbers as evidence:
Applying expository writing
techniques to writing about numbers
Jane E. Miller, PhD
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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)
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Figure 1. Gun and Non-Gun Homicides
United States, 1985-2000
Gun
Non-gun
All
30,000
number of victims
25,000
20,000
15,000
10,000
5,000
0
1985
1990
1995
2000
Year
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Figure 2. Gun Homicides by Age of Offender
United States, 1985-2000
12,000
14-17
18-24
25+
number Offenders
10,000
8,000
6,000
4,000
2,000
0
1985
1988
1991
1994
Year
1997
2000
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
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.”
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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 gunrelated 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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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”
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Poor summary
• Poor: “In the two youngest groups of offenders, gunrelated 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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Better summary
• Better: “The rise in the total number of homicides in
the early 1990’s was due to increases only in gunrelated 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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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.
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Suggested online resources
• Podcasts on
– Reporting one number
– Comparing two numbers or series of numbers
– Summarizing a pattern with many numbers
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Contact information
Jane E. Miller, PhD
jmiller@ifh.rutgers.edu
Online materials available at
http://press.uchicago.edu/books/miller/multivariate/index.html
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.