Basics of writing about numbers:
Reporting one number
Jane E. Miller, PhD
The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition.
Overview
• Which information to include when reporting a
number
– Context
– Units
• Illustrative examples
– Poor/better/best
The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition.
Setting the context (“the W’s”)
• For every example or fact (numeric or other), specify:
– When?
– Where?
– Who?
• Everyone?
• Subgroup (by race, age, gender, or some other trait)?
• Without this context, readers can’t
– Interpret the facts correctly.
– Compare them against numbers from other sources.
The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition.
Why does context matter?
• Suppose you are comparing two unemployment
rates.
• They could legitimately have different values if
they are from
– Different times (e.g., 1995 vs. 2005)
– Different places (e.g., New York vs. US as a whole)
– Different groups (e.g., men vs. women)
• Can’t do a good, systematic comparison unless
can specify on which “W’s” the rates differ.
The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition.
Specifying units
• System of measurement
• Scale
• Level of aggregation
The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition.
Specifying units:
System of measurement
• British?
• Metric?
• Other?
The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition.
Specifying units: Scale
• Length in centimeters or meters?
• Weight in grams or kilograms?
• Mortality rate percent, per 1,000 or per
100,000?
The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition.
Specifying units:
Level of aggregation
• Price per piece or per dozen or per gross?
• Population by census tract or town or county?
• Poverty rates for individuals or families or
towns?
The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition.
Why do units matter?
• Must compare within a consistent
– System of measurement
• E.g., 1 meter is longer than 2 feet, so can’t just say “2 > 1”
without considering different systems of measurement.
– Scale
• E.g., 1 meter is longer than 10 centimeters, so can’t just
say “10 > 1” without considering that even though both
are metric measurements, the scale is different.
– Level of aggregation
• E.g., $1 per piece is more expensive on a per-unit basis
than $10 per dozen, so can’t just say “10 > 1” without
considering level of aggregation.
The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition.
Reporting a single number
– “During the 3rd century, the Black Plague killed 25
million people in Europe.”
– “In 2001, the average temperature in the New York City
area was 56.3 degrees Fahrenheit.”
– “Median household income was $49,445 in the US in
2010.
– Check:
• When? Where? What? How many? Units?
• Note that the W’s don’t always appear in the same
order. Many types of sentence structures are
possible.
The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition.
Teaching device: “Poor/better/best”
• Introduce and explain a general principle.
– E.g., “setting the context”
• Illustrate concept with sentences.
– “Poor” – doesn’t follow the principle
– “Better” – partially follows the principle
– “Best” – follows the principle
• Annotate each sentence to show why it is
“poor” or “better.”
• Make abstract ideas concrete.
The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition.
Too little information
• Poor: “The height was 27.”
– What are we measuring?
– In what context?
– In what units?
• Better: “The plant measured 27 centimeters tall.”
– Now we have size, units, and “what” concept (plant height).
– When? Which plant (e.g., under what conditions)?
• Best: “Two weeks after germinating, the plant that was
watered daily measured 27 centimeters tall.”
– When, what (plant height), which plant, size, and units.
The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition.
Rote, list-wise reporting of the W’s
• Poor: “The plant I am talking about was watered daily.
It was measured in centimeters. I measured it two
weeks after it germinated. It’s height was 27.”
– In your rough notes, you might need to write a separate
sentence about each W, just to get the information correct.
– Then condense and simplify the W’s into one sentence for a
more concise, conversational sentence.
• Better: “Two weeks after germinating, the plant that
was watered daily measured 27 centimeters tall.”
– All of the W’s and units in one sentence.
– With practice, you will get closer to this version on your first
try.
The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition.
Repetitive information
• Poor: “The first day after germinating, the plant that
was watered daily was 0.7 centimeters tall. The third
day after germinating, the plant that was watered
daily. . . Two weeks after germinating, the plant that
was watered daily measured 27 centimeters tall.”
– Once a “W” has been reported, don’t repeat it unless it
changes. Here, the same plant, concept (height), and
units of measurement are discussed throughout.
– Only the date changes, so it and the updated value
(number) are the only W’s required in the second and
subsequent sentences.
The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition.
Better reporting of several numbers
• Better: “The first day after germinating, the plant that
was watered daily was 0.7 centimeters (cm) tall. Two
days later, it measured 3.8 cm. By two weeks after
germination, it had reached 27 cm.”
– The word “it” stands in for “the plant that was watered
daily,” and for references to height, averting repetition of
what and “who” (which plant).
– The abbreviation “cm” replaces the full word
“centimeters” after being defined in the first sentence.
The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition.
Finding W’s and units for your numbers
• To be able to write correctly and completely about the
W’s and units for the numbers you are working with,
you need to read for and take notes on that
information.
– In source documents of published numbers.
– In codebooks or questionnaires for data sets.
• Also label
– Units on all variables in your data sets.
• Raw variables (used in the form they came in the original data set).
• Those you calculate.
– W’s and units in all tables and charts you create.
The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition.
Summary
• Mental checklist for reporting one number
– Context (W’s)
– Units
• Same fundamentals apply when
– Comparing two or more numbers or series
• See the podcast by that name
– Reporting results of advanced statistical analyses
• E.g., coefficients from multivariate regression
– Designing effective tables and charts
• See associated podcast
The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition.
Suggested resources
• For basic principles, see chapters 1 and 2 in
– Miller, J. E. 2004. The Chicago Guide to Writing about
Numbers
OR
– Miller, J. E. 2013. The Chicago Guide to Writing about
Multivariate Analysis, 2nd Edition.
• For additional examples, see
– 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, 2 nd edition.
Suggested practice exercises
• Study guide to The Chicago Guide to Writing
about Multivariate Analysis, 2nd Edition.
– Question #1 for problem set for chapter 4
– Suggested course extensions for
• Chapter 2
– “Reviewing” exercise #1
• Chapter 4
– “Reviewing” exercise #1
– “Applying statistics” exercise #1
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
The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition.