Choosing a comparison group
Jane E. Miller, PhD
The Chicago Guide to Writing about Numbers, 2 nd edition.
Overview
• What is a comparison group?
• Choosing comparison groups based on
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Theoretical criteria
Previous literature on the topic
Writing patterns
Sample size
The Chicago Guide to Writing about Numbers, 2 nd edition.
What is a comparison group or value?
• For each nominal or ordinal variable, the comparison
group is the one against which all other categories of
that variable will be compared.
– In multivariate regression, the comparison group is known
as the “reference category.”
• For each continuous variable, the comparison value is
the value against which all other values of that
variable will be compared.
• Choice of a comparison group or value for each
variable in your analysis should NOT be arbitrary.
The Chicago Guide to Writing about Numbers, 2 nd edition.
Choosing a comparison group
based on theoretical criteria
• Your specific research question will often determine
choice of comparison group. E.g.,
– If you are analyzing effects of a medication compared to a
placebo, the placebo condition is the logical comparison
group.
– If you are comparing other states to your home state, your
home state should be the comparison group.
The Chicago Guide to Writing about Numbers, 2 nd edition.
Choosing a comparison group based
on prior literature
• If previous studies of your topic have standard
conventions of a comparison group, often you will use it
as your comparison group as well.
– Doing so facilitates comparison of results across studies.
• BUT, it is important to think through whether their
choice fits your study.
– Identify the reasons why other researchers have chosen that
comparison group.
– Check those reasons against your own.
The Chicago Guide to Writing about Numbers, 2 nd edition.
Choosing a different comparison group
than the prior literature
• If you have strong reasons to use a different
comparison group than a major study of your topic
– In your methods section, explain the theoretical or empirical
basis for why you chose a different comparison group.
– In the discussion section, translate your results to compare
against the same comparison group as other leading studies.
The Chicago Guide to Writing about Numbers, 2 nd edition.
Choosing a comparison group
based on writing patterns
• If your sentences tend to read “compared to group X,”
then group X should be your comparison group.
• Doing so will ensure that your calculations are
consistent with how you will write about the results.
• But see
• Empirical criteria for sample size
• Precedent in the literature
The Chicago Guide to Writing about Numbers, 2 nd edition.
Anticipating what you will write
• Think ahead about what you want to write.
– E.g., For a ratio, write “(the numerator) is (some amount)
higher/lower than (the denominator).
• If you want to word it the other way around, flip your ratio over!
• E.g.,
– “IMR among blacks is twice that among whites.” is the same as
– “IMR among whites is half that among blacks.”
• Whichever way you decide to write it, make sure the
number in the prose matches the number you present
in a table or chart.
– Reversing your comparisons from table to text is a good way
to confuse your readers!
The Chicago Guide to Writing about Numbers, 2 nd edition.
Choosing a comparison group
based on sample size
• Lacking some other basis for selecting a comparison
group, choose the largest (modal) group.
– Doing so maximizes statistical power.
• Sometimes this will mesh with theoretical criteria, as
when the majority racial ethnic group is chosen as the
comparison group.
• Sometimes, the comparison group based on theoretical
criteria or prior literature includes very few cases in
your data set.
– In that case, you might need to pick a different group to
provide stable statistical estimates.
The Chicago Guide to Writing about Numbers, 2 nd edition.
Comparative writing
• For every comparison (e.g., rank, difference, ratio,
or percentage difference)
– Specify what is being compared to what.
• If all you write is “X is 20% higher”, the reader
doesn’t know higher than what?
– Especially if you are comparing several groups, places, or
time periods, failure to specify the reference group or
value can be very confusing!
The Chicago Guide to Writing about Numbers, 2 nd edition.
Reference group for multiple comparisons
• E.g., if you are comparing age
distributions for two time
periods in two regions, “The
elderly age group is smaller”
doesn’t tell your reader
whether you mean:
– Smaller than other age groups in
the same region, or
– Smaller than the same age group
in the other region, or
– Smaller than it used to be, in the
same region.
The Chicago Guide to Writing about Numbers, 2 nd edition.
Summary
• Choice of a comparison group or value for each variable
in your analysis should NOT be arbitrary.
• Consider the following criteria when selecting a
comparison group for each of your variables.
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Theoretical
Previous literature
Writing patterns
Sample size
• Write your prose interpretation to convey
– Which groups or values are being compared to one another.
– The order in which the calculation was done.
The Chicago Guide to Writing about Numbers, 2 nd edition.
Suggested resources
• Miller, J. E. 2015. The Chicago Guide to Writing about
Numbers, 2nd Edition.
– Chapter 5, section on choosing a comparison group
– Chapter 9
The Chicago Guide to Writing about Numbers, 2 nd edition.
Suggested online resources
• Podcasts on
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Reporting one number
Comparing two numbers or series of numbers
Getting to know your variables
Types of quantitative comparisons
Writing about ratios
The Chicago Guide to Writing about Numbers, 2 nd edition.
Suggested practice exercises
• Study guide to The Chicago Guide to Writing about
Numbers, 2nd Edition.
– Problem sets for
• Chapter 5, questions #3, 4 and 5
• Chapter 8, questions #5 and 7
– Suggested course extensions for chapter 5
• “Reviewing” exercise #1b
• “Applying statistics” exercise #1
The Chicago Guide to Writing about Numbers, 2 nd edition.
Contact information
Jane E. Miller, PhD
jmiller@ifh.rutgers.edu
Online materials available at
http://press.uchicago.edu/books/miller/numbers/index.html
The Chicago Guide to Writing about Numbers, 2 nd edition.