1. The Chicago Guide to Writing about Numbers, 2 nd edition. Choosing a comparison group Jane E. Miller, PhD

2. The Chicago Guide to Writing about Numbers, 2 nd edition. Overview What is a comparison group? Choosing comparison groups based on – Theoretical criteria – Previous literature on the topic – Writing patterns – Sample size

3. 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.

4. 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.

5. 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.

6. 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.

7. 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

8. 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!

9. 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.

10. 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!

11. 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.

12. 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. – 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.

13. 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.

14. Suggested online resources Podcasts on – Reporting one number – Comparing two numbers or series of numbers – Getting to know your variables – Types of quantitative comparisons – Writing about ratios

15. 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

16. 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