Basics of writing about numbers: Reporting one number

1. Basics of writing about numbers: Reporting one number Jane E. Miller, PhD

2. Overview • Which information to include when reporting a number • Context • Units • Illustrative examples • Poor/better/best

3. Setting the context (“the W’s”) • For everyexample 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.

4. 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., 2005 vs. 2015) • 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.

5. Specifying units • System of measurement • Scale • Level of aggregation

6. Specifying units: System of measurement • British? • Metric? • Other?

7. Specifying units: Scale • Length in centimeters or meters? • Weight in grams or kilograms? • Mortality rate percent, per 1,000 or per 100,000?

8. 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?

9. 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.

10. Reporting a single number • “During the 3rd century, the Black Plague killed 25million people in Europe.” • “In 2001, the average temperature in the New York City areawas 56.3degrees 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.

11. 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.

12. Too little information • Poor: “The height was 27.” • What are we measuring? • In what context? • In what units? • Better: “The plant measured 27centimeters 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 plantthat was watered daily measured 27centimeterstall.” • When, what (plant height), which plant, size, andunits.

13. 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 plantthat was watered daily measured 27centimeterstall.” • All of the W’s and units in one sentence. • With practice, you will get closer to this version on your first try.

14. Repetitive information • Poor: “The first day after germinating, the plant that was watered daily was 0.7centimeterstall. The third day after germinating, the plantthat was watered daily. . . Two weeks after germinating, the plantthat was watered daily measured 27centimeterstall.” • 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. • Onlythe date changes, so it and the updated value (number) are the only W’s required in the second and subsequent sentences.

15. Better reporting of several numbers • Better: “The first day after germinating, the plant that was watered daily was 0.7centimeters (cm) tall. Two days later, it measured 3.8cm. By two weeks after germination, it had reached 27 cm.” • The word “it” stands in for “the plantthat 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.

16. 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.

17. 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; see Chicago Guide to Writing about Multivariate Analysis, 2nd Edition. • Designing effective tables and charts • See associated podcast

18. Suggested resources • For basic principles, see chapters 1 and 2 in Miller, J. E. 2015. The Chicago Guide to Writing about Numbers, 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 Forum74 (4): 334–46.

19. Suggested practice exercises • Study guide to The Chicago Guide to Writing about Numbers, 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

20. Contact information Jane E. Miller, PhD jmiller@ifh.rutgers.edu Online materials available at http://press.uchicago.edu/books/miller/numbers/index.html