The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Choosing tools to present numbers: Tables, charts, and prose Jane E. Miller, PhD

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Overview Three tools for presenting numbers General tasks involved in writing about numbers Criteria for selecting the right tool(s) for each task Examples

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Pick the right tool(s) for the job Prose – Body of text. – Footnotes. – Appendices. Tables – To accompany text. – Appendices. Charts – To accompany text. – Appendices.

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Strengths and weaknesses of different tools

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Tools for each task In most writing about numbers, will have several separate tasks, e.g., – Few numeric facts in the introduction; – Descriptive statistics on several variables; – Estimated coefficients from multivariate models; – Complex patterns, e.g., polynomials or interactions; – Summary of major findings in discussion section. For each task, choose the 1 or 2 best tools – Complementary use of prose with table or chart.

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. When to use prose To ask and answer questions using numbers as evidence – Introduce the topic (“word problem”) – Explain the purpose of numbers to be presented – Show how numbers or patterns answer the word problem at hand To report or interpret a few numbers – Describe trends – Explain numeric contrasts – Summarize patterns

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. When not to use prose When you there are more than a handful of numbers involved in a pattern, e.g., – Annual prices for several regions and products over a period of several years or decades – Individual values that comprise a bivariate or three- way association – Estimated coefficients and standard errors for each of a dozen variables – Estimated coefficients for a variable in each of several nested or stratified models

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Why not to use prose to report lots of numbers To identify and interpret each number, need the associated W’s and units. – What, when, where, who – How many – Units Reporting lots of numbers in prose requires many sentences. – All those W’s and units clutter up the prose; – Make it difficult to find the pertinent number; – Also hard to see overall pattern among the numbers.

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Prose versus table Standard & Poor 500 StockOpenCloseHighLow ABC$$$$ AQR$$$$ …………… BBB$$$$ …………… …………… …………… ZAB$$$$ ZZZ$$$$ Do you really want to read separate sentences reporting the opening, closing, high, and low prices for 500 stocks every day? A table provides – An easy to follow structure for locating the specific stocks and prices – Precise prices (to the cent)

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Table versus chart This chart displays 70 numbers  For each of past five days  Record high and low (blue)  Average high and low (yellow)  Actual high and low (pink)  For each of the next five days  Record high and low (blue)  Average high and low (yellow)  Range of forecast high (pink)  Range of forecast low (pink)

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Table version Record, average, and actual or forecast high and low temperatures (°F), New York City, January 14 – 23, 2005 Fr.Sa.Su.Mo.Tu.We.Th.Fr.Sa.Su. Record high## Average high## Actual high## Forecast high range## Forecast low range## Actual low## Average low## Record low##

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. When to use a chart Charts are good for quickly conveying – Approximate values and patterns. – Direction and magnitude of associations. Useful for – Speeches, where your audience only has a little time to see the shape of a pattern. – Displaying complicated patterns. Nonlinear Comparing lines that are diverging, converging, crossing

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Comparisons on this chart Easy to see – Trends across time in Record values Average values Actual values – Comparison of actual to record or average – Range of temperatures on a given day – Level relative to a comparison value, e.g., freezing point

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Trend in actual temperature “The high temperature plummeted 30° between January 14 and 15 (63°F and 33°F, respectively).” “The high temperature on January 15 barely reached the level of the low temperature from the preceding day.”

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Actual versus record and average Put that change in context by comparing actual to record and average temperatures: “Although the high temperature on the 14th neared record levels for that date, by the next day, temperatures were back in the normal range.”

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. When to use a table Tables are good for organizing lots of numbers when exact values are needed. – Comparing test statistics against critical values, – Making calculations with others’ data, E.g., comparing temperatures or prices New York to Chicago to Los Angeles from published data. Useful for reporting – Detailed statistical results from multivariate models, – Data for others to use in their own computations.

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Record, average, and actual or forecast high and low temperatures (°F), New York City, January 14 – 23, 2005 Fr.Sa.Su.Mo.Tu.We.Th.Fr.Sa.Su. Record high## Average high## Actual high## Forecast high range## Forecast low range## Actual low## Average low## Record low##

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Record, average, and actual or forecast high and low temperatures (°F), Los Angeles, January 14 – 23, 2005 Fr.Sa.Su.Mo.Tu.We.Th.Fr.Sa.Su. Record high## Average high## Actual high## Forecast high range## Forecast low range## Actual low## Average low## Record low##

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Estimated coefficients from an OLS models of birth weight (grams) by race/ethnicity, socioeconomic status, and smoking, U.S., 1988–1994 VariableCoefficientStd. error Intercept3,318.8**25.1 Race/ethnicity (Non-Hispanic White) Mexican American– Non-Hispanic Black–172.6**17.5 Mother’s education Less than high school–55.5**19.3 High school graduate–53.9**14.8 (College+) Boy117.2**12.0 Mother’s age at birth of child (yrs.)10.7**1.2 Income-to-poverty ratio (IPR) a 80.5**14.5 IPR 2 –9.9**2.3 Mother smoked during pregnancy–194.7**14.4 F-statistic (df)94.08 (9) BIC-728.4; Adjusted R *p < 0.05 **p < 0.01 Using a table like this on a slide is *not* recommended! This is only to illustrate what is meant by “detailed #s.”

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. When not to use a table Avoid using tables with lots of detailed numbers in – Slides for a speech Type size will be too small for audience to read – Formats for nonscientific audiences Too many numbers will overwhelm rather than inform

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Revising tables for use on slides For slides or nonscientific audiences: – Revise a table with many detailed statistics into several smaller tables. – Create chart versions of portions of the table. Each slide will address one major point. E.g., – An association between one independent variable and the dependent variable. – How a coefficient changes across nested models.

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Summary To decide among tables, charts, and prose for presenting numbers, consider – How many numbers? – How much time? – Precise values versus general levels or trends? Often, will complement a table or chart with prose narrative description. Rarely use a table and a chart of the same pattern.

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Suggested resources For basic criteria for deciding among tables, charts and prose, see chapters 1 and 2 in – Miller, J. E The Chicago Guide to Writing about Numbers (“WA#”) OR – Miller, J. E The Chicago Guide to Writing about Multivariate Analysis, 2nd Edition. (“WAMA”). Chapters in WA# or WAMA on – Creating effective tables – Creating effective charts – Writing about distributions and associations – Speaking about numbers Chapter 20 in WAMA, on presenting to nonstatistical audiences.

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Suggested online resources Podcasts on – Reporting one number – Summarizing a pattern – Creating effective tables and charts – Designing slides for a speech – Presenting statistical results to nonstatistical audiences

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 #3 in the problem set for chapter 2 – Suggested course extensions for chapter 2 “Reviewing” exercise #4 “Writing” exercise #1 “Revising” exercises #1 and #2

The Chicago Guide to Writing about Multivariate Analysis, 2 nd edition. Contact information Jane E. Miller, PhD Online materials available at