Writing prose to present results
of interactions
Jane E. Miller, PhD
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Overview
• Review of “generalization, example, exception”
approach.
• Complementary use of table, chart and prose.
• Present the overall pattern of the interaction.
– Calculated behind the scenes.
• “Poor, better, best” illustration.
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
The GEE approach
to presenting interactions
• Conduct the calculations behind the scenes.
– Present the results of the calculations.
• Generalize the overall pattern, rather than
reporting each coefficient or value.
• Communicate direction and magnitude of
pattern.
– Often easiest to see using a chart instead of a table.
• See earlier podcast on charts to present interactions.
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Introducing the interaction pattern
• Orient readers to the purpose of testing for
interactions, referring to the specific topics you are
studying
• Name the dependent variable
• Name the two independent variables involved in the
interaction.
• Use phrasing that alerts your readers to the fact that
the association among those variables escapes a simple
generalization.
• For wording suggestions, see podcast on summarizing a
pattern among many numbers.
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Generalization, example, exception
• Generalization:
– Describe an overall pattern, rather than going through
every cell in the table or point on the chart.
• Example:
– Give 1 or 2 representative numeric contrasts to illustrate
generalization.
• Exception(s):
– If parts of the pattern deviate from your generalization,
describe that departure.
– Give a numeric example to illustrate the exception.
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Example coefficients on
main effects and interaction terms
Table 1. Estimated coefficients for a model of
monthly earnings (NT$) in Taiwan, 1992
Variable
Coefficient
Man
Married
Interaction: Man and married
3,205*
–1,595*
4,771*
Compared to unmarried women. Based on multivariate model with
controls for work experience, tenure, monthly hours worked,
educational attainment, residence, and occupation characteristics.
* p < .05
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Poor writing about interactions
“The main effect of ‘man’ was 3,205 and the
main effect of ‘married’ was –1,595, while the
interaction term ‘man and married’ was
4,771 (all p < .05; table 1).”
• Fails to mention dependent variable (earnings).
• Does not explain that the main effect and
interaction terms must be considered together to
calculate net effect of interaction.
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Another poor way
to write about interactions
“Gender and marital status interacted in their
effects on earnings.”
• Conveys that there is an interaction.
• Names the concepts under study.
• Does not explain the direction or size of the
relationship.
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Better, step 1: Table showing
overall pattern of interaction
Table 2. Predicted difference in monthly earnings
(NT$) by gender and marital status, Taiwan, 1992
Women
Men
Married
Unmarried
–1,595
0
6,381
3,205
Unmarried women = reference category.
For married men, the net effect involves both main
effect terms and the interaction term: βman + βmarried
+ βman_married = 3,205 + (–1,595) + 4,771 = 6,381.
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Better, step 2: Prose description
“The net effect of being a married man on
earnings was NT$6,381 compared to unmarried
women (p < .01; table 2).”
• Reports result of calculation involving two main effects
terms and interaction term pertaining to married men.
• Specifies the reference category (unmarried women).
• Does not
– Interpret meaning of the calculation.
– Compare other gender and marital status
combinations to reveal the overall pattern.
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Best, step 1:
Chart showing overall interaction pattern
Figure 1. Predicted difference in monthly earnings (NT$)
by gender and marital status, Taiwan, 1992
Compared to unmarried women. Based on multivariate model with controls
for work experience, tenure, monthly hours, educational attainment,
residence, and occupation characteristics.
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Best, step 2: Prose GEE of the
interaction pattern
• “As shown in figure 1, men earn
more than women regardless of
marital status. But, the effect of
marriage on earnings works in
opposite directions for men than for
women: although marriage confers a
substantial earnings advantage for
men (NT$3,176 extra per month for
married compared to unmarried
men), it is associated with a sizeable
deficit for women (NT$1,595 less per
month for married compared to
unmarried women).”
Figure 1. Predicted difference in monthly
earnings (NT$) by gender and marital
status, Taiwan, 1992
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Annotated prose GEE of interaction
• “As shown in figure 1, men earn more than women regardless of
marital status.”
– Generalizes one part of the pattern, covering all four gender/marital
status groups.
• “But, the effect of marriage on earnings works in opposite
directions for men than for women.”
– Identifies the exception.
• “Although marriage confers a substantial earnings advantage for
men (NT$3,176 extra per month for married compared to
unmarried men), it is associated with a sizeable deficit for
women (NT$1,595 less per month for married compared to
unmarried women).”
– Documents the exception including direction and size, citing evidence
from the behind the scenes calculation of the net effect from the OLS βs.
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Summary: Advantages of the GEE
approach for interactions
• Uses tables and charts to report detailed
numbers for the full pattern.
• Uses prose to summarize the patterns, relating
• The values to one another;
• The observed pattern to the hypothesis about how the
two independent variables together determine the value
of the dependent variable.
• Avoids reporting every number involved in the
interaction in the narrative description.
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Suggested resources
• Miller, J.E. 2013. The Chicago Guide to Writing
about Multivariate Analysis, 2nd Edition.
– Chapter 2, section on “generalization, example,
exception”
– Chapter 14, section on “generalization, example,
exceptions revisited”
– Chapter 16, on interactions
– Appendix A, on step-by-step approach to identifying
and writing a GEE
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Supplemental online resources
• Podcasts on
– Calculating interaction pattern from regression
coefficients
– Choosing tools to present numbers
– Summarizing a pattern with many numbers “GEE”
– Creating charts to present interactions
The Chicago Guide to Writing about Multivariate Analysis, 2nd edition.
Suggested practice exercises
• Study guide to The Chicago Guide to Writing
about Multivariate Analysis, 2nd Edition.
– Questions #3, 4, and 5 in the problem set for Chapter
16
– Suggested course extensions for Chapter 16
• “Reviewing” exercises #3, 4, and 5.
• “Applying statistics and writing” exercises #3 and 4.
• “Revising” exercises #1, 2, and 3.
The Chicago Guide to Writing about Multivariate Analysis, 2nd 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, 2nd edition.