Differentiating between
statistical significance and
substantive importance
Jane E. Miller, PhD
The Chicago Guide to Writing about Numbers, 2nd edition.
Overview
• Substantive significance defined
• Quick review of statistics
– What questions can they answer?
– What questions can’t they answer?
• How to implement a balanced presentation of
multivariate results. Both
– Statistical significance
– Substantive importance
The Chicago Guide to Writing about Numbers, 2nd edition.
Objective of most research papers
• Few people who write about multivariate analysis are
focused solely on statistical mechanics such as
developing new computer algorithms or formal
statistical tests.
– Some statisticians and methodologists will have those
interests.
• Most of us are interested in studying some relationship
among social science or health concepts.
– Test a hypothesis, derived from theory or previous empirical
studies.
– Inferential statistics are a necessary tool for hypothesis
testing in quantitative research.
The Chicago Guide to Writing about Numbers, 2nd edition.
What is substantive significance?
• Substantive significance of an association between two
variables.
– “So what?”
– “How much does it matter?”
• Real-world relevance to topic
• In various disciplines, substantive significance =
–
–
–
–
“clinically…
“economically…
“educationally…
…meaningful” variation.
The Chicago Guide to Writing about Numbers, 2nd edition.
Example: Body Mass Index & mortality
• Body mass index (BMI) shows a statistically
significant positive association with mortality.
• But is that gradient substantively significant?
– Is it worth designing an intervention to decrease
BMI as a way of decreasing mortality?
The Chicago Guide to Writing about Numbers, 2nd edition.
Key criteria for assessing
substantive significance
• Is the association causal?
– Will changing the hypothesized cause lead to change
in the purported effect?
– Will weight loss (reduced BMI) yield lower mortality?
• Is the effect big enough to matter?
– Is the excess mortality among overweight or obese
persons large enough to justify a program?
• Can the hypothesized cause be changed?
– Is BMI malleable?
The Chicago Guide to Writing about Numbers, 2nd edition.
Example prose
• “For every hour a boy played a video game, he
read just two minutes less than a boy who
didn’t play video games. Notably, non-gaming
boys didn’t read much at all either, spending
only eight minutes a day with a book.”
• From a NYT summary of Cummings and Vandewater, 2007.
“Relation of Adolescent Video Game Play to Time Spent in
Other Activities,” Archives of Pediatrics and Adolescent
Medicine.
The Chicago Guide to Writing about Numbers, 2nd edition.
Quick review of statistical
significance testing
The Chicago Guide to Writing about Numbers, 2nd edition.
Start with a hypothesis
• The authors hypothesized that the more time
adolescents spent on video games, the less time they
spent on homework.
– So far, description is purely in terms of the concepts under
study.
– No statistical jargon, yet…
• To formalize this for statistical testing
– Homework time = dependent variable (Y)
– Gaming time = independent variable (Xi)
– Ha= gaming time is negatively associated with homework
time.
• In other words, Xi is inversely associated with Y
The Chicago Guide to Writing about Numbers, 2nd edition.
Contrast it against the null hypothesis
• The assumption of “no difference between groups” is
called the null hypothesis (H0).
• In the study on effects of gaming on homework time
H0: time among gamers = time among non-gamers
OR
time among gamers - time among non-gamers = 0
• In words, the null hypothesis states that there is no
difference in the amount of time spent on homework
by gamers versus non-gamers.
The Chicago Guide to Writing about Numbers, 2nd edition.
What ? does inferential statistics answer?
• “How likely would it be to obtain a difference at
least as large as that observed between groups in
the sample if in fact there is no difference between
groups in the population?”
• The p-value tells us the probability of falsely
rejecting the null hypothesis.
– Conventional levels of “statistical significance” : p<.05
– Strictly speaking, p<.05 tells us that for a large sample
such as that used in the gaming study (N~1,400), the
estimated effect size on time spent gaming is at least 1.96
times its standard error.
The Chicago Guide to Writing about Numbers, 2nd edition.
What questions DOESN’T it answer?
• Whether the relationship is
– Causal
• Association ≠ causation
– In the expected direction
• The difference could be statistically significant but in the
opposite of the hypothesized direction.
– Big enough to matter in the real-world context
• Each hour spent gaming reduced reading time by 2
minutes. Is that enough to induce genuine concern from
parents or teachers?
– Malleable
The Chicago Guide to Writing about Numbers, 2nd edition.
Conclusion: Don’t stop at “p<.05”!
• “p<.05” answers only part of what we want to know
about our research question.
– It is a necessary but not sufficient part of statistical analysis.
• Also need to consider questions about:
– Substantive significance
• Direction
• Size
– Causality
• Non-causal associations should not be used to inform
policy or program changes.
• Confounding or spurious associations should be ruled out.
– Often why a multivariate model is estimated.
The Chicago Guide to Writing about Numbers, 2nd edition.
Substantive significance overlooked
• Many statistics textbooks show how to assess
and present statistical significance.
• Few if any show how to assess and present
substantive significance.
The Chicago Guide to Writing about Numbers, 2nd edition.
Balance presentation of statistical
and substantive significance
• How to include both:
– Inferential statistics for formal hypothesis testing.
– Interpretation of substantive significance of findings
in the context of the specific research question.
• Critical for policy-makers and others not formally trained
in statistics.
The Chicago Guide to Writing about Numbers, 2nd edition.
Principles for presenting results
• Name the specific variables. Avoid
– Writing about “my dependent variable” or “the
effect size.”
– Using acronyms from your database 
• Report numbers in tables.
• Interpret numbers in text.
– Incorporate units and categories for variables into
the prose description.
The Chicago Guide to Writing about Numbers, 2nd edition.
What to report when comparing numbers
• Direction (AKA “sign”)
– For categorical independent variables (IV), which
category has higher value of the dependent variable
(DV)?
– For continuous IVs, is the trend in the DV up, down,
or level?
• Magnitude
– How big is the difference in the DV across values of
the IV?
• Statistical significance
The Chicago Guide to Writing about Numbers, 2nd edition.
Gender as a predictor of birth weight
• Poor: “Boys weigh significantly more at birth than
girls.”
– Concepts and direction but not magnitude.
– Statistical significance is ambiguous: Is the term “significant”
intended in the statistical sense or to describe a large
difference?
• Slightly better: “Gender is associated with a difference
of 116.1 grams in birth weight (p<.01).”
– Concepts, magnitude, and statistical significance but not
direction: Was birth weight higher for boys or for girls?
• Best: “At birth, boys weigh on average 116 grams
more than girls (p<.01).”
– Concepts, reference category, direction, magnitude, and
statistical significance.
The Chicago Guide to Writing about Numbers, 2nd edition.
Substantive significance
in the discussion
• Place findings back in the broader perspective of the
original research question.
• Do they correspond to your hypothesis in terms of
– Direction (sign) of the effect?
– Size?
– Whether the effect size was attenuated when potential
confounders or mediators were taken into account?
• What is the evidence for a causal relationship?
– If not causal, what explains the association?
– If causal, what are the implications for policy, programs, etc.?
The Chicago Guide to Writing about Numbers, 2nd edition.
A substantive issue from gaming study
• “But the meaning of the finding [that girls who
are gamers spend less time than non-gamers on
homework] is not clear, as high-academic
achievers often spend less time on homework as
well.”
– Places the finding in broader context by discussing
other correlates of homework time.
The Chicago Guide to Writing about Numbers, 2nd edition.
Another substantive issue
• “Although only a small % of girls played video
games, our findings suggest that gaming may
have different social implications for boys than
for girls.”
– Raises the question of selection effects: which girls
play video games, and do their other characteristics
affect how they spend their time?
The Chicago Guide to Writing about Numbers, 2nd edition.
Relate findings to previous studies’
• Are your findings consistent with the published
literature on the subject in terms of statistical
significance, sign, and approximate size?
• If not, why not?
– Different sample (place, time, subgroup)
– Different data source or study design
– Different model specification
• Included potential confounders not previously analyzed.
• Tested for possible mediating effects of 1+ factors.
The Chicago Guide to Writing about Numbers, 2nd edition.
Statistical significance in the discussion
• Describe in words, not numbers.
– No detailed standard errors, p-values, or test
statistics in the discussion section.
• Focus on the purpose of the statistical tests
– Did the main variable of interest increase
proportion of variance explained by the model?
– Did some other variable “explain” the association
between your key variable and the outcome?
The Chicago Guide to Writing about Numbers, 2nd edition.
Summary
• Emphasize the substantive issues behind the
statistical analyses.
– Design the specification to match topic and data.
– Choose plausible, relevant numeric contrasts.
• Aim for a balanced presentation of statistical
significance and substantive importance.
– Use prose to ask and answer research question.
– Use tables to report comprehensive, detailed
statistics.
– Use charts if needed to convey complex patterns.
The Chicago Guide to Writing about Numbers, 2nd edition.
Suggested resources
• Chapter 3 (Statistical significance, substantive
significance, and causality) in
– Miller, J.E., 2015. The Chicago Guide to Writing about
Numbers, 2nd Edition
• Miller J.E. and Y.V. Rodgers, 2008. “Economic
Importance and Statistical Significance: Guidelines for
Communicating Empirical Research.” Feminist
Economics. 14(2):117-149.
The Chicago Guide to Writing about Numbers, 2nd edition.
Suggested online resources
• Podcast on comparing two numbers or series
The Chicago Guide to Writing about Numbers, 2nd edition.
Suggested practice exercises
• Study guide to The Chicago Guide to Writing
about Numbers, 2nd Edition.
– Questions #2 and #4 from the problem set for
chapter 3
– Suggested course extensions for chapter 3
• “Reviewing” exercises #1–3
• “Writing and revising” exercises #1–3
The Chicago Guide to Writing about Numbers, 2nd 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, 2nd edition.