Effect Sizes
E0420
Week 13
Cohen's d: How to interpret it? | Scientifically Sound Illustration of the population, with a
part exposed to a risk factor. (AFp = 1/9).

Why do we report effect sizes?
•Statistical significance ≠ practical significance
•We need to know how large the obtained effect is
•Effect size = objective (and standardized) measure of the magnitude of the observed effect
•Standardized = comparable across studies
•Meta-analyses
•Population impact measures
•Measures used to describe the impact of health risks and benefits in a population (to inform
health policy)
•Odds Ratio (OR), Relative Risk (RR)
•Number needed to treat (NNT), Population attributable fraction (PAF)

Effect sizes for common statistical tests
Test
Effect Size
Chi-square – 2x2 table
Phi (φ), Odds Ratio (OR), Relative Risk (RR)
Chi-square – bigger table
Cramer’s V
T-test
Cohen's d
ANOVA
η2, Cohen’s f
Correlation
R
Regression – linear
β, R2
Regression – logistic
OR, RR
Mediation
R2, proportion mediated, standardized indirect effect
Moderation
R2, f2

Cohen's d
•Standardized mean difference
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•d = Cohen's d effect size; X1 and X2 = means of the two groups; s1 and s2 = standard deviations of
the two groups
•https://rpsychologist.com/cohend/
d = Cohen's d effect size; X1 and X2 = means of the two groups; s1 and s2 = standard deviations of
the two groups.

Sources: Larner, A. J. (2014). Effect size (Cohen's d) of cognitive screening instruments examined
in pragmatic diagnostic accuracy studies. Dementia and geriatric cognitive disorders extra, 4(2),
236-241.

Relative risk
•The relative risk (=risk ratio [RR]) is the ratio of risk of an event in one group (e.g., exposed
group) versus the risk of the event in the other group (e.g., nonexposed group).
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•The group exposed to treatment (left) has half the risk (RR = 4/8 = 0.5) of an adverse outcome
(black) compared to the unexposed group (right)
•Equivalent information to Odds Ratio (OR)
Illustration of two groups: one exposed to treatment, and one unexposed. Exposed group has smaller
risk of adverse outcome, with RR = 4/8 = 0.5.

Sources: https://en.wikipedia.org/wiki/Relative_risk

Relative Risk vs Odds Ratio

Sources: Ranganathan, P., Aggarwal, R., & Pramesh, C. S. (2015). Common pitfalls in statistical
analysis: Odds versus risk. Perspectives in clinical research, 6(4), 222–224.
https://doi.org/10.4103/2229-3485.167092

Population attributable fraction (PAF)
•PAF is the proportion of incidents in the population that are attributable to the risk factor
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•A quarter of the population is exposed to a risk factor (i.e., radiation) and has a higher risk of
an adverse outcome (black). In the whole population, one ninth of the adverse outcomes can be
attributed to the exposure (PAF = 1/9)
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Illustration of the population, with a part exposed to a risk factor. (AFp = 1/9).

Sources: https://en.wikipedia.org/wiki/Attributable_fraction_for_the_population

Real-life Example
•The population attributable fractions to compare the contributions of different sources of alcohol
supply are shown in Table 4. They suggest that due to high prevalence in this sample (~ 18%) as
well as consistently increased risk for later alcohol use, parental supply of alcohol emerged as
the major contributor to frequent use at age 15, with PAF 0.17 and 0.12 for less frequent use
(adolescent and pediatrician report) and 0.23/0.23 for frequent use. Supply of alcohol from other
family member was also considerable, with PAF between 0.10 and 0.13 for the adolescent report and
between 0.05 and 0.11 for the pediatrician report.

Final Assignment (80 points)
•Topic and data selection (10 points)
•Please, fill this spreadsheet on 16/12 at the latest:
https://ucnmuni.sharepoint.com/:w:/t/ERAGroup-internal/ESaph_FXvC1IvKZLlSPsjyEBnzdRc10xt8yV-RHBNzQK
7g?e=5IMYRY
•Data analysis and write-up (70 points)
•Submit SPSS syntax, output, and a word document to is.muni Homework Vaults (“Odevzdávárna”) on
11/2 at the latest.
•Papers must be double-spaced, typed, and follow a specific reference/formatting style (e.g., APA,
Chicago, CSE)
•Example is in is.muni -- Study Materials -- Course-related instructions