Binomial Effect Size Display
What is it?
How do I prepare it?
What is It?
• An interesting way to look at a magnitude of
effect estimate.
• A 2 x 2 contingency table
– Total N = 200
– For each row N = 100
– For each column N = 100
– Treat the cell entries as conditional percentages
Calculating the Cell Entries
• Obtain the r for the effect of interest.
• On one diagonal the cell entries are
100(.5 + r/2)
• On one diagonal the cell entries are
100(.5 - r/2)
Physicians’ Aspirin Study
•
•
•
•
φ2 = .0011
r = φ = .034
100(.5 + r/2) = 100(.5 + .017) = 51.7
100(.5 – r/2) = 100(.5 - .017) = 48.3
Treatment
Aspirin
Placebo
Heart
Attack
48.3
51.7
No Heart
Attack
51.7
48.3
Interpretation
• The treatment explains 0.11% of the variance in
heart attacks.
• This is equivalent to a treatment that reduces the
rate of heart attacks from 51.7% to 48.3%.
• Odds ratios can be revealing too. Here the odds
ratio is (189/10,845)/(104/10,933) = 1.83.
• The odds of a heart attack were 1.83 time higher
in the placebo group than in the aspirin group.
Predicting College Grades From SAT
(Verbal and Quantitative)
• Multiple R = 0.41
• 100(.5 + r/2) = 100(.5 + .205) = 70.5
• 100(.5 – r/2) = 100(.5 - .205) = 29.5
Low SAT
High Sat
Low Grades High Grades
70%
30%
30%
70%
Effect from ANOVA
• η2 = .06 (medium-sized effect)
• 100(.5 + r/2) = 100(.5 + .12) = 62
• 100(.5 – r/2) = 100(.5 - .12) = 38
Low Mean DV
Low Group
62%
High Group
38%
High Mean DV
38%
62%