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 φ 2 =.0011 r = φ = (.5 + r/2) = 100( ) = (.5 – r/2) = 100( ) = 48.3 TreatmentHeart Attack No Heart Attack Aspirin Placebo

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) = 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 = (.5 + r/2) = 100( ) = (.5 – r/2) = 100( ) = 29.5 Low GradesHigh Grades Low SAT70%30% High Sat30%70%

Effect from ANOVA η 2 =.06 (medium-sized effect) 100(.5 + r/2) = 100( ) = (.5 – r/2) = 100( ) = 38 Low GroupHigh Group Low Mean DV62%38% High Mean DV38%62%