Binomial Effect Size Display What is it How

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% 70%

Effect from ANOVA • η 2 =. 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%