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Binomial Effect Size Display

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.

jennifer-rodriquez
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Binomial Effect Size Display

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  1. Binomial Effect Size Display What is it? How do I prepare it?

  2. 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

  3. 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)

  4. 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

  5. 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.

  6. 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

  7. Effect from ANOVA • η2 = .06 (medium-sized effect) • 100(.5 + r/2) = 100(.5 + .12) = 62 • 100(.5 – r/2) = 100(.5 - .12) = 38

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