Binomial effect size display
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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.

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Binomial Effect Size Display

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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


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


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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