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

Binomial Effect Size Display

What is it?

How do I prepare it?


What is 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

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

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

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

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

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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