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Binomial Effect Size DisplayPowerPoint Presentation

Binomial Effect Size Display

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## PowerPoint Slideshow about ' Binomial Effect Size Display' - jennifer-rodriquez

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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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