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Multiple Paired Binary Variables

3c. Effect size measure

For the omnibus test (the Cochran's Q test) there are two effect size measures that are sometimes used. The first is a maximum-corrected version, known as eta-squared (η²) (Serlin, Carr, & Marascuilo, 1982), while the other is a chance-corrected version with symbol R (Berry, Johnston, & Mielke, 2007). The chance corrected version seems to be the one that is preferred, but is also more difficult to calculate.

The less prefered eta-squared can be calculated by subtracting one from the number of variables. In the example we had four variables so this would be 4 - 1 = 3. Then multiply this by the number of cases. In the example we had 150 respondents, so 3 x 150 = 450. Then divide the test statistic (Q) by this result. In the example Q was 19.385, so we get η² = 19.385 / 450 ≈ .043.

In the example the chance-corrected measure was R = .026 which is very weak. We can add this to our report.

Cochran's Q test indicated that there are differences between the proportions among the four options of visited cinemas, χ²(3, N = 150) = 19.38, p < .001. The overall effect of the cinema on the results is relatively weak,R = .03.
A pairwise post-hoc Dunn test with Bonferroni adjustments was only significant for Munt vs. Arena (p = .024) and Munt vs. Movies (p < .001).

FAQ:

Q: How do I get that strange R in MS Word?
A: Type in a regular capital R, select it and change the font to 'Monotype Corsiva'.

3+ binary

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Impression

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Test

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Effect size

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