Dominance Score
Explanation
A simple effect size measure that shows the difference between the proportion of cases that were above the hypothesized median, and those below it. It can range from -1 to 1. A -1 would indicate all scores are below the hypothesized median, +1 all above, and 0 the same amount of scores above as below.
Mangiafico (2016, p. 223-224) also describes a Vargha Delaney A (VDA) like variation on this, that re-scales the dominance score to 0 to 1, with 0.5 as indication that half fall above, and half below..
Obtaining the Measure
with SPSS (somewhat)
Formulas
The dominance score can be calculated using (Mangiafico, 2016, p. 223-224):
\(D = p_+ - p_- \)
Where \(p_+\) is the proportion of scores above the hypothesized median, and \(p_-\) the proportion below, i.e. \(p_i = \frac{n_i}{n}\).
To re-scale to 0 to 1 for the VDA like measure use (Mangiafico, 2016, p. 223-224):
\(V = \frac{D + 1}{2} = \frac{p_+ - p_- + 1}{2} \)
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