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| $$\omega = \sqrt{ \sum_text{1}^text{no. groups} \frac{\mbox{(observed proportion - expected proportion)}^text{2}}{ \mbox{ expected proportion}}}$$ | \omega = Sqrt{ Sum_(1^no. groups) (observed proportion - expected proportion)}^2 ^} / expected proportion |
The spreadsheet gives the total sample size required for inputted group proportions (which should sum to 1), Type I error and a given power. The expected proportions are assume equal group sizes.
The expected effect size, $$\omega$$, defined below is from Cohen (1977,1988, Chap 7).
\omega = Sqrt{ Sum_(1no. groups) (observed proportion - expected proportion)}2 ^} / expected proportion
The thresholds 0.1, 0.3, 0.5 correspond to small, medium and large $$\omega$$ effect sizes.