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| $$ \sqrt{ \Sum_text{i}^text{no. groups} \mbox{(observed proportion - expected proportion)}^text{2} / expected proportion} $$ |
$$\sqrt{ \sum_text{1}^text{no. groups} / (observed proportion - expected proportion)^text{2} / expected proportion}$$ |
The [attachment:prop1s.xls spreadsheet] gives the power for inputted group proportions (which should sum to 1), Type I error and given total sample size. The expected proportions are assume equal group sizes.
The expected effect size w is
$$\sqrt{ \sum_text{1}text{no. groups} / (observed proportion - expected proportion)text{2} / expected proportion}$$