The [[attachment:prop1sn.xls|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 (1 to no. 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.