Collect the other variables required in the calculation. In nearly all cases, if the researcher already has a reliable P2 statistic, he has everything else he needs. These statistics are the sample size and the significance level. The sample size is the number of subjects in the study. Call this statistic “n.” The significance level is determined by the researcher; it is the false positive rate. Most research projects use significance levels from 0.01 to 0.1. The most common value is 0.05. Call the significance level “alpha.”
Use a Z-table to find the Z-scores needed in the effect size calculation. Almost every introductory statistics textbook includes such a table. You will need the Z-scores for 1-P2 and 1-(alpha/2). Calculate these two numbers, and then find the Z-score corresponding to them in the Z-table. Call these numbers ZP and ZA, respectively.
Calculate the effect size. Add the Z-scores together. Multiply the result by the square root of 2. Divide this result by the square root of the sample size. In mathematical notation, the effect size is equal to sqrt(2)*(ZP + ZA)/sqrt(n), where “sqrt” refers to the square root function.