Can you let me know the formula to calculate effect size for mean difference using proportions and CI (95%)?
I am not sure I fully understand your questions but there are at least three ways of estimating effect size for sample/power calculations:
1. From past literature: If studies have shown that an a control population A has x proportions with the outcome and the intervention population B have y proportions with the outcome, the effect size=proportion in B - proportion in A=y-x.
2. If no past literature is available, one can do a small pilot study to determine the effect size.
3. Clinical expectations: Here is where investigators set a certain threshold of difference in proportions that will be clinically significant and use this to estimate the sample size/power calculations.
Remember that the effect size is a denominator in most sample size estimation formulas. Therefore, the larger the effect size, the smaller the sample size required.
If you have the poportions given as "cases" (and "sizes") ("binomial data"), then you best run a logistic regression. The respective coefficient is the effect size estimate. It is typically provided together with its CI.
If the proportions are onyl values (like precent values of something), then you can run a beta regression. Again you get the coefficients as effect size estimates together with the CIs.
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