first time asking question here so I hope I will not mess up.
I am in the process of calculating the sample size for a study that utilizes an independent t-test design: comparing some outcome before and after a certain policy, subjects in the pre and post periods are not linked. Simply put, the study is about infant weaning food distributed in developing countries. The outcome is percent weight of cooking ingredients that is oil, which is fortified with nutrients.
The current recommendation is 9% weight of the baby's meal should be the fortified oil (about 1 part of oil to 10 part of powered grains). The organization is trying to promote a new amount of 16% oil, which was shown to be associated with better anthropometric outcomes.
I could use the usual t-test sample size formula, but I'm concerned that the SD of the mean 9% point may not be meaningful because the outcome is bound between 0% to 100%, the distribution of the percent point at the extremes (like 9%) is likely to be non-normal, and additionally not all caretakers follow the cooking guideline so the SD is probably huge.
So my question is: do you know of any formula is applicable to this situation of comparing mean when the individual (not group) level data are proportion?
Many thanks for reading. I appreciate any advice or reference.