I have a continuous outcome (0 - 100) that is quite skewed, I have attached a graph. I want to calculate the sample size to conduct a study. I am unsure as how to proceed. We are looking to recruit 10000+ patients to the study - sample size required to be certain what the number will be.
Would it be okay to use an approach that assume gaussian assumption? When it comes to testing, there is literature out there to suggest that it would be okay to use a test that assume normality even if the underlying data doesn't seem to follow it. Does it follow for sample sizes in anyway? Or would i need to use a non-parametric approach? I have not found a non-parametric approach that would account for clustering.
How would i be able to quantify the error that is likely to occur if I used an approach that assumed normal distribution?