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?

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    $\begingroup$ To answer this question, you will have to detail more your data, the type of test that you want to perform and your ultimate goal... $\endgroup$
    – Pitouille
    Oct 11 at 14:37
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    $\begingroup$ "I have a continuous outcome (0 - 100)" So, it's a percentage? If your expect values close to one of the limits (0 or 100) as shown in the histogram, you should definitely not assume a normal distribution. $\endgroup$
    – Roland
    Oct 11 at 14:40
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    $\begingroup$ Sounds like the use of a finite mixture model of 1 component versus k components to approximate another distribution might work. I don't know if the asker realizes how little of the problem is in the question. what do you think the "true" distribution is. How is the test performed? What is the nature of the population from which samples are being drawn? Is there stratification along indicators? What are the sources of variation? Can you give some bibliography? $\endgroup$ Oct 11 at 14:46
  • $\begingroup$ Above all, the sample size depends on the nature of the study and what its aims are. Please include that information in your post. BTW, this sounds like an enormous study and these data are not very skewed, so in many situations the skewness is unlikely to present a problem. $\endgroup$
    – whuber
    Oct 11 at 15:41

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