Hello

I need some advice regarding sample size calculations.

I need to calculate a sample size for a study testing a new drug. In the study there will be 4 groups: 2 groups of the drug with different doses, and 2 control groups: one is the gold standard drug and one is placebo.

The response variable can get the values: 0,0.5,1,1.5,2,2.5,3,3.5,4,4.5,5 where 0 is the lowest and 5 highest.

The required effect size between the drug and control is assumed to be known (call it delta) and the standard deviation in each group is also known (sigma1 - sigma4).

I need to make 2 calculations, once for a scenario of superiority of the new drug over the placebo and once for non-inferiority of the new drug in compare to the gold standard.

I need your advice, which formulas would you use for the calculations ? Let's say for the matter that I do not wish to use a statistical software, but to do it by hand, which formulas are most suitable in your opinion and why ?

thank you very much !!