I'm trying to code out some equations in a paper to help test some sample data, but having trouble interpreting the statistical equations and converting them to code in R. I'm trying to define H and G such that I will have a function to perform that corresponds to p # of variables measured, a # of treatments, and n sample size. The two equations that I would like to make functions of are included in the pictures attached. I'm not sure how to incorporate the R bars and then the prime function of the first one.. not entirely sure what they even represent?
Appreciate any and all help on this one. 