DeclareDesign Community

Why need rho in two-arm experiment?

I am currently reading about the two-arm experiment in the DeclareDesign library. I realize that this is probably a very basic question, but I’m honestly confused about declaration of the population and potential_outcomes code:

population <- declare_population(N = N, u_0 = rnorm(N), u_1 = rnorm(n = N, 
    mean = rho * u_0, sd = sqrt(1 - rho^2)))

potential_outcomes <- declare_potential_outcomes(Y ~ (1 - 
    Z) * (u_0 * control_sd + control_mean) + Z * (u_1 * treatment_sd + 
    treatment_mean))

Here are my questions:

  1. For defining the population, I’m confused about why we need rho at all. What does this do? I just thought that the code would ensure the u_0 and u_1 are the same like when rho = 1 (not sure why we wouldn’t want u_0 and u_1 to be the same). This is what I thought this code would look like:
population <- declare_population(N = N, 
                                 u_0 = rnorm(N), # Take mean = 0, sd = 1
                                 u_1 = u_0) # Make sure u_0 and u_1 are the same
  1. For potential_outcomes, I’m somewhat confused about this piece of the code: u_0 * control_sd + control_mean and this piece u_1 * treatment_sd + treatment_mean. What is this code trying to accomplish? I feel like I need a better grasp so I can adjust it in future designs.

Thanks in advance for the help!

Hello all, I am still needing help with this question. Any assistance would be greatly appreciated!