# Thread: Experimental Design - Distribution Question

1. ## Experimental Design - Distribution Question

Hi, I'm studying a module called Experimental Design. I don't think my question is too difficult but I can't get my head around it.

Background:
Clinical trial conducted on Mars comparing two treatments A and B on frostbite. Allocation is simple randomisation, Pr(allocation to A)=1/2.
So I have that the distribution of the number of martians, T, allocated to treatment A is: T ~ Bin(N,1/2)

Now to the question:
There are 2 kinds of martian, Red and Green. Red are more likely to have frostbite that green. Of the N Martians in the trial. What is the distribution of G, the number of Green martians allocated to treatment A?

Question 2
To avoid preponderance of Red or Green on one of the treatments, martians are stratified by colour. Both colour allocated to A or B using Simple Randomization. No of Green on A is G_A etc... Give distributions of G_A and R_A?

2. ## Re: Experimental Design - Distribution Question

The total number of green martians is $G_A + G_B$

So applying the same methodology we end up with

$G_A \sim Bin\left(G_A+G_B,~\dfrac 1 2\right)$

There are $N-(G_A+G_B)$ red martians

$R_A \sim Bin\left(N-(G_A+G_B),~\dfrac 1 2\right)$