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Thread: Experimental Design - Distribution Question

  1. #1
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    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?

    Can somebody please help/guide me! I've looked at it for hours and gotten nowhere with it.
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  2. #2
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    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

    $R_A \sim Bin\left(N-(G_A+G_B),~\dfrac 1 2\right)$
    Thanks from BettyBuzz
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  3. #3
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    Re: Experimental Design - Distribution Question

    Thank you for your help!
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