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Thread: Needing some correlation quick advice

  1. #1
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    Needing some correlation quick advice

    I have created a sample set of data, and I would like to find the right approach that would give me the kind of result I am looking for. I will explain:
    In column A half of the results are a 1 (patient took a pill) and half are a 0 (patient did not take a pill). For all of the results in column B adjacent to a 1 (took a pill) I generated a random number between 90 - 100. For the results next to a 0 (did not take a pill) I generated random numbers between 100 - 110.
    This should indicate that there is an extremely high and consistent chance that taking a pill will reduce the value of the disease represented by column B by -10. Yet, CORREL function returns a result of .10, which is low.
    I would like to know which formula would return the result telling me that there is a close to 100% chance that taking the pill would reduce column B value by -10. Thanks!

  2. #2
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    Denote X and Y be the result in B which presenting the patient did not/did take a pill respectively. Then X ~ Uniform(90, 100) and Y ~ Uniform(100, 110)
    The problem is, if you just compute Pr{Y - X > 10} = 1/2, this surely what not you want.
    Computing the correlation of Xi and Yi (two sequences of i.i.d. sample you generated) will not help also, as this should give you a value close to 0 if your random generator is good enough.

    I guess you want to compute something like:
    1) By central limit theorem, for sufficiently large n,
    (Y1 + Y2 + ... + Yn)/n - (X1 + X2 + ... + Xn)/n → 10

    2) You may want to paired the samples, like setting Yi|Xi ~ Uniform(Xi+5, Xi+15)
    Then the correlation should be very high as they are related by Yi = Xi + 10 + Ui
    and Ui ~ Uniform(0, 10) can be considered as the uniform random noise

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