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Probability that A is smaller than B?

  1. Sep 30, 2015 #1
    Given two data sets A and B, we can, say, conduct ANOVA to see if the average is statistically different.

    Is there a way to determine what is the probabilty that A is smaller than B?

    Let's say that we can NOT assume anything about A and B e.g. if they follow a normal distribution.
     
  2. jcsd
  3. Sep 30, 2015 #2
    ? Do you mean the probability that the average of A is smaller than the average of B? If we know nothing at all, then we can conclude nothing at all.
     
  4. Sep 30, 2015 #3
    Yes, something to that effect. Is it possible to say "A is smaller than B X% of the time" ?
     
  5. Sep 30, 2015 #4

    If we know that A and B are iid (independent identically distributed) random variables then we can say that avg of A is smaller or equal to avg of B at least 50% of the time.

    Proof: Since they are iid, P[ avg(A)<= avg(B) ] = P[avg(B) <= avg(A)].

    P[ avg(A)<= avg(B) ] + P[avg(B) <= avg(A)] >=1

    P[ avg(A)<= avg(B) ] + P[ avg(A)<= avg(B) ] >=1

    2P[ avg(A)<= avg(B) ] >=1

    P[ avg(A)<= avg(B) ] >=1/2
     
  6. Sep 30, 2015 #5

    pwsnafu

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    You can do non-parametric analysis, such as the Wilcox test.
     
  7. Oct 1, 2015 #6

    jim mcnamara

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    I think Wilcoxon signed rank requires the samples be from a single population. Does that fit what we are looking at here?
     
  8. Oct 1, 2015 #7

    pwsnafu

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    I linked to wrong test. Here's the two sample version.
     
  9. Oct 1, 2015 #8

    jim mcnamara

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    Much better - thank you. I thought maybe I had lost my last remaining brain cell.
     
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