Probability that A is smaller than B?

[wavingerwin]

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 probability 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.

 

[Hornbein]

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 probability 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.

? 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.

 

[wavingerwin]

? 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.

Yes, something to that effect. Is it possible to say "A is smaller than B X% of the time" ?

 

[Hornbein]

Yes, something to that effect. Is it possible to say "A is smaller than B X% of the time" ?

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

 

[pwsnafu]

Let's say that we can NOT assume anything about A and B e.g. if they follow a normal distribution.

You can do non-parametric analysis, such as the Wilcox test.

 

[jim mcnamara]

I think Wilcoxon signed rank requires the samples be from a single population. Does that fit what we are looking at here?

 

[pwsnafu]

I think Wilcoxon signed rank requires the samples be from a single population. Does that fit what we are looking at here?

I linked to wrong test. Here's the two sample version.

 

[jim mcnamara]

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