Tom Steichen
> Guillaume Frechette writes:
>
> > Dear Statalisters: I have two variables x1 and x2 for
> > which I want to test the null hypothesis x1 = x2 (let's
> > say 2 sided at the 10% level). I would normally use
> > Signtest which I believe takes x = x1 - x2 and compares
> > x to a binomial with mean 1/2. Thus, if you have 5
> > observations, such that x can be written as the vector
> > [1,2,3,4,5] you would reject the null. Now, add 1 million
> > 0's to x and the Signtest (at least as it is implemented
> > in Stata) would still reject the null. However, at an
> > "intuitive" level, it seems to me that x1 and x2 are much
> > more similar in the second case (with the million
> > observations where they are exactly the same) than in the
> > original case. My (very limited) understanding of the
> > problem is that since the variables should be continuous,
> > an x of 0 happens with zero probability. Is there a test
> > which takes into account my "intuitive" understanding or
> > is my intuition simply wrong? I apologize for the non-Stata
> > question. Thanks in advance.
>
> The sign test is only interested in whether the
> ordering, by size, of the values within x1 and x2 are the
> same. Adding or multiplying by a constant does not change
> the ordering so the interpretation of the sign test is
> unchanged.
>
> You need to move to a parametric test, such as the t-test,
> if you wish the test to echo your intuition given a change
> of the type you propose.
It seems to me that Tom misses the point of the
thought experiment here, which was adding extra
observations, not transforming the existing
data.
In any case, I don't quite agree with his
conclusion, as some other non-parametric procedures
are possible for the problem.
-ranksum- works quite well in this situation. A valuable
adjunct, since an update to Stata 7 on Friday 13th [sic]
April 2001, is the quantity calculated by the -porder- option.
Cue Roger Newson, for an exordium on the
merits of Somers' d...
("Shall I compare thee to a Somers' d?" W. Shakespeare,
Sonnets, modern reading)
Nick
[email protected]
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