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.
Guillaume,
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.
Tom
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