st: Signtest (statistics question)

["Guillaume Frechette" <gurst1@hotmail.com>]

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.

Best,

Guillaume

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