# st: RE: Signtest (statistics question)

 From "Steichen, Thomas" <[email protected]> To <[email protected]> Subject st: RE: Signtest (statistics question) Date Mon, 12 May 2003 10:38:57 -0400

```I replied, as below, and obviously misinterpreted the type
of change Guillaume proposed. Please disregard my previous
message.  Tom

> 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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