Is there an unpaired version of the sign test? I wasn't able to find one on Google, and was wondering if one exists...
 A: Good (2005) defines the one-sample sign-test for the location parameter $\theta$ for a continuous symmetric variable $X$ as follows:


*

*Take the difference $D_i$ of each observation to the location parameter $\theta_0$ under the null hypothesis.

*Define an indicator variable $Z_i$ as $0$ when $D_i < 0$, and as $1$ when $D_i > 0$. Since $X$ is continuous, $P(D_i = 0) = 0$.

*Calculate test statistic $T=\sum_i Z_i$.

*The distribution of $T$ is is found by generating all $2^N$ possible outcomes of the $Z_i$ indicator variables (2 possibilities for each observation with equal probability $\frac{1}{2}$ under H0). This leads to the binomial distribution as in the sign test for 2 dependent samples.
The justification for step 4 is: 

Suppose we had lost track of the signs
  of the deviations [...]. We could
  attach new signs at random [...]. If
  we are correct in our hypothesis that
  the variable has a symmetric
  distribution about $\theta_0$, the
  resulting values should have precisely
  the same distribution as the original
  observations. That is, the absolute
  values of the deviations are
  sufficient for regenerating the
  sample. (p34f)

I agree that this reasoning seems somewhat different from a 2-sample permutation test where you re-assign experimental conditions to observations with the justification of exchangeability under H0.
Good, P. 2005. Permutation, Parametric, and Bootstrap Tests of Hypotheses. New York: Springer.
A: I'm not sure if such a test can exist conceptually. The sign test uses the pairing of the data to decide whether one value is bigger than the corresponding other value. But in an unpaired situation there is nothing like a corresponding other value (every value in the other group could be a potential counterpart for comparison). Correct me please, if I'm not getting the point...
A: O.k,
I found that there is an unpaired solution to a sign test (A test of medians).  It is called "Median test" And you can read about it in Wikipedia.
A: The extension goes thorugh introducing rank to somewhat regulate the order of data and the result are Wilcoxon tests (Mann-Whitney in particular).
