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One-sample Wilcoxon sign-rank test against test value Theta is
equivalent to the two-sample Wilcoxon sign-rank test when one of the
two paired samples (variables) is the constant equal to Theta (see
Algorithms, Nonparametric tests). OK.
We know that Wilcoxon test is about symmetry of the distribution of
the differences. In 1-sample case, therefore, it tests whether the
distribution of values in the population is symmetric about
Theta. Note that it is not exactly the same as to say that Theta is
the median. Theta could be median, but the distribution
could still be not symmetric about it. The test which precisely
addresses the median and only median (without symmetry
assumption) issue would be 1-sample sign test, not Wilcoxon
test.
Then, why does SPSS One-sample Nonparametric tests option
1) incorrectly describes Wilcoxon as the test for the median
(instead as the test of symmetry about the value)?
2) not offer 1-sample sign test which would be just the test for the
median?
I'm hoping that IBM SPSS representatives will see the question.
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