[Gretl-users] Re: One-sample Wilcoxon signed-rank test (difftest command)
Am 06.03.2022 um 14:44 schrieb Alecos Papadopoulos:
Good morning. Do I suspect correctly that, in
<hansl>
difftest X Y --singed-rank
</hansl>
if Y is a series of constant value, say, Y = c, then we are testing
whether the median of X is equal to "c"?
In principle, yes I think that should be the case.
Some additional remarks:
- In the "extra" gretl addon, there are functions WSRcritical and
WSRpvalue that attempt to provide more exact small-sample critical
values of the relevant distribution.
- Wikipedia says the underlying distribution must be assumed as
symmetric. (https://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test) I
wasn't really aware of this and cannot say whether this is correct, but
the article cites sources and discusses the issue, so it sounds
relatively reliable.
- Semantic reminder (also to self): There is an ambiguity with the term
median in the sense of whether the population concept is meant or the
empirical sample finding. The test hypothesis concerns the population,
of course. But if the previous point is right and the distribution must
be symmetric, then we might as well talk about the expected value of X
instead. (Provided that it exists, which is probably not a requirement
for the signed-rank test.)
cheers
sven