[R] wilcox.test construction in r

[Peter Ehlers]

Dear Stefan,

See two comments inserted below.

Stefan Grosse wrote:
> On Sun, 1 Nov 2009 00:47:50 -0700 (PDT) jomni <jomni1 at gmail.com> wrote:
> 
> J> So do I write the function as wilcox.test(original, test,
> J> alternative="l")? or wlcox.test(original, test, alternative = "g")?
> J> or wilcox.test(test, original, alternative="g")?
> J> or wilcox.test(test, original, alternative="l")?
> 
> J> How do I interpret the p-value given my criteria?
> J> Do I reject null when p-value less than 0.05? 
> J> or greater than 0.95?
> 
> The interpretation of the p depends on how you have tested the
> hypothesis.
> 
> J> Not a statistics major here so I'm really confused. 
> 
> You don't need to be that but please read the documentation and try the
> given examples in the documentation.
> 
Comment 1:
   As you point out, one should at least scan the documentation.
   Here's a quote from ?wilcox.test:

    'the one-sided alternative "greater" is that x is shifted
    to the right of y'

   That's pretty unambiguous.

> If you would have typed example(wilcox.test) you would have seen for
> example:
> 
> wlcx.t> ## Two-sample test.
> wlcx.t> ## Hollander & Wolfe (1973), 69f.
> wlcx.t> ## Permeability constants of the human chorioamnion (a placental
> wlcx.t> ##  membrane) at term (x) and between 12 to 26 weeks gestational
> wlcx.t> ##  age (y).  The alternative of interest is greater
> permeability 
> wlcx.t> ##  of the human chorioamnion for the term
> pregnancy. 
> wlcx.t> x <- c(0.80, 0.83, 1.89, 1.04, 1.45, 1.38, 1.91,
> 1.64, 0.73, 1.46)
> 
> wlcx.t> y <- c(1.15, 0.88, 0.90, 0.74, 1.21)
> 
> wlcx.t> wilcox.test(x, y, alternative = "g")        # greater
> 
> 	Wilcoxon rank sum test
> 
> data:  x and y 
> W = 35, p-value = 0.1272
> alternative hypothesis: true location shift is greater than 0 
> 
> 
> This I think makes it very easy to interprete. Here it is tested as the
> text says whether x is greater than y. So if you want to test the
> hypothesis that x is smaller than y so you do
> wilcox.test(x,y,alternative="less")
> then the lower your p is the higher is the probability that the samples
> are different. hence p<0.05 would match your confidence level. Now the

Comment 2:
  I know that you know better, but with p-values it's always
  best to be careful with the language. "... the probability
  that the _samples_ are different" makes little sense. The
  samples _are_ different, period (or why do the test?). The
  p-value says something about the distribution from which
  the samples are obtained.

Cheers,
Peter Ehlers


> surprising news:
> wilcox.test(y,x,alternative="greater")
> would work as well! 
> 
> If you are in doubt create an x and an y where you are sure that x is
> smaller than y.
> 
> One final remark: if you have ties (several identical values in one
> sample) you should use wilcox_test of the coin package.
> 
> hth
> Stefan
> 
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