[R] interpretation of R output for exact permutation test

[Duncan Murdoch]

On 07/06/2019 3:08 a.m., massimo bressan wrote:
> given this reproucible example
> 
> library(coin)
> 
> independence_test(asat ~ group, data = asat, ## exact null distribution
> distribution = "exact")
> 
> I'm wondering why the default results are reporting also the critical value
> Z by considering that this method is supposed to be "exact", i.e. computing
> the direct probability:

I don't think that is the critical value, I think it is the observed 
value of the statistic being used.
> 
> pvalue(independence_test(asat ~ group, data = asat, ## exact null
> distribution distribution = "exact"))
> 
> my question is: what is the correct interpretation (if it exists at all) of
> the Z value printed out by the 'plain' function 'independence_test' when it
> is asked for an 'exact' test?

Simply the value of the the statistic.  I don't know its formula, but 
presumably one of the references in the help page ?independence_test 
would give it.

The p-value is the probability of such a value or a more extreme one 
(possibly with some sort of continuity correction; you'd have to check 
the references).  The "exact" argument says to use the exact permutation 
distribution for the statistic when calculating that probability.

Duncan Murdoch


> 
> am I completely out of track?
> 
> sorry but I'm here missing the point somewhere, somehow...
> 
> thank you for the feedback
> 
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