[R] effect sizes for Wilcoxon tests

[Thomas Lumley]

On Tue, 15 Nov 2005, Claus Atzenbeck wrote:

> On Tue, 15 Nov 2005, Peter Dalgaard wrote:
>
>>>> However, for Wilcoxon tests, the formula for effect sizes is:
>>>> r = Z / sqrt(N)
>>>>
>>>> I wonder how I can calculate the Z-score in R for a Wilcoxon test.
>>>
>>> Does anyone know how to calculate effect sizes for Wilcoxon tests as
>>> SPSS can do? I wonder if it would be very difficult to do so with R.
>>
>> If the above formula is correct, it can't be hard. What I wonder is
>> whether (and if so, how) it makes sense. (& the fact that SPSS does it
>> is no guarantee...)
>
> According to my references, the formula is OK.
>

I think you have misinterpreted the direction of Peter's scepticism. The 
question is whether an effect size defined this way means anything useful. 
For example, even if your data are Normally distributed with equal 
variance this definition will not agree with the definition based on the 
mean. This is only the start of the potential problems, especially if the 
distributions do not have the same shape.


> However, how do I get Z from a Wilcoxon test in R?

wtest <- wilcox.test(y~group,data=d, alternative="greater")
qnorm(wtest$p.value)


 	-thomas