[R] Wilcoxon versus glm

[Prof Brian D Ripley]

On Mon, 25 Feb 2002, Dominik Grathwohl wrote:

> Hi all,
> running the following code:
> > n <- 25
> > y0 <- rpois(n, 0.04)
> > y1 <- rpois(n, 0.34)
> >
> > resp <- c(y0, y1)
> > group <- c(rep(0,n), rep(1,n))
> >
> > wilcox.test(y0, y1)
>
>         Wilcoxon rank sum test with continuity
> correction
>
> data:  y0 and y1
> W = 250, p-value = 0.02074
> alternative hypothesis: true mu is not equal to 0
>
> Warning message:
> Cannot compute exact p-value with ties in:
> wilcox.test.default(y0, y1)
> >
> > glm.M1 <- glm(resp ~ group, family=poisson())
> > summary(glm.M1)
>
> Call:
> glm(formula = resp ~ group, family = poisson())
>
> Deviance Residuals:
>       Min         1Q     Median         3Q
> Max
> -0.692820  -0.692820  -0.004968  -0.004968
> 2.227342
>
> Coefficients:
>             Estimate Std. Error z value Pr(>|z|)
> (Intercept)  -11.303     34.531  -0.327    0.743
> group          9.875     34.533   0.286    0.775
>
> (Dispersion parameter for poisson family taken to
> be 1)
>
>     Null deviance: 28.216  on 49  degrees of
> freedom
> Residual deviance: 19.899  on 48  degrees of
> freedom
> AIC: 34.512
>
> Number of Fisher Scoring iterations: 9
>
> I would interpretate this that the Wilcoxon detect
> a group difference, while glm not. I expected the
> beta for the group greater than zero.
> Can somebody explain me such an difference of two
> methods of rejecting a hypothesis? Where am I
> wrong?

In interpreting the glm output.  You should be using the likelihood ratio
test (28.216 - 19.899 on 1df) rather than the Wald test (the `z value').
Wald tests are dangerous in non-Gaussian glm's (look up the Hauck-Donner
effect) and I wish R had followed S and not quoted p values for them.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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