Wilcoxon versus GLM

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 a difference in two 
methods of rejecting a hypothesis? Where am I 
wrong?

Kind regards,

Dominik

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