[R] Wilcoxon versus glm

[Göran Broström]

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?

If you take a look at your simulated data, you will probably guess the 
answer.

> 
> Regards,
> 
> Dominik
> 
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-- 
 Göran Broström                      tel: +46 90 786 5223
 professor                           fax: +46 90 786 6614
 Department of Statistics            http://www.stat.umu.se/egna/gb/
 Umeå University
 SE-90187 Umeå, Sweden             e-mail: gb at stat.umu.se

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