Wilcoxon versus glm
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.
Exactly
I expected the beta for the group greater than zero.
and so it was. It was nearly 10
Can somebody explain me such an difference of two methods of rejecting a hypothesis? Where am I wrong?
Well, there's a number of issues here 1/ There's no necessary reason why these two tests should agree as they have different null hypotheses. The Wilcoxon tests P(y1>y0)=1/2, the glm compares two weighted means. 2/ The Wald tests done by glm() can perform badly when the difference between the groups is very large as it is here. A coefficient of 9.87 is infinite for practical purposes (remember it is a ratio of e^9.87, about 20000, in the means), so you were probably unlucky enough to get all zeros in y0. The MLE is then infinite. If you used anova(glm.M1) you would get a likelihood ratio test, which would behave better. -thomas -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._