GLM and normality of predictors

Hi,

I have found quite a few posts on normality checking of response variables, but I am still in doubt about that. As it is easy to understand I'm not a statistician so be patient please.
I want to estimate the possible effects of some predictors on my response variable that is n? of males and n? of females (cbind(males,females)), so, it would be:

fullmodel<-glm(cbind(males,females)~pred1+pred2+pred3, binomial)

I have n= 11 (ecological data, small sample size is a a frequent problem!).

Someone told me that I have to check for normality of the predictors (and in case transform to reach normality) but I am in doubt about the fact that a normality test can be very informative with such a small sample size.
Also, I have read that a normality test (Shapiro, Kolmogornov, Durbin, etc.) can't tell you anything about the fact that the distribution is normal but just that there is no evidence for non-normality.
Anyway, I am still looking for some sort of thumb of rule to be used in these cases.

The question: is there some simple advice on the way one should proceed in this cases to be reasonably confident of the results?

Thanks for any help you might provide

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Normality of the predictors doesn't belong to the assumptions of the
GLM, so you don't have to check this.

Note, however, that there are all kinds of potential problems which to
detect is fairly hopeless with n=11 and three predictors, so you
shouldn't be too confident about your results anyway.

Christian

On Fri, 15 Apr 2011, Simone Santoro wrote:

Hi,

I have found quite a few posts on normality checking of response
variables, but I am still in doubt about that. As it is easy to
understand I'm not a statistician so be patient please.
I want to estimate the possible effects of some predictors on my
response variable that is n? of males and n? of females
(cbind(males,females)), so, it would be:

fullmodel<-glm(cbind(males,females)~pred1+pred2+pred3, binomial)

I have n= 11 (ecological data, small sample size is a a frequent
problem!).

Someone told me that I have to check for normality of the predictors
(and in case transform to reach normality) but I am in doubt about the
fact that a normality test can be very informative with such a small
sample size.
Also, I have read that a normality test (Shapiro, Kolmogornov, Durbin,
etc.) can't tell you anything about the fact that the distribution is
normal but just that there is no evidence for non-normality.
Anyway, I am still looking for some sort of thumb of rule to be used
in these cases.

The question: is there some simple advice on the way one should
proceed in this cases to be reasonably confident of the results?

Thanks for any help you might provide

[[alternative HTML version deleted]]

*** --- ***
Christian Hennig
University College London, Department of Statistical Science
Gower St., London WC1E 6BT, phone +44 207 679 1698
chrish at stats.ucl.ac.uk, www.homepages.ucl.ac.uk/~ucakche

Am 15.04.2011 20:14, schrieb Christian Hennig:

Normality of the predictors doesn't belong to the assumptions of the
GLM, so you don't have to check this.

On Fri, 15 Apr 2011, Simone Santoro wrote:

I want to estimate the possible effects of some predictors on my
response variable that is n? of males and n? of females
(cbind(males,females)), so, it would be:

fullmodel<-glm(cbind(males,females)~pred1+pred2+pred3, binomial)

if you count no of males and females, shouldn't you choose the poisson 
family? maybe whoever you told you to check for normality referred to 
that, since count data are not normally distributed (neither are their 
errors)! maybe thats all he/she wants!