[R-sig-eco] dispersion parameter in binomial model

[v_coudrain at voila.fr]

Dear all,
I computed a binomial model with a proportion as response variable using glm(cbind(realized, not realized)~x,family="binomial"). The output tells me that the 
dispersion parameter taken is 1. For comparison I computed the same model using family="quasibinomial" and I get a dispersion parameter of 0.5. The resultats are 
very different between the two models and in regard to the plotted data, the quasibinomial model seems to be more accurate. I am a bit confused about how to know 
if my data are accurately fitted by a binomial model or if they are under- or overdispersed and I'd rather use the binomial or another fitting model. 
I found this formula to calculate the dispersion parameter, but I am not sure if it is accurate for a binomial model:

phi=sum(((realized/(realized+not realized))-model$fitted)^2/model$fitted)/model$df.residual

With this formula I get for both the binomial and the quasibinomial model a phi=0.4. Is this a sign of underdispersion?

Thank you!
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