Interpreting Over-dispersion test for Poisson regression I did the over-dispersion test for my Poisson regression model in R, to check whether negative binominal is a better option.
I used  stats  package for conducting Poisson regression and  AER  package for testing overdispersion.
dispersiontest(m2.int,trafo=1) 

Below is the output of the test
Overdispersion test

data:  m1.int
z = 8.0174, p-value = 0.0000000000000005401
alternative hypothesis: true alpha is greater than 0
sample estimates:
   alpha 
0.5118541  

I don't know how to interpret the result. Does the significant p-value mean that the model is over-dispersed?


Does the significant p-value mean that the model is over-dispersed?

Yes.
If you inspect ?AER::dispersiontest you will see that the function assesses

the hypothesis that this assumption holds (equidispersion) against the alternative that the variance is of the form:
$$
\mathrm{Var}[y] = \mu + \alpha \cdot\mathrm{trafo}(\mu)\,.
$$

By default (alternative = "greater"), AER::dispersiontest checks for overdispersion ($\alpha > 0$).
