Is normal dist OK for these count data?




I am modelling some count data (ANCOVA). I use R for statistical computing.

I am not sure if I must use a glm with poisson errors.

There are 120 counts in 4 groups and only one zero count.

The maximum count is 12.

The median is about 4 and the distribution of counts is fairly symmetrical.

I have applied linear models and there are no zero predictions.

The residuals look OK, no trend, constant variance except the qqnorm plot indicates slight right-skew.

I then applied glm and poisson, but with identity link.
A log link produces inflated predictions for large fitted values.

The qqnorm plot improved slightly with poisson errors.

And 1 or 2 possible leverage points are no longer important with poisson errors, I think because the model allows for larger variance for high counts.

Otherwise, the lm and glm produce similar estimates for the coefficients.

Only the fact that the data are integers suggests I might use poisson.

Should I necessarily assume poisson errors?
Anything I should check for?
The only thing that bothers me with the lm is the slight skew in the qqnorm plot.



The AIC scores are on different scales because of the different distributions and link functions, so aren't comparable?

One suggestion is to check the residuals and make sure there is no pattern. Then, lm might be OK. It's not a sin to apply lm to count data, is it?