title: Checking interpretation of GLM summary in R
body: <p>Just want to check that what I'm doing is all correct!</p>
  
  <p>I have bird counts in several sites categorised into two habitats - farmland and wetland. I simply want to see which habitat has higher counts.</p>
  
  <p>I'm using a GLM with a Poisson function (as they are count data):</p>
  
  <pre><code>&gt; mod &lt;- glm(count ~ habitat, family = "poisson")
  
  &gt; summary(mod)
  
  
  Call:
  glm(formula = count ~ habitat, family = poisson)
  
  Deviance Residuals: 
      Min       1Q   Median       3Q      Max  
  -0.5868  -0.4603  -0.2496  -0.2141   2.8464  
  
  Coefficients:
                              Estimate Std. Error z value Pr(&gt;|z|)
  (Intercept)                  -0.2695     1.0000  -0.269    0.788
  habitatWetland                1.7331     1.0954   1.582    0.114
  
  (Dispersion parameter for poisson family taken to be 1)
  
      Null deviance: 37.802  on 91  degrees of freedom
  Residual deviance: 34.373  on 90  degrees of freedom
  AIC: 48.987
  
  Number of Fisher Scoring iterations: 6
  </code></pre>
  
  <p>So far so good?</p>
  
  <p>My understanding is that (using the default contrasts) the Intercept refers to habitat:Farmland - so the estimated average count on farmland sites would be exp(-0.2695). The estimated average count on wetland would be exp(1.7331).</p>
  
  <p>The intercept p-value (0.788) gives the probability that the intercept (i.e. count in farmland) is significantly greater than zero (although I'm not particularly interested in this). The wetland p-value (0.114) gives the probability that the count in wetland is different from the intercept (i.e. different from the count in farmland). So in this case there is no significant (at the 5% level) difference between the two habitat types.</p>
  
  <p>Is that all correct? Anything else I should be thinking of or doing differently?</p>