Test for significant differences in two groups of binomial data In a study per-field disease incidences were collected by sampling 35 plants in each field and counting proportion of infected ones (# of infected/total sampled). In result, each sampling location corresponds to a value between 0 and 1. I have about 100 locations in total, each sampled in the same way.
I have then a column representing two groups of growers knowledge. There are people who have a knowledge and I have a set of disease incidences in their field and I have a group of people who have no knowledge and I have a set of incidence scores in their fields.
What test do I use to see if there is a significant difference in the mean incidence between the groups? 
Data are not normally distributed.
My data looks
 like in those barplots:

 A: Mixed effect logistic regression is a good choice.
Let $Y_i$ be the number of infected plants in field $i$. The model is:
$$Y_i \sim Binomial(35,\pi_i)$$
$$\mathrm{logit}(\pi_i)=\log(\frac {\pi_i}{1-\pi_i})=\beta_0 + \beta_1 X_i +\gamma_i$$
where $X_i =1$ if grower on the $i$-th field is have a knowledge, = 0 for otherwise. $\gamma_i$ is random intercept for field $i$ to account for possible over-dispersion. $\beta_1$ is log odds ratio between knowledge vs no knowledge. The mean proportion of infected is $\frac{\exp(\beta_0)}{1 + \exp(\beta_0)}$ for no knowledge grower, and $\frac{exp(\beta_0+\beta_1)}{1+\exp(\beta_0+\beta_1)} $ for knowledge grower.  
Data format:
    field    plant   infected     knowledge   
  -------------------------------------------------
      1       1        0            0
    ....................................
      1       35       1            0
      2       1        1            1
   ....................................
     100      35       0            0
  ------------------------------------------------

