= Solution
\b[This is the appropriate command for the full <contingency table>.] It fits a <log-linear model> to the nine cell counts, with <logarithmic link function> and no interaction:
$$
Y_{ij}\sim\operatorname{Poisson}(\mu_{ij}),\qquad\log\mu_{ij}=\alpha+g_i+d_j.
$$
With baseline constraints on $g_i,d_j$, there are five parameters. The factorized means express <independence> of treatment group and damage category. The <maximum-likelihood estimates> are
$$
\boxed{\widehat\mu_{ij}=\frac{Y_{i+}Y_{+j}}{Y_{++}}=(18,4,8)\quad\text{in each row}.}
$$
Although the experiment fixes each row total at 30, conditioning these independent <Poisson random variables> on those totals produces the appropriate row-wise <multinomial distribution>. The <Poisson trick> therefore gives the correct likelihood inference for this <independence log-linear model for a two-way contingency table>; the margins are nuisance parameters. It tests whether treatment changes the distribution of damage, rather than modelling a binary outcome.
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