I have a data set in which I measured a continuous variable (positive, continuous data) in response to different treatments(15 different pathogens) and I am unsure how to statistically analyse the data. In response to some treatments, the dependent variable is normally distributed, but in others not and the usual transformations that are often applied do not result in a normal distribution among all treatments. Moreover, there is quite some variation in the data and variances are not homogenous. Could a generalized linear model be a good possibility or am I overlooking a much more simple solution? Thanks a lot in advance!
Yes, generalized linear models could be a good idea here. It comes down to whether or not you can find a suitable exponential family. First, I would plot the fitted values against the variance for all 15 categories. In a toy example(10 observations per treatment) it may look like this This gives you an idea of the variance function, $V(\mu)$. The goal is then to find an exponential family which yields a similar variance function (See for example tweedie class). In the plot, the variance function is $V(\mu)=\lambda \mu^2$ which corresponds to a gamma distribution. If you find a suitable exponential family and the residuals of the GLM looks fine, you can use the GLM to make t-test for all your pairwise comparisons.
Alternatively, you can use pairwise rank tests to see if there is difference between the groups. Perhaps it is even better to use the rank tests than the GLM because you do not have to do model checking with rank tests.