Question about continuous and categorical variables We have 211 measurements of iron and carbon export rates across 5 sites and 2 temperatures, and each of those 5 sites has its own discrete set of physical and chemical characteristics. Would it be correct to treat those physical and chemical characteristics as continuous variables? If we perform a simple ANOVA, the sites are found to be significantly different across the sites. Similarly, if we treat the physical and chemical characteristics as categorical variables, they will explain the same amount of variation as the sites do and all of them are found to be significant but each of those categories has its own coefficients (beta). 
What would be the correct approach to obtain some sort of trend for physical and chemical characteristics in this case? 
 A: What you are telling us is that $E(y|x)$ is a significant function of $x.$ Excellent! Now you need a physical-chemical-engineering-motivated model to explain your data!
Since you only have 5 "sites" and 2 temperatures, your input space is limited to 10 points. That doesn't sound like much, but in astrophysics, that's a lot. You absolutely should develop some continuous models around temperature and "site" specifications, hopefully involving a small number of parameters. Then use reasonable engineering/physical/chemical arguments to limit the values of these parameters. Can they be negative? Can they be larger than some value? Should some parameters always be less than others? Then move forward with a Bayesian analysis, which multiplies the maximum likelihood estimate of your data with your well-reasoned prior estimates of the values of the parameters.
Any "trend" that you will see will arise from the best fit model, which will correspond to the most likely parameters given a) the data and b) good engineering limitations on what those parameters should be. In practice, you will select the parameters that maximize the $likelihood \times prior.$ Whatever trend they describe is the trend you can report. 
But before you are done, you should test to see how robust your best result is. This gets into evaluating the Hessian of the posterior. If you would like guidance on that, feel free to write back. 
