Before using adonis() with factors as explanatory variables in R, it is important to check for group dispersion (betadisper()) so that you know whether your significant p-value from adonis is real, i.e., not influenced by a large dispersion effect. How can this be done for continuous variables? It is my understanding that adonis() can use both factors and continuous variables as indicated by the R-documentations, but what is not clear is how this is done. It seems that adonis() is applying PERMANOVA to factors and a distance-based linear model (DISTLM) to continuous variables, but this is just my interpretation, I have no confirmation on this. If this is the case both statistical analyses have the assumption of homogenous dispersion. If betadisper() (dispersion test) is used with continuous variables in R, it seems like they are being treated as factors such that samples with similar depths (20 and 21m) are treated as different. Overall I am asking 3 main questions:
1) What is the best way to test for heterogenous dispersion for non-normal continuous variables?
2) Should I be using adonis() with continuous variables?
3) How is adonis() treating factors vs. continuous variables?
Thank you in advance.