Shall I treat vegetation group as an ordinal or nominal variable? As a follow on from here: Correlation between vegetation and erosion, I am having some trouble with the type of data that I have. I am confused as to whether my four categories are ordered.
Specifically, my four groups within my categorical variable are:


*

*vegetation loss,

*no change non vegetated areas,

*no change in vegetated areas and 

*vegetation gain. 


While they are in order of an increasing amount of vegetation, I'm not sure if they would be considered nominal or ordinal. 
 A: Effectively, if you visit the same sampled space twice, observed the magnitude of vegetation, and assign a + if there was an increase, 0 if nothing changed, and - if there is a loss, the corresponding signs for your categories will then be:


*

*vegetation loss (-)

*no change non vegetated areas (0)

*no change in vegetated areas (0)

*vegetation gain (+)
Because the middle two zeroes cannot be ranked, it's strictly speaking not an ordinal variable. So, your plan on Kruskal Wallis seems to be legitimate.
Some side comments, the question indicates that there is an underlying "order of an increasing amount of vegetation." I found that hard to believe because your second option has no vegetation at all, while the first only experienced "loss" which can be complete or more likely partial. I'd recommend when reporting the analysis, be very clear about what the underlying construct is, is it the magnitude of vegetation change, or vegetation.
Considering the details from your original scenario in Correlation between vegetation and erosion, it probably does not make too much sense to merge options 2 and 3 because vegetated land and non-vegetate land are likely to have very different erosion risks and profiles. This probably means you'd need to refine your research question. For instance, is it "erosion associated with change in vegetation," or "erosion associated with change in vegetation, adjusted for baseline vegetation level?" I believe with the actual research question we may be more able to give you better advices.

Yes, for my study, the differences between category 2 and 3 are important. Forgive me though, I am not too sure what you mean by "baseline vegetation level"?
There are many ways to investigate this question. For instance, you can just focus on "erosion associated with change in vegetation," in which you'd compare the means ($\mu$) of soil erosion in these categories:


*

*$\mu _{erosion}$ when vegetation increased.

*$\mu _{erosion}$ when vegetation remained unchanged.

*$\mu _{erosion}$ when vegetation decreased.


Another way to ask this question is "erosion associated with change in vegetation, adjusted for baseline vegetation level," which is more like comparing the means in these categories:


*

*$\mu _{erosion}$ when vegetation increased & the land was vegetated to begin with.

*$\mu _{erosion}$ when vegetation remained unchanged & the land was vegetated to begin with.

*$\mu _{erosion}$ when vegetation decreased & the land was vegetated to begin with.

*$\mu _{erosion}$ when vegetation increased & the land was not vegetated to begin with.

*$\mu _{erosion}$ when vegetation remained unchanged & the land was not vegetated to begin with.


Category 6. "$\mu _{erosion}$ when vegetation decreased & the land was not vegetated to begin with" is illogical so we can take that out. Now we are looking at the erosion corresponding to change in vegetation, while also considering their original vegetation status. This is roughly what I mean "adjusted for baseline." According to your original scheme, you'll merge categories 1 and 4 together, and categories 2 and 5 together, ignoring their baseline erosion risk.
In a nut shell, I feel that there are two variable lurking around, and your scheme tries to force them into one. I think a multivariable regression (possibly with interaction) may be a better choice.
A: It really depends on how you want to use those variables. You can never treat a nominal variable as ordinal but you can always treat ordinal data as categorical. The price you will have to pay for the latter is that you no longer use the information present in the ordering. Whether that price is acceptable or too steep depends on the application and your preferences or style.
