Hello all,
I'd greatly appreciate any help to clear my confusion about two-way crossed and nested design!
I am counting the abundance of each common genera of microalgae from the mangroves and tidal flats of 2 different sites, 1 sandy and oligotrophic, and the other muddy and eutrophic. The data that I have collected look like this:
1. muddy site - mangrove (n=6)
2. muddy site - tidal flat (n=8)
3. sandy site - mangrove (n=6)
4. sandy site - tidal flat (n=8)
And each set of data is a genus-abundance matrix.
I have always thought that my design is two-way crossed, but was just made aware that it could be a nested design, since the data obtained from say, muddy-mangrove is dependent on it being in the muddy site...
Is this a nested design, afterall? I read that sample sizes must be equal for a nested ANOVA, is that also a requirement for ANOSIM?
Thanks a lot in advance!
I suggest to you to check a book on : Design of Experiments, it will clarify to you that question, and your confusion will be gone.Regards.
The fact that data depend on site is just a given fact in any study and has no bearing on the experimental design. Data from the muddy site does depend on the site being muddy but that is exactly why its data will be different from the tidal flats. Dependence is not the same as nesting. Nesting requires a hierarchy of effects. The sites are not nested in each other and you are simply measuring micro algae genera at different sites (also not nested), so there is no nesting and therefore the design must be crossed. Throw mangrove mud at that guy :)
You have not provided us with enough information to determine what your design was. Try this:
Imagine that you had mapped all possible tidal flat and mangrove, muddy and sandy areas within your study region, colour-coding them as mud/mangrove, mud/flat, sandy/mangrove, sandy/flat. If you then randomly chose your sampling locations as 6 or 8 in each of the four habitat types, you would have a two-way design.
However, if you randomly chose 4 muddy sites and 4 sandy ones, each a broad area within your study region, then afterwards randomly chose two mangrove sampling locations (exact locations) and two tidal flat sampling locations within each of your 8 sites, you would have a nested design.
And, just to be sure: If you did not randomize, you would not have an experiment that could be validly analyzed with ANOVA at all. On the other hand, I don't think that equal sample sizes are a requirement for a nested ANOVA, though it has been a very long time since I had to concern myself with that detail, so I can't be certain.
As to your second question: Use of ANOSIM often involves a different kind of inference from what we would draw from an ANOVA.
With a properly designed experiment, ANOVA can give you a probability that the factors in your design affected the thing that you measured (e.g. presence of mangroves affects abundances of particular microalgae, under your experimental conditions). There is no point in asking whether the thing you measured (the abundances of microalgae) differed among your sampling sites. They are 100% certain to differ, so the test is for the causal role of the factor (presence of mangroves), not the difference in abundances. However, drawing that inference needs rigorous experimental design. If your design was defective, there may be no point in using ANOVA at all.
ANOSIM, in contrast, gives you a probability that the community composition differed between areas by more than the vagaries of sampling within each area. With data as intractable as community compositions, that is often useful to know, even if you cannot draw definitive conclusions about the cause of the observed difference. For example: You might have found different microalgae on tidal flats than amongst mangroves because you chanced to sample the flats at a different time of day or when there had been more rain, not because of the presence or absence of the mangroves. For ANOVA to be useful, you need to have designed your experiment so as to eliminate those alternatives. If you have not eliminated them but ANOSIM finds differences between groups of samples within your dataset, you can go exploring for alternative explanations afterwards. Your inferences will not be conclusive but they may still be useful.
Yes, you have sampled both levels of each factor (sediment sandy/muddy, mangrove presence/absence) for both levels of the other, so it is a crossed design.
ANOSIM doesn't require a balanced design (though imbalance may lead to a loss of power).
Comparing the R values in a 2-way crossed ANOSIM will allow you to assess the relative strengths of the effects of sediment (removing effect of mangroves) vs the effect of mangrove (removing the effect of sediment).
- Badges
- Science topic
- Similar topics
- Phytochemistry
- Extracts