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I am conducting a vegetation study of the effects of prescribed fire. I have an experimental area that will be burned and a control area that will not be burned. The experimental area has three types of vegetation present so I am stratifying the survey locations proportional to relative size (area) of each vegetation type. The same three vegetation types are present in the control area, but the relative proportion of each is different than the experimental area, despite the total size (area) being very similar. The plan is to use an ANOVA for anyalyses, looking at data from before and after the fire.

My question is, what is the relative importance of maintaining equal sample sizes versus equal sample densities?

In other words, should I sample the same number of points in each control strata as its equivelant experimental strata, or should I sample the control strata with equal density as its equivelant experimental strata? In the second option, because the overall areas are the same, the overall sample sizes would be the same, but the individual strata would have different sample sizes between the control and experimental areas.

Searching online shows virtually endless information about sample size, but less about sample density, and I didn't find anything comparing the two.

Note: Technically, I believe there is only a sample size of one here since the treatment (fire) is only being applied to one area. What I am refering to as samples are really replicates since they aren't independent of each other, but I think the ideas will be the same and I figured discussing this for samples would interest a broader audience.

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  • $\begingroup$ "what is the relative importance of maintaining equal sample sizes versus equal sample densities?" <- depends. What are you trying to achieve? This will determine what's important. For an extreme example, if you only care about the rarest type of vegetation, there's not much point having equal sample in each of the three strata. $\endgroup$
    – Alex J
    Commented Apr 9 at 4:55
  • $\begingroup$ We are more focused on the general plant community than rare species. We are planning to look at things like species richness and native vs non-native cover. $\endgroup$
    – ia200
    Commented Apr 9 at 20:20
  • $\begingroup$ "less about sample density," <- try looking for references about "sampling fraction" rather than "sample density". The sampling fraction is the ratio of sample size to population size (within stratum, for stratified sampling) $\endgroup$
    – Alex J
    Commented Apr 9 at 22:22
  • $\begingroup$ To determine what's optimum, a good way is to a) identify a few key research questions, and then b) do a power analysis to design a study that can answer those questions. For example, if you think that each vegetation type has the same variance, and you are interested in doing comparisons between vegetation types, then a design with the same amount of sample in each stratum is probably ideal. If one is way more variable than others, you might need to relatively oversample that type (etc.) $\endgroup$
    – Alex J
    Commented Apr 9 at 22:27
  • $\begingroup$ Thinking of it in terms of how much variance is expected makes a lot of sense. I'll what I can find for "sample fraction" too. If you want to put these into an answer, I'll accept them. This is what I looking for. $\endgroup$
    – ia200
    Commented Apr 11 at 0:09

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To determine what's optimum, a good way is to first identify a few key research questions. Then, do a power analysis to design a study that can answer those questions. The key takeaway is, what you're trying to achieve in your study will determine what your survey design is.

For example, if you think that each vegetation type has the same variance, and you are interested in doing comparisons between vegetation types, then a design with the same amount of sample in each stratum is probably ideal. If one type is way more variable than others, you might need to relatively oversample that type (etc.).

There may be other constraints that are logistical rather than statistical, such as cost (e.g. if one type of vegetation is more difficult to sample than other due to access issue, you may need to account for that).

I also suggest looking for the term "sampling fraction" (in combination with "stratified sampling" as a keyword, rather than "sampling density".

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