Analysing bird diversity data across 2 sites and 2 time periods - Ordinal data. Shannon's and Jaccard?

Question

I am looking for the best way to analyse the data below to measure and compare the bird diversity between 3 sites and across 2 time periods - basically are they different from each other and have they changed over time.

I don't have count data from 1992 so have applied the categories used in a historical publication to my own data. I was planning to use Shannon's on the table below and Jaccard's using presence/absence data. Is that the most appropriate, and will these give me p values? If not what further tests would be needed?

Answer 1

Update: see also answers here.

I would strongly recommend reading more about species co-occurrence analysis, e.g. here and here. This is a big field where a lot of work has been done on its statistical analysis and interpretation.

You can apply any metric that you want for a a basic idea of correlations in the data, and for that the simple distances are a reasonable place to start (I would probably just look at a correlation matrix or do principal component analysis to start, but it's a matter of taste). But you will likely want to use something more sophisticated to account for multivariate structure in the data.

In terms of statistical inference, e.g. p-values, you will need to do something more than those metrics. Distance measures are just metrics, they don't apply tests and they don't have a null hypothesis per se. The easiest thing to do would be to apply an empirical null distribution by generating a large set of permuted datasets (where you shuffle the labels of the rows and columns), compute the metric for each permuted dataset, and then use that distribution of metrics as a null distribution. That's still a fairly naive analysis, but it is at least accounting for some of the structure of the data.

I think that your best bet is to go read some more about how people have analyzed this kind of data in the past, and use some of those tools. If you are comfortable with R, the vegan library is a good place to start, it has already implemented a lot of the basic analyses you might use.

Update on ordinal data: For helpful background on ordinal data analysis, I would suggest reading this paper. As for transforming ordinal data to ranks, that is fairly simple as long as it's ok for the method for you to have ties in rank.

I am also assuming that you have data that look like this, in addition to the table that you screenshotted:

Site |  Species  |  Amount   |
A    |     X     |  common   |
A    |     Y     |very common|
A    |     Z     |    rare   |
B    |     X     |    rare   |
B    |     Y     |   common  |
B    |     Z     |very common| 

You can turn this into ranks:

Site |  Species  |  Amount   |
A    |     X     |  2        |
A    |     Y     |  1        |
A    |     Z     |  3        |
B    |     X     |  3        |
B    |     Y     |  2        |
B    |     Z     |  1        |