Dear Mohammad,

That depends a bit on the design of your study. I used a paired design to study differences in biodiversity and compared the indices with t-tests, which worked fine.

You should refer One way or two way ANOVA or also student t test to compare the level of significance of the raw data or you should refer the Turkey Karmer multiple comparison test also. It provides you the exact level of significance of your results.

As Sarah has rightly put it - much depends on the "study design" used. Just to make it explicit, 'genuine' replication and randomization are important elements of a good 'study design' for a valid application of any statistical test and the confidence you can have in the results from these tests.    

Well, these are already indexes. Why should you compare them? I think you would insert statistical error within the second comparison.

To Sarah, 

thanks, what you do if you have more than two groups?

To Kamala,

carefull study design and randomization all take place before measuring diversity indices, diversity numbers have different characteristics from observation numbers.

To Leonardo,

thanks for answer

Dead Mohammad,

I've read a paper which suggests the use of a T test (or ANOVA) to compare biodiversity indexes. But my point is that these indexes have inherent statistical errors within their formula. Thus, if you do a second statistical comparison to compare these indexes, maybe you are just increasing type II errors. That's why other papers just suggest the comparison between the absolute index numbers, withour any further analyses.

Jerrold Zar's textbook (Biostatistical Analysis, 5th ed, and earlier) proposes a method for comparing 2 individual Shannon diversity indices, based on a paper by Hutcheson (1970, J. Theoret. Biol. 29: 151-154).  If one has a set of replicate diversity indices from  two or more sites, e.g., where one calculated the diversity index for each sample,  then these numbers are, mathematically, simply observations which can be subjected to parametric statistics the same as any other observations.  One might want to check to be sure the distribution isn't weird, but otherwise I see no reason why diversity indices cannot be compared by ANOVA or t-tests or post-hoc tests or whatever.  I have never encountered difficulty doing so or interpreting the results.

It depends what is your hypothesis and what are your objectives. You can apply as many statistical analysis as you want. If you just wanted to show statistical difference between the groups, ANOVA is good followed by post hoc tests. And ANOVA is very powerful test and it can independently take care of type I and type III .

If you have meaurements of ecosystem productivity, area or disturbance besides biodiversity, you could check some of the theoretical models, which have been put forward as explanations of biodiversity. Basically the idea is, that biodiversty increases with productivity and/or area (linear regression approach) or that there is a curvilinear relation between disturbance and biodiversiyt (intemediate disturbance theory).

Below I give a citation, which may be helpful.

Colin R. Townsend, Mike R. Scarsbrook and Sylvain Doledec

Limnology and Oceanography

Vol. 42, No. 5, Part 1 (Jul., 1997), pp. 938-949

You can download it from:

http://www.jstor.org/stable/2838897

kind regards

Irene

If you use R, check out the R package "BiodiversityR" - it explains a lot, and does a lot. Also, "EstimateS" by Caldwell does some of the same. Finally, depending on how you collected your data will determine what other kinds of analysis you may use, such as ANOVA or other options.

Hey, I think you better use Hill numbers (so exponential Shannon and inverse Simpson) for diversity calculations and comparisons. Cf. Jost, L. (2006). Entropy and diversity. Oikos, 113(2), 363–375.

or: Chao, A., Chiu, C.-H., & Jost, L. (2014). Unifying Species Diversity, Phylogenetic Diversity, Functional Diversity, and Related Similarity and Differentiation Measures Through Hill Numbers. Annual Review of Ecology, Evolution, and Systematics, 45, 297–324. doi:10.1146/annurev-ecolsys-120213-091540

Hi Mohammad

"BiodiversityR"is nice to use but package "vegan" is also nice, both have good tutorials! Rather than focussing on diversity metrics, it can be also interesting to investigate the response of species to the measured variables. This can be done with multivariate analysis with "vegan", for example nMDS gives good results.

There's an ongoing debate on which diversity index is the best to use, I think it's better to explore them all and choose the best or most explaining index.

Kind regards Maarten

I agree, use all the known indices but start with H'. Likewise use as many statistical tests as possible, do not just depend on one approach because for sure although the underlying distributions may/will depart from "normal" never-the-less there is something to be gained by cautiously using well-known tests. The measure of your discrimination will emerge when you get different answers from different procedures - both indices and statistical - (ie "significant" vs "non-significant") results on the same data-sets. Not even monte-carlo methods will be definitive because one has to rely on some sort of data-feed to represent the background expectation & thus the result becomes "circular".

Not exactly what you asked, but if you are considering using any of the diversity indices, do see:

Devictor & Robert 2009 Diversity and Distributions, 15, 122–130

and

Hurlbert 1971 Ecology, Vol. 52, No. 4 , 577-586

there is no mathematical reason not to try ANOVA on diversity indices. Indices are just number if you want to compare it!

but you can also try to compare your community directly, for example with hierarchical clustering! be carefull with the metric you will use, since you probably have a lot of zero, you will need the Bray Curtis distance. In fact, most of the statistical analyses based on Bray Curtis can be applied to community database, depending on your question of course!

Wouldn't the issue with comparing two samples with just their diversity index values mean you'd need to use a non-parametric test?

Hello Mohammad,

EstimateS 9 has a new way of comparing richness of reference samples of biodiversity, developed by Colwell et al. (2012): Comparing Species Accumulation Curves: Rarefaction and Extrapolation of Reference Samples. For this, Colwell et al. 2012 wrote "...curves representing 95% confidence intervals for interpolated and extrapolated richness estimates also meet smoothly, allowing rigorous statistical comparison

of samples not only for rarefaction but also for extrapolated richness values. The confidence intervals widen as the extrapolation moves further beyond the reference sample, but the method gives reasonable results for extrapolations up to about double or triple the original abundance or area of the reference sample."

Colwell et al. 2012. Models and estimators linking individual-based and sample-based rarefaction, extrapolation and comparison of assemblages. Journal of Plant Ecology Volume 5, Issue 1Pp. 3-21. http://jpe.oxfordjournals.org/content/5/1/3.short

Two difficulties arise in your situation, as noted by Leonardo and Thomas Peter. First, unless you have a large number of observations (sites/quadrats sampled) per habitats, you might need to use non-parametric tests, as the assumptions for using Student's t-test (normal distribution) or the Normal approximation for estimating the mean of large samples are not met. Mann-Whitney and Kruskal-Wallis might then be more suitable.

Then, indices are not "just numbers". They include a level of uncertainty that can vary from one observation to the next depending on the number of individuals and species/taxa found in each. Try estimating the confidence interval of your indices for each observation through bootstrapping just to understand what I mean. When performing an Anova, strong assumptions are made on this uncertainty which are probably not met with these indices, and in particular that it is the same for each observation. Check the litterature on meta-analyses (where summary statistics are routinely used in analyses) to get a better understanding of the problem.

The sbdiv function from the simboot R package will allow you to test for differences in the Shannon and Simpson indices, as well as Hill number, between sites while circumventing this statistical problem.

Numerical Data

• T-test
• ANOVA

Categorical Data

• Chi-Square Test

ANOVA and T-Tests works well for comparison of indices of biological diversities

I follow Dr.Dickson Adom

best regard

Most diversity indexes behave non-linearly, while most statistical tests assume linearity. So no, you cannot just use ANOVA and t-tests to compare them.

After these years, I think the best way to compare diversity indices is using Hill diversity indices and bootstrapping procedure. For doing so, I recommend the iNEXT R package.

The key to answering this question lies in what one is trying do (in an ecological or biological) sense in the first place. Never mind the restrictions presented by any of the so called "indices" in themselves - use them all and then apply transformations at will!

The elements circumscribed by the quest will define what data can be obtained (and how). In general one would like to have the incidence of sample space quantified in terms of kinds, frequencies and associated measurements thereof, not to mention something about the spatial disposition of each element in respect of all of the others.

So start simple: #s of species represented per defined unit of sample space - (never mind the spatial variance involved) is a good way to go.

The important proviso being to collect as much of the associated variance as is possible the first time around. Now lump everything into a nice big matrix, apply whatever additional transformations you think are appropriate to both rows and columns and Bob's your uncle! If you have thought about the problem a bit beforehand and gathered data accordingly you can then plot and test almost anything out of the resulting phase-space.

I would caution using ANOVA or T-test on diversity indices. Some indices require a Ln transformation, and may require a further transformation to reach a normal distribution (if sample size is too low). Make sure that your diversity indices meet the assumptions of an ANOVA.

Hey dear researchers,

Could you please share a simple and basic material regarding Shannon and other indices widely used in ecology. I do not know what they are and for what purposes they are used. I looked at the statistics books but unhappily I could not find it.

Thanks million.

I used a rarefaction analysis to compare species richness among forest stands. This would help you.

Article The influence of environmental factors on species compositio...

Diversity itself has a meaning in it. Additional, analysis may compromise the importance of ecological needs.