Dear everyone who might be able to help:
Hello!
I'm currently a student in marine science and I am writing my master thesis about Elasmobranchs and the big numbers that are being caught by small-scale fisheries in Brazil (Rio de Janeiro state, six sample sites, or better: landing sites).
My aim was, to get an idea of the species diversity/composition of the different sample sites, looking at sharks and rays that have been landed by fishers.
Because of unforeseeable events, the amounts of individuals sampled by me is pretty low, samples for each of the sites range from 1-20 individuals, in total I sampled 43 individuals from 14 species. My question is now: Does anyone have any suggestions what statistical analysis I can do with such a small sample size, that yields some interpretable and relevant results? I am open for anything that might contribute positively to the value of my thesis, in all directions. So far, I have been suggested to use EcoSimR for a co-occurrence null model, because it only utilises presence/absence data.
If there is some descriptive information for my problem missing, please let me know.
In any case, I'm grateful for all advice.
Kind regards,
Benoit Moreaux
Dear Benoit,
If you are comparing your sampling sites, I would suggest using Dunn's tests. Dunn's tests work very much in the same way as a Kruskal-Wallis test (a non-parametric equivalent of the ANOVA test that does not assume normal distribution or equal variances) and is great for small sample sizes. However, unlike Kruskal-Wallis tests the Dunn's tests allow for post-hoc pairwise comparisons. There is an R package that allows you to perform Dunn's tests very easily:
https://cran.r-project.org/web/packages/dunn.test/dunn.test.pdf
Hope this helps!
Best wishes,
Dan
Use Bayesian methods. Traditional (classical statistics) is frequentist, i.e. it works great in large samples. Bayesian methods work in both, large samples and small samples. The only difference is that in your case you may need to compensate your low sample size with theoretical assumptions or previous research evidence to properly and carefully elicitate the prior.
Hello Benoit; One additional little tip is that using incidence data, as you said you might, is helpful if the range of n is large for the various species, places. When a few species are numerous compared to the rarer ones, the common ones tend to swamp the contribution of the rarer ones. Jim Des Lauriers
Hello Benoit,
If your aim is to compare the six sampling sites, and you have no strong background in statistics, then you can use Kruskal-Wallis test as the easiest method to apply and interpret.
Good luck with you thesis!
Dear Benoit,
If you are comparing your sampling sites, I would suggest using Dunn's tests. Dunn's tests work very much in the same way as a Kruskal-Wallis test (a non-parametric equivalent of the ANOVA test that does not assume normal distribution or equal variances) and is great for small sample sizes. However, unlike Kruskal-Wallis tests the Dunn's tests allow for post-hoc pairwise comparisons. There is an R package that allows you to perform Dunn's tests very easily:
https://cran.r-project.org/web/packages/dunn.test/dunn.test.pdf
Hope this helps!
Best wishes,
Dan
Thanks everyone very much, I will carefully consider every suggestion and will see what my professor thinks about those - From other people, including another professor of mine, I was already suggested to stick to reporting means as this can be viewed as baseline data and sometimes you should consider not doing elaborate statistics on a dataset if it looks like mine - which I think is a fair answer too. In any case, thank you guys and if anyone has anything else regarding this comment of mine right here, don't hesitate do let me know if there's a flaw in the logic.
Best regards,
Benoit
I would suggest looking into the permutation tests found in the R packages "coin" (https://cran.r-project.org/web/packages/coin/coin.pdf; Hothorn et al. 2006, 2008), and "rcompanion" (Mangiafico 2019) as they are robust to small sample size, unequal variance, and non-normal distribution.
Paul
Hothorn, T., Hornik, K., Van De Wiel, M. A., & Zeileis, A. (2006). A Lego system for conditional inference. The American Statistician, 60(3), 257–263.
Hothorn, T., Hornik, K., Van De Wiel, M. A., & Zeileis, A. (2008). Implementing a class of permutation pests: the coin package. Journal of Statistical Software, 28(8), 1–23.
Mangiafico, S. (2019). rcompanion: Functions to Support Extension Education Program Evaluation. https://CRAN.R-project.org/package=rcompanion
During my study, I have this kind of issue, too. However, I use varied sampling size for different seasons. My answer may not able to solve your problem.
- To make the data comparable under varied sampling size, I use species accumulation curve (Crist & Veech 2006) to interpolate data;
- Chao estimator (Chao et al. 1987) or Jacknife estimator can be used to compute the number of "unseen" species (which you haven't collected) based on probabilistic methods. You should be very careful that Chao estimator will not tell you which species you would sample, but tell you how many species you would sample).
methods
All the methods conduct in R version 3.6.0, function specaccum( ) in package vegan and Chao1( ) in package fossil are used to perform species accumulation curve and Chao estimator (abundance based), respectively. Hope can be helpful!
references
Chao, A., 1987. Estimating the Population Size for Capture-Recapture Data with Unequal Catchability. Biometrics.
Crist, T. O., & J. A. Veech, 2006. Additive partitioning of rarefaction curves and species–area relationships: unifying α-, β- and γ-diversity with sample size and habitat area. Ecology Letters.
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