Discussion
Started 18 June 2024

How can I statistically compare shannon wiener index values between two years?

I have six ecosystems in two substrate categories (Triplicates essentially). I have determined shannon wiener index values for each ecosystem and also for the two categories separately. I have done this for two separate sets of data that were sampled in two separate years. Is it possible to statistically compare the development of the biodiversity between each of the categories i.e., the development of biodiveristy in ecosystem 1 between the two years, using the shannon wiener values somehow? Are there any other tests that could work? I am aware of the hutcheson t test however, some of my data is not normally distributed.
I would really appreciate some help!

Most recent answer

Chuck A Arize
Texas A&M University – Commerce
To statistically compare Shannon-Wiener index values between two years:
  1. Calculate Shannon-Wiener Index: Compute the Shannon-Wiener index separately for each year using appropriate ecological data.
  2. Normality Check: Ensure that the index values follow a normal distribution, typically assessed using statistical tests like the Shapiro-Wilk test or visual inspection (e.g., histograms).
  3. Choose a Test: Use a paired t-test if the data for both years are paired (i.e., measurements from the same sites or samples) and normally distributed. Alternatively, use a Wilcoxon signed-rank test if the data are not normally distributed or if the assumptions for the t-test are not met.
  4. Perform the Test: Conduct the chosen statistical test to compare the mean or median Shannon-Wiener index values between the two years.
  5. Interpret the Results: Evaluate the test statistic and p-value to determine if there is a statistically significant difference in the Shannon-Wiener index values between the two years. Adjust for multiple comparisons if necessary.
By following these steps, you can effectively compare Shannon-Wiener index values between two different years in a statistically rigorous manner.
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All replies (4)

Wim Kaijser
University of Duisburg-Essen
Yes, you can, but can you provide more information on the response and independent variables and number of samples? The assumption of normality only accounts for the distribution of your model residuals not about the data.
In theory a linear mixed model (https://gkhajduk.github.io/2017-03-09-mixed-models/ and ). or generalized linear mixed model with gamma distribution would suite your needs. The latter will likely because, I assume your sample size is low (this is a general thing in ecology). The assumption of normality of your test-statistics then becomes a bit wonky with smaller sample sizes (https://stats.stackexchange.com/questions/25235/what-test-should-i-use-with-shannon-diversity-index-values).
The dependency between your sample before and after as well as some potential hierarchical structure (I am unawere of) in your data should also taken in consideration. This dependent on how you obtained the data, which assumptions you are willing to make, the sample size, and the eventual question you want to answer. The question is there a difference is always answerable with yes. Because the mean of group1 is always different from group2. The question is, is the difference clearly observable and "ecological meaningful" and two do I have arbitrarily enough information against a null model (p<...). p does not tell you if there is or is not a different or else: me throwing two babies out of a 100 story building and dropping two softly on a table does not make me a murder because (i.e., chisq.test(data.frame(`out of the window`=c(2,0), `on the table`=c(0,2), row.names = c("death", "alive")))) p=0.32.
In any case, assuming your question is about two groups and you work in R you could do something like this:
library(vegan)
library(glmmTMB)
library(DHARMa)
library(emmeans)
data("varespec")
data("varechem")
shannon <- data.frame(y=diversity(varespec), substrate=sample(c("A", "B", "C"), size=nrow(varespec), T),
ecosystem=sample(c("eco1", "eco2", "eco3"), size=nrow(varespec), T))
model <- glmmTMB(y~substrate+ecosystem, data=shannon, family = gaussian(link="identity"))
DHARMa::simulateResiduals(model, plot=T)
sub_mod <- emmeans(model, "substrate")
pairs(sub_mod)
plot(sub_mod)
Nicole Frantová
Mendel University in Brno
Hi, Titas,
I suggest the Kruskal-Wallis Test (non-parametric), which can help you determine if there are statistically significant differences in the Shannon-Wiener index values between the ecosystems, substrate categories, and years (as groups). I also recommend post-hoc testing (when there are statistical significance differences), which is pairwise comparisons using, for example, Dunn's test. This will help identify specifically which pairs of ecosystems, categories, or years are different.
To compare the development of biodiversity within each ecosystem between the two years, you can use the Wilcoxon signed-rank test for paired samples. This test will help determine if there are significant differences in the Shannon-Wiener index values for each ecosystem between the two years.
Andrew Paul McKenzie Pegman
University of Auckland
I agree with Nicole Frantová But you can do anything you like since there are no rules in ecology :)
Chuck A Arize
Texas A&M University – Commerce
To statistically compare Shannon-Wiener index values between two years:
  1. Calculate Shannon-Wiener Index: Compute the Shannon-Wiener index separately for each year using appropriate ecological data.
  2. Normality Check: Ensure that the index values follow a normal distribution, typically assessed using statistical tests like the Shapiro-Wilk test or visual inspection (e.g., histograms).
  3. Choose a Test: Use a paired t-test if the data for both years are paired (i.e., measurements from the same sites or samples) and normally distributed. Alternatively, use a Wilcoxon signed-rank test if the data are not normally distributed or if the assumptions for the t-test are not met.
  4. Perform the Test: Conduct the chosen statistical test to compare the mean or median Shannon-Wiener index values between the two years.
  5. Interpret the Results: Evaluate the test statistic and p-value to determine if there is a statistically significant difference in the Shannon-Wiener index values between the two years. Adjust for multiple comparisons if necessary.
By following these steps, you can effectively compare Shannon-Wiener index values between two different years in a statistically rigorous manner.
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