I have fish density data (n per 100m sq) for fish populations in three river systems. Each river has a site immediately above a effluent discharge, a site immediately below it, and two further downstream sites. Each site was surveyed biannually for two years. Is there a way to statistically compare densities between upstream and downstream sites that does not contravene the assumption that samples are from independent populations? I have evidence of limited migration of brown trout between sites on the same river. I have read papers that seem to ignore the assumption, and perform ANOVA or Kruskal-Willis between sites on a river regardless of the apparent pseudoreplication. Many thanks in advance.
Hi,
To account for the apparent pseudoreplication on your river, you could just include it in your analysis via an asymmetric eigenvector map (AEM). This technique allows you to create directional eigenvector that correspond to your unidirectional phenomenon (here the river's flow). You'll only need your geographic coordinate if you use R. You can, then include those vector into the analysis of choise, as a new explanatory value and include the link between your site without ignoring the potential pseudoreplication.
One or more points to consider. Sampling immediately below effluent site, may be prior to effluent mixing, unless the effluent is released and dispersed through a system of dispersal across the channel. Effluent discharged along one bank may take a substantial distance downstream to achieve mixing. Sampling just below discharge if not mixed, will give areas heavily effected, as well as areas marginally or even unaffected. In addition, the further downstream, the effluent concentration may decrease unless effluent discharge is relatively constant.
Different streams and rivers in this case, may have differences in size, substrates, channel types, habitats, etc. The one site above each effluent discharge becomes the way to help compare these unaffected differences, so it would have been good to take a few more samples (replicates).
Another assumption may be the effluents are the same types, and their delivery had similar timing and concentration with respect to sampling. If the contaminant concentrations as well as information on past or periodic contaminant loading and frequency, these type details could impact your results. And as well, some fish species are more tolerant to pollution than others, so one might consider this also as to whether there us enough sampling and species diversity to capture the desired detail on effects.
Sometimes we take or have access to data, and analyze it for our own edification, learning exercise or as a class project. But then we might also see what additional might be needed to compare unequal systems, determine cause -effect, or produce reliable statistical results. It is not unusual for substantial thought and design to go into research level work. The question begins with statistical analysis - many things might be compared with statistics, but whether there is enough in this instance to acieve the goals and intent, talking to a statistician can be not only informative, but a real awakening.
If the data is normally distributed, you can use anova since you have 3 groups. While if the data is not normally distributed you can use kruksal wallas.
If you include "river" as a factor in ANOVA (with upstream/downstream as another factor; and sampling period as another one), this explicitly acknowledges the lack of independence among samples from the same river.
If the river and sampling period include in the analysis, the analysis became more complicated and need two way or three way anova. While If the data is distributed abnormally, you need to go to kruskal willis test which not have two way or three way technique.
To address the issue with the KW test previously mentioned, data can be ranked and then the two-way(+) ANOVA performed. For additional information on this technique see:Article [Rank Transformations as a Bridge Between Parametric and Non...
The research you mentioned show equations for the transformation, but without any application of these equations. I think after the application of these equations, the interpretation of the results will be very complicated.
In considering multiple lines of evidence, I wouldn't rely exclusively on any one inference test, such as ANOVA. I would also look at gradient effects, including the pollution itself (e.g. BOD, DO, etc.) plus natural environmental gradients (change in channel slope, flow, substrate, etc.). Are there natural gradients that coincide with the pollution gradient? Can these be teased out with multiple regression? Again, done in addition to inference tests. Prior knowledge, stressor mechanisms, etc. come in as other lines of evidence.
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