Statistical issues in this paper studying relation between air quality and LULC
A paper got published in Environmental Monitoring and Assessment. It studied relation between land-use classes (Urban, Shrubland, Forest, Water, Green areas) and air quality (O3, NO2, SO2 concentrations). Basically, it compared the concentration values in each of the classes using Kruskal-Wallis H Test.
Issues with the use of Kruskal-Wallis H Test
Kruskal-Wallis H Test is sensitive to sample size. When we compare groups with large samples, the test will show statistical significance even when practical significance is less. It seemed like practical significance is less in this paper — A difference in median Ozone concentration from 0.1131 mol/m2 (Urban) and 0.1130 mol/m2 (Shrubland) is identified as statistically significant. Is it practically significant? An atmospheric chemist should answer that. For more information on this: Is there a maximum sample size for a Kruskal Wallis test? — Mathematics Stack Exchange
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The paper did not mention the exact sample size of each land cover class. But, to its merit, it mentioned that the analysis was done using a stratified sample using 0.01% sample from each land cover class. Nevertheless, it seems like they just picked one stratified sample and performed a Kruskal Wallis Test. A better approach would be to do a Monte Carlo simulation. Take 1000 stratified samples with same approach and conduct a 1000 Kruskal Wallis tests. Report the number of times null hypothesis can be rejected. That would’ve made the analysis stronger. For reference, check this paper: Link. They performed 1000 K-S tests and reported the median p-value.
Assumption of Independence
The paper justified the use of Kruskal-Wallis test by assuming that the concentration values within a group (land cover class) are independent.
First of all, between groups independence is also needed.
Secondly, I don’t think it is such an easy assumption to make — even within a group. I suspect pollution concentrations to have spatial correlation. If a pixel next to me has high pollution, even I would have so! Moran’s I test would have ruled it out.