I have a water quality data set ( Fecal Coliform). This dataset includes right-censored values ( >600), left-censored values (
Initial thoughts... The appropriateness of a test like Kruskal-Wallis may depend on the proportion of censored data in your samples. If the proportion is relatively small, and you use a version of the K-W test that handles ties in ranks, the test may be relatively fine.
Another approach may be to categorize data by if it meets a regulatory benchmark concentration or not and then use a test for nominal data (e.g. chi-square test of association).
There appear to be multiple tests described as a generalized Wilcoxon test, so you may need to be more specific with that.
ADDITION:
One source I've used for guidance on censored data is USEPA, 2000, Guidance for Data Quality Assessment: Practical Methods for Data Analysis, Section 4-7, https://www.epa.gov/quality/guidance-data-quality-assessment . There you'll also find a document called Data Quality Assessment: Statistical Methods for Practitioners .
These may be helpful as a reference.
You need interval regression. Interval regression is important in this case because the values below 10 and above 600 should not be treated as being equal to 10 or 600. This will result in the estimate differences between groups being biased if one group has more censored data than the other.
Convert your counts to log10 (which seems to be industry standard for bug counts in the water literature) and then follow the instructions for the package you are using. Both Stata and R support interval regression, using the intreg command in Stata or installing the intReg package in R. In either case, you need to format your data is two variables which give the upper and lower boundaries for each observation. In Stata, the lower boundary for your lower value (10) is unknown so you code it as missing, and likewise the upper boundary for 600. In Stata observations that are measured precisely have the same value for upper and lower boundary, while in R a little extra step is needed to make sure that R doesn't treat these observations as lying within an interval of zero width.
I haven't used the R package, but it looks pretty good. I've used Stata and can vouch for its power. More info here
https://rdrr.io/rforge/intReg/man/intReg.html
and here
https://www.stata.com/manuals/rintreg.pdf
The Stata manual entry is very useful because you can read up on interval regression and see worked examples. It also handles clustered data, which are typical of water quality studies.
Another set of R packages are the NADA and NADA2 packages which address censored data. Unfortunately, I am not sure that they address left- and right-censored data at the same time.
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