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I am using cenken to perform a nonparametric trend test on concentration data with multiple detection limits (the detection limit changed when a change of labs was made).

I have seven years of data with four samples per year (one sample per each of 4 "summer" months- June, July, August, September). I used cendiff to test whether the data display seasonality, which they do not. As an aside I wouldn't want to use a seasonal Kendall in this case anyways because I would have to set all of the values below the max detection limit at the max detection limit, which would make all except two values equal (the max detection limit was quite high in two years)

When performing the analysis, I see three ways (a,b,c, below) of representing the concentrations over the 7 years, but cannot find guidance on what the correct method is.

a) compute the median concentration from the four months of data per year, perform the trend analysis on these medians (i.e. one concentration value per year). My only concern here is that it reduces the sample size.

b) To "honour" all of the data, use all of the data, with sampling date represented by decimal date- I am concerned this would lead to serial correlation (that a given concentration from one of the four sampling dates within a year might be more similar to the other samples within that year than to samples in other years). Additionally, this approach just seems weird to me in that concordance of "pairs" will be computed within years as well as across years.

c) use all of the data, but use "year" instead of "decimal date" so that there are four concentrations for each single year value- thus "x values" are tied for data within the same year and pairs would only "count" if they are between-year pairs (I think!!). I am not sure if this is "allowed".

Does anyone know what the approved approach is here? I haven't seen it explicitly addressed anywhere (and if you do have a reference for an example I could look at that would also be appreciated!)

An additional question: if the data were to display seasonality, would it be appropriate to use the annual medians if (as explained above) I cannot use the seasonal Mann Kendall because I would lose too much information in censoring at the highest detection limit?

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You need to determine correlation between your concentration data to decide between options A and B. If your data are not correlated, I see no issues in using all of the data with the given dates. If a correlation is significant between months within a given year you would need to address before determining trend.

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