Temporal sampling- paired or unpaired?

[gpblack]

I have a dataset of WWTP effluent from 3 different plants. Samples were collected throughout the year and we’re looking for features that have significant variation between seasons (Fall, Winter, Spring, Summer). We have a different n for each season at each plant (e.g. WWTP1: Spring (n=17), Fall (n=6), Summer (n=10), Winter (n=2)- not ideal, I know). I’m assuming this would be un-paired data, is that correct? On one hand, temporal sampling could be considered “before and after”, but on the other, since I don’t have equal sample sizes for each season, I don’t know if I can even perform a paired test and so for that reason, it seems like maybe it’s un-paired. I am planning on using a Wilcox un-paired test with a BH FDR adjustment. What other tests would stats-savvy folks use for this?

[ulrichem]

I’m not a very good statistician, but your setup reminded me strongly of this one: https://doi.org/10.1021/acs.est.3c07514
Brunelle, L. D., et al. (2024). “De facto Water Reuse: Investigating the Fate and Transport of Chemicals of Emerging Concern from Wastewater Discharge through Drinking Water Treatment Using Non-targeted Analysis and Suspect Screening.” Environmental Science & Technology 58(5): 2468-2478.

I just read the paper this week, and don’t know that they performed stats tests, but rather qualitatively reviewed the data. Perhaps that’s a good approach here?

[JMS]

Also not a statistician, but I think this is unpaired t-test for sure. Like you say, you have different numbers of samples in each time point. I guess you want to see if there is a systematic difference (increase or decrease) from season to season, which would be a good case for paired. If it was paired, it would have to be on the means, since the individual replicates can’t really be linked to each other I don’t think. Do you have to do ANOVA also?

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