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I have a dataset which displays the effect of a pollutant on the productivity of microorganisms and I am wanting to use a statistical test, to see if there are any statistical differences between the concentration of the pollutant and the productivity of the microbial community.

To investigate this, three different pollutant concentrations were trialed simultaneously over an 11 day period: a high pollutant concentration, a low pollutant concentration, and no pollutant. Each pollutant concentration had 4 replicates and productivity was measured every day over an 11 day period. The four replicates have been averaged and all data has been normalized.

Similar answers to this question e.g. this one, this one or this one are not exactly similar because the data in these examples differs to mine. I have data which is measured at equal intervals, I want to see if the pollutant effect is statistically significant in comparison to the no pollutant samples and I want this to be done for the entire time series, not just at a small number of time points.

From initial inspection, the ARIMA test seems to fit what I am looking for, I would, however, welcome any advice on using this test and any other options available.

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  • $\begingroup$ What do you mean by the ARIMA test? Are you planning on fitting ARIMA models and then comparing these series? $\endgroup$
    – Michael R. Chernick
    May 19, 2017 at 17:02
  • $\begingroup$ Yes, that was the idea. $\endgroup$
    – WSmith
    May 23, 2017 at 16:13

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In the end I used a linear mixed-effect model (LMEM) because it allowed the inclusion of time-series data and both fixed and random effects. Pollutant concentration and day were included as fixed effects in the LMEM, and sample was included as a random effect. Significance of pollutant concentration was assessed using a log-likelihood ratio test; this compared models with and without the pollutant as a fixed effect and was fitted using restricted maximum likelihood.

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  • $\begingroup$ Thanks for sharing this solution, even so long after the original question was posed. $\endgroup$
    – rolando2
    May 18, 2018 at 15:33

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