I am trying to analyse a data set with a pseudoreplication problem and would be grateful if someone could give me some guidelines on the best way to deal with it.
We have a set of subjects exposed to crossed treatments `Temperature` and `Light`, consisting of 4 and 5 levels, respectively (total of 20 conditions). In each condition, we monitored every individual daily for a given duration, looking for an irreversible change of their status (“inactive” -> “active” in our example). This is similar to survival data (“alive” to “dead”), so we thought Kaplan-Meier representations and Log-rank tests would be appropriate in our case.
However, we have faced unexpected issues during the experiment and had to optimize space in the climatic chambers, which caused a mix-up in the original plan: the 20 conditions are not replicated. Each of the 20 conditions corresponds to a separate box containing several individuals, but there is only one box per condition (20 boxes total). The conditions of `Temperature` and `Light` in each crossed condition were controlled continuously and confirmed to be reliable (with limited to no biases due to laboratory conditions).
To our knowledge, and from what we know of the study system, the status of individuals does not depend on the status of surrounding ones, and they are likely independent. However we have only one pool of individuals in each condition, with a ratio between “inactive” and “active” changing over time. We are not sure that statistical analyses for survival can be used without several groups of individuals per condition. Are there any workarounds for this situation? Alternatively, can we calculate the average duration until status change on all individuals in each box, and use that with tests for comparisons of means? If yes, how should we deal with individuals that did not change status during the monitoring period?
I can give example data if required, though the issue is more about whether this pseudoreplication can be circumvented with a different approach, at the cost of statistical power.
Thanks in advance for the advice.
Agriculture lives on pseudoreplication. Every field trial where all the plots of one treatment are sprayed in one pass with the tractor are pseudoreplicated. The counter argument s that I don't really care about small differences in mixing, or weighing chemicals, or operator fatigue. Also it is expensive to constantly return to the barn, clean the tractor, and reload. Also it may not be possible to fill a 300 liter tank with 2 liters of solution to reliably treat the 10 meter by 2 meter plot.
Ideally: You have one replicate. Rerun the experiment once or twice more to get more replicates. In this case analyze all the data together and treat each run of the experiment as a block. You could also analyze each run separately and compare outcomes.
Run a check: This is risky because there is no guarantee that the check will agree with the original experiment. At any rate, select two treatments that are of greatest interest (ten chambers for each treatment). Does the outcome here agree with the outcome of the more complicated experiment?
Accept the problem: If these are 20 growth chambers that is a large number.
No problem? Think carefully about the sources of variability that you are (and are not) measuring. Also consider what you are trying to accomplish. If you are developing a model of the effect of temperature on developmental rates in an aphid, then having 20 different temperatures from 5 degrees C to 45 degrees C is a perfectly reasonable experiment.
Also, read some papers on the within and between growth chamber variability. Typically such chambers are very homogeneous from a people perspective, but plants growing in the chambers suggest that there are significant differences both within a chamber and between two chambers.
Just analyse the data as usual but state that it is not replicated. It will still be useful information as a local trial
It depends on the problem of pseudoreplication, but basically, I think the important thing is to divide the sample into compatable fragments of analysis; for example; by theme or data type.
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