Fit Statistics Missing when negative binomial distribution is used for Non-Gaussian Data.

[sld]

Hmm. Do you think that the gene was truly not there or there at very low levels, or do you think you might have had a problem with the process by which counts are acquired? What is the detectability limit for your process? You can clearly see that how you deal with non-detectable results has a big impact on the statistical analysis. This is not a context that I am not very familiar with, so I cannot offer you much advice about an analysis approach.

I'm struck by the low variability among the duplicate samples at N16, and I wonder whether your process was running well for these samples.

[aroebuck]

I don't think there should be any issues with that well in particular (29 in N16). The samples from well 30 and 28 were sampled processed exactly the same way. To quantify genes one uses a thermocycler. I don't think there should be a problem because I randomly ran my samples in the thermocycler (you can do up to 96 at a time).  Samples from well 29 were run at the same time as those from 28 & 30 for that sampling event and both of those worked. I can't think of a reason that well should be different.

[aroebuck]

Sorry I missed some of your other questions. qPCR can detect genes down to almost a single copy (I think the technical limit is 3). I filtered large water samples, then extracted DNA and quantified gene copies in the extract using the thermocycler. You only load a very small amount in the thermocycler but then back-calculate to copies/100mL groundwater.

[sld]

I'll play devil's advocate: Are you even the tiniest bit skeptical that Well 29, which was similar to the other two wells at the other 3 sampling dates, should be non-detectable at N16? What biological/hydrological mechanisms would explain that? (I don't need to know, but you do.)

Are there procedures in your protocol, from sampling to inserting into the thermocycler, where something might have gone awry? Are the duplicate samples processed entirely separately, or are they two aliquots of the same sample? Did you count other genes, and do any of them show a similar pattern?

Once you've resolved the data validity issues to your satisfaction, you can return to the statistical analysis. Making the zeros be anything "small" will produce the same thing you've seen so far and will trigger significant results for well, date and interaction. If you want to see the impact of the detectibility-replacement, run the analysis without N16. The heterogeneous variances model probably is about as good as is feasible; you won't see any difference in the residual plots, but you'll note differences in SEs for different dates and fit statistics.

[aroebuck]

You have made me think of something actually! My data set is composed of multiple depths (which I am not supposed to factor into this analysis). (Eg. 1 "sample" at 1 depth in a well has reps A & B which are my "duplicates" and I have 1 "sample" (duplicated) per depth (up to seven depths) for each well. However, each "sample" is not representative of the entire well; they are very different due to the geology, so these samples cannot be used a replicates for the well. Instead, what I did was take an average of Rep A for all the depths and another average of Rep B for all the depth to represent the well overall. These two values I am using as "replicates" for the analysis we have been discussing. What you said made me think that due to some restraints, were were unable to sample all of the same depths at each date. In N15 all 6 depths were sampled, but in N16 only three were sampled. You made me realize that an entire "well" average would therefore not be comparable between dates. What I should do instead is find the depths that were sampled on all four dates and only look at those. This, I think should balance things out quite a bit more. This will help with well 29 as well; two of the three depths were non-detect, while one had detection in only one of the replicates (this can happen particularly at very low copy numbers). I will give it a shot and see how it affects the outcome.

[sld]

Cool! Let me know how it sorts out.