I am analysing the transportation rate for a number of different mutants in a particular transportation system. I want to know how I can perform statistical tests on this data in a valid way, given that we have had to adjust for the fact that there is extreme variation between data taken on different days, which is unavoidable.
Essentially, on any given day, I measure the transportation rates of a number of mutants, as well as the wildtype control (WT), and a negative control that should be dead for transportation (which I will call NC). If you normalise the data for each day by subtracting background (NC) and then (arbitrarily) setting WT rate = 1, and dividing all other observations by WT, you get much less variation within each genotype. Biologically, I think this is caused by the fact that the substrate kits that we use are not very uniform.
Assuming the above is OK (it may not be, but I can't think of a better solution), I don't know how I can carry out statistical testing, because the WT population (to which I want to compare all my other samples) is now arbitrarily set to have mean 1 and variance zero. If this were a T-test, I would just do a one-sample t-test with u = 1, but for an ANOVA I don't know how to go about including WT. Regardless, there is sufficient difference between groups that the ANOVA will show significant difference caused by genotype as a factor, but the real issue comes when doing post-hoc tests. I know generally Tukey's is the best way of testing all pair-wise comparisons, but if I can't include the WT data in my dataset, then I can't tell if each of my mutants is significantly different from WT (or indeed from the NC, because this is now arbitrarily set at 0). I was considering doing pairwise t-tests between all mutants, and then 2x one-sample t-tests for each mutant, with u set to 1 and then 0.
I would obviously have to correct for multiple testing - I was planning on using Benjamini-Hochberg. My question is whether it's valid to do so when I'm using a mixture of different statistical tests, or indeed whether it's valid at all to include the aforementioned one-sample t-tests in my post-hoc analysis given that they weren't included in the ANOVA.
Any help on this would be amazing!
