Solved – Statistical test for normalised data

I am working with culture cells where one dish has been transfected with a scrambled knockdown clone and two dishes which have been transfected with two knockdown clones each knocking down the expression of a single gene.

An example of an experiment I have performed is to measure the mitochondrial membrane potential (using a fluorescent dye) in these cells using a confocal microscope.
This experiment was repeated on three independent occasions.

On each experimental day, the intensity of the laser which I used (the laser "gain") varies therefore I cannot combine all experimental days without expressing the dye intensity of each knockdown clone as a percent of the control "scrambled" clone (e.g. control = 100% mean intensity; knockdown clone 1 = 50% mean intensity).

Therefore, I need to test for a difference in means between my control scrambled clone and each of the knockdown clones, where my control scrambled clone is set to 100% dye intensity on each experimental day and my knockdown clones are normalised to this control. Therefore, my control has no variance (100% for all three experimental days) while my knockdown clones do have variance.

I know an ANOVA would not be feasible given the difference in variance. I will look into the procedure suggested by Michael Lew, but would a t-test be unacceptable as well? (I have seen papers using ANOVA and t-tests in these circumstances, but in spite of this I am assuming these should not be used). Thanks in advance.

You are correct in assuming that you can't (shouldn't, really) analyse the data with the controls having zero variance.

It sounds like you should consider using a two-way ANOVA on the raw data with the within day variance accounted for in the manner of a paired test. I wrote about the approach in this paper that is intended for pharmacologists with little statistical background:

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