I work in cell culture and normally don't have to use anything more than T-tests, but this project has me stumped...
The study design: 1 control treatment and 7 experimental treatments with one continuous primary outcome.
The problem: The work was done over 2+ years in multiple iterations so, although the relative changes compared to the control treatment remained consistent (ex. experimental treatment 1 always showed 40% increase vs control), the raw values varied greatly over the course of the 2+ years as the cells aged. Control samples were run in each iteration.
The question: Running a dummy-multiple regression with the control treatment as the reference group would be ideal, but it doesn't work due to the iteration variation.
I've tried "normalizing" for iteration by dividing the outcome values by their overall iteration mean, then using these adjusted values as the dependent variable in a dummy-multiple regression with treatments as the predictor and the control as the reference group. This yields expected results in terms of direction and magnitude of the regression coefficients, but is it legitimate? If so, doing this removes units from the outcome variable, so how would I best represent/explain the regression coefficients?