normalization – What statistics can I use on qPCR data composed of several runs if all normality tests fail on the dataset?

I have >100 qPCR experiments that I’d like to analyze together, each containing the same set of genes (10 genes of interest and 2 reference genes).
I have four different samples (untreated & 3 treatments) from the same cell culture. Our setup allows two of them to be run at once, i.e. the samples from the same cell culture are split to two qPCR runs.

  1. I would like to do statistics with the dCq values after normalizing to the reference genes, but the dataset doesn’t pass any normality tests.
    What methods are suitable for finding valid differences between treatments (or any other features like age)?

  2. If the same amount of cDNA was used and reference genes were added to every run, is it still necessary to normalize between runs or between cell cultures?

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