# Normalization results in regression to the mean and inflated Type I error conditional on the reference values

Fig 1C of the Replication Study: Melanoma exosomes educate bone marrow progenitor cells toward a pro-metastatic phenotype through MET uses an odd (to me) three stage normalization procedure for the quantified western blots. The authors compared blot values between a treatment (shMet cells) and a control (shScr cells) using GAPDH to normalize the values. The three stages of the normalization are

- first, the value for the Antibody levels were normalized by the value of a reference (GAPDH) for each Set. This is the typical normalization throughout bench biology.
- second, the GAPDH-normalized values were rescaled by the mean of the GAPDH-normalized values for the shScr Condition within each combination of Antibody+Type+Blot. And,
- third,
*all*values in the shScr group were assigned to 1 (since the mean within the Condition level is 1). The statistical test then is a one-sample t-test of shMet with \(\mu=1\).

As shown in the simulation below and summarized in the section [Summary of simulation results for n=4], Stage 1 can introduce inflated *conditional* type I error due to regression to the mean while stage 2 and 3 renormalizations introduce inflated marginal (or unconditional) type I error.