Does TOST equivalence test handles subgroups within the group? I just started on statistics so this is pretty hard for me. I have two identical experiments. Each experiment have gene expressions for 12 samples with different conditions: untreated. Dosage 50. 100. 200. I want to prove that these two experiments are identical or replicable. Each experiment has n = 1500 so 3000 samples together. I have the data frame in long format (Columns are gene,dosage,experiment,value).
With the help of another user here, I learned about TOST. So far I have the R code:
library(TOSTER)
dataTOSTtwo(data = df,
            deps = 'value',
            group = 'experiment',
            low_eqbound = -0.05,
            high_eqbound = 0.05,
            desc = TRUE,
            plots = TRUE)


The results are as above. So, I'm concluding that the two Experiments are NOT replicable or identifical. And that there are significant effects? Is there anyway to put the 'Dosage' variable in the method? Does it consider that effects and means may vary between 'Dosage'

You're correct, omitting Dosage from the model is a bad idea; I wouldn't recommend using a t-test for a regression design such as this.
However, it's possible to fit a regression model to one dataset and use that to make predictions for the second dataset. You can then do an equivalence test between these predictions and the measurements from the second dataset (with a bootstrap to account for the uncertainty). The equiv.boot function from the R package equivalence allows you to do this: https://search.r-project.org/CRAN/refmans/equivalence/html/equiv.boot.html
