I am trying to find out which test would fit best my samples.
I am comparing the response of a new drug on a continuous physiological parameter with the same old treatment we use in the hospital; this is a small internal pilot study in which we want to have an idea if the new treatment does something, to help us decide if it is worth it to enter a larger trial, so increasing n is really not an option.
I have a control group (n=1200, all the patients we treated with the old drug in the last 2 years) and the group of new treatment (n=23).
The averages among the two groups are comparable, as well as the medians.
I would like to apply an independent t test, but I am afraid that the difference in sample size would be too much.
I also though about sampling randomly from the 1200 a smaller group of patient as control group,
Another possibility is to use the same 23 new treatments as their own controls (each patient using the new treatment did, last year, use the same old drug, so I could use a paired t test).
You would normally try a pooled variance estimate t-test when sample sizes differ. However I would check out "When does the pooled variance t-test fail?" by Yin and Othman and check the homogeneity of variance assumption.
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