I have a data set of control and paired test values in which the control variability can be relatively high. I'd like to answer whether or not the the test values have increased relative to controls. Specifically, I wanted to examine the increase as a function (percentage/ratio) of the control value (i.e. divide observations by the individual control values). I am having trouble coming up with an appropriate statistical test.
To clarify, let's consider the following data example. Control/test values are paired.
Controls: 0.5 1 2 Tests: 1 2 3.5
In this case, the test values have nearly all doubled relative to controls. Normalizing test values to each individual control, would yield:
Norm Test: 2, 2, 1.75
In general, the question is how to determine if the test values have increased relative to the controls, whether that be through normalization or some test done on the original (non-normalized) data.