I have a unconventional question arising from my current master thesis on

regression modeling. Suppose we have fitted a (linear) relationship between

a dependent variable y and an independent variable x. Now we choose two

points on the x-axis, i.e. according to percentiles x10 and x90. These two

points are chosen to select the data points for two groups in order to

perform pairwise comparisons. In the first run, we choose 20 data pairs

around the x-values of x10 and x90 and run a statistical test in order to

infere if their y-values differ significantly. In a subsequent step, we

choose, say 30 data points around x90 and test against x10; in the next step

40 data points around x90 and test against x10 and so on. The intention for

this is to determine the group size and consequently the corresponding

lowest x-value where the comparison turns out to be significant.

How would you approach this problem. I thought of a many-to-one procedure

like the Dunnett test where multiple groups are tested against the same

control (which could be x10 in our example) (package multcomp or others).

However, these multiple groups would contain partly the same subjects. Or is

some sort of adaptive design the right choice. Or something completely

different?

I'd be very happy for any kind of help since I'm completely stuck with this

question and have no idea how to solve it

Kind regards

Andres

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