How to test if a treatment yields twice the response of a reference?

[#1]

I have a dataset with a control treatment, a reference treatment, and an experimental treatment. The question I want to answer is if the experimental treatments gives twice the response of the reference treatment after correcting both for the control. I tried using a 'custom test' with the statement 'experimental - 2 * reference + control = 0' [reworked from 'experimental - control = 2*(reference - control)']. Trick is that this is the hypothesis I need to proof, not reject. Any suggestions? 

[#2]

Hi @tvkmez11 : Assuming you have a one-way ANOVA with three levels (Control, Exp, and Ref) there are a couple ways to approach this; Ratios or Differences. What you show are differences. And with that approach, you are almost there. From the Custom Test output, you can construct a confidence interval (Value +/- t*Std Error, where t = the (1-alpha)th quantile from a t-tistribution, with df=DFDen ) and if the lower bound is > zero then you've rejected the null (H0) and favor of the alternative (Ha, the thing you want to show/prove):

H0: experimental - control  - 2*(reference - control) <0

Ha: experimental - control  - 2*(reference - control) >=0

If you set alpha=0.05, then you will construct a 90% confidence interval since it is a one-sided test.