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I am conducting an empirical study, I applied 3 treatments on the sample of 23 objects. The treatments 1 and 2 are independent but the treatment 3 is the combination of the first two. I want to test the hypothesis that the treatment 3 (i.e combination of 1 & 2) give better results than 1 or 2 alone.

I thought about Friedman’s Test, but this one has the assumption that all the pairs are independent, which is not the case of treatment 3. Or should I do two Wilcoxon's tests (treatment 1 vs treatment 3) and (treatment2 vs treatmet3) and then Mann-Whitney's test to show that the treatments 1 and 2 are different.

Karolis Koncevičius
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Ak.tech
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  • Why not some sort of ANOVA type regression with an interaction? – Demetri Pananos Jan 21 '21 at 16:34
  • I answered a similar question here https://stats.stackexchange.com/questions/501054/how-to-use-multivariate-analysis-to-analyse-two-simultaneous-a-b-tests/501060#501060. The context is in AB testing, but the approach remains the same – Demetri Pananos Jan 21 '21 at 16:36

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Usually multi-arm, MA, treatment evaluations are compared using Factorial designs. It uses 2x2 factorial model which has two factors and two levels for each factors. It assumes the absence of an interaction between the two treatments, directly implying the additive effect of the combination of both. Method can be referred here in the article: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6059117/ or more specifically in the book -chapters 11 to 16 https://books.google.com/books?hl=en&lr=&id=qBrpTcAYtNQC&oi=fnd&pg=PR11&ots=XU0FYRVtkD&sig=pkK_SPftr061X4G21J95KHhxl3o#v=onepage&q&f=false

CanarySci
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