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Given reference samples $R_i$, I have two dichotomous responses $X_i$ and $Y_i$ I wish to compare. Each dichotomous response (relevant vs. irrelevant to the reference $R_i$) is generated by an algorithm based on $R_i$. I can also ask subjects to rank paired samples by relevance ($X_i ≷ Y_i$). I want know if algorithm $y$ is significantly better than $x$:

$$\begin{align}H_0: r_x &= r_y \\ H_1: r_y &> r_x \end{align}$$

What is the best test to apply? What if there are than two treatments?

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