Suppose that we have samples $x$ and $y$, where $x_i$ and $y_i$ are the $i$-th subject's responses to the first and the second treatment respectively.
Then, we perform a two-sided statistical test, trying to reject the null hypothesis that both treatments have the same effect. For example, the Wilcoxon signed ranked test can be used.
Then, we find the neutral value $s_0$ of statistic $s$ that used in the test (the value that one would get if $x_i = y_i$ for all $i$). Let's assume that $s > s_0$ means that the first treatment is better than the second.
Suppose that the obtained value $s_c = s(x, y)$ is greater than $s_0$ and the null hypothesis was rejected.
I wonder whether I can conclude that the first treatment is better than the second, since the negation of the null hypothesis in our case is that the treatments have different effect.