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Mar 30, 2019 at 19:58 comment added Martin J.H. Yes, but why even bother discussing such a hypothesis? You can just state the measured effect size $\theta\pm\delta\theta$ and then discuss what the best/worst case ramifications are. This is how it is typically done in physics, for example when measuring the mass-to-charge difference between proton and antiproton. The authors could have chosen to formulate a null hypothesis (maybe, to follow your example, that the absolute difference is greater than some $\Delta$) and proceeded to test it, but there is little added value in such a discussion.
Mar 30, 2019 at 19:35 history edited Martin J.H. CC BY-SA 4.0
minor: spelling
Mar 23, 2019 at 21:48 comment added Alexis That depends on one's null hypothesis. For example, rejecting $H_{0}:|\theta|\ge \Delta$ provides evidence of an absence of effect larger than an arbitrarily small $\Delta$.
Mar 22, 2019 at 11:11 history edited Martin J.H. CC BY-SA 4.0
minor edit
Mar 22, 2019 at 9:44 history answered Martin J.H. CC BY-SA 4.0