the sharp null hypothesis
<br>Methodological Description: (i.e., that the treatment effect is 0 for all units) One of the advantages of conducting a randomized trial is that the researcher knows the precise procedure by which the units were allocated to treatment and control. Randomization inference considers what would have happened under all possible random assignments, not just the one that happened to be selected for the experiment at hand.
Source Excerpt: In order to simulate all possible random assignments, we need to stipulate the counterfactual outcomes – what we would have observed among control units had they been treated or among treated units had they not been treated. The sharp null hypothesis of no treatment effect for any unit is a skeptical worldview that allows us to stipulate all of the counterfactual outcomes. If there were no treatment effect for any unit, then all the control units’ outcomes would have been unchanged had they been placed in treatment. Similarly, the treatment units’ outcomes would have been unchanged had they been placed in the control group. Under the sharp null hypothesis, we therefore have a complete mapping from our data to the outcomes of all possible experiments. All we need to do is construct all possible random assignments and, for each one, calculate the test statistic (e.g., the difference in means between the assigned treatment group and the assigned control group). The collection of these test statistics over all possible random assignments creates a reference distribution under the null hypothesis. If we want to know how unusual our actual experimental test statistic is, we compare it to the reference distribution. For example, our experiment might obtain an estimate of 6.5, but 24% of all random assignments produce an estimate of 6.5 or more even in the absence of any treatment effect. In that case, our one-tailed p-value would be 0.24.
Link to Data Source: * https://egap.org/resource/10-things-to-know-about-randomization-inference/