In the current manuscript, I believe "Evidence" is not really defined (formally or informally). I believe this can lead to confusion, because most readers would assume evidence is the collected data. But the paper takes a "research design/process + statistical model agnostic approach", so we kind of say the evidence is whatever "follows" from the hypothesis.
For example, in the t-test setting, evidence = significant test. This is in line with your statement that we only consider binary evidence in this paper. But again, this could lead to confusion, because in a t-test setting, data (!= evidence) is not binary, but the test is non-randomized.
But then again, let's assume in the t-test setting evidence = significant. I am now wondering which philosophical standpoints we can model. Because in the manuscript, you often talked about corroboration (which I now changed to confirmation), because I suspect we can not model the philosophical standpoint that comes with "corroboration", e.g. the collection of evidence against the 0-Hypothesis until we reject it.
This is because in this philosophical direction, a non-significant result is not interpreted. Therefore, we can never collect evidence against the alternative (which is H in our notation): I therefore believe we can not model this in our framework.
In the current manuscript, I believe "Evidence" is not really defined (formally or informally). I believe this can lead to confusion, because most readers would assume evidence is the collected data. But the paper takes a "research design/process + statistical model agnostic approach", so we kind of say the evidence is whatever "follows" from the hypothesis.
For example, in the t-test setting, evidence = significant test. This is in line with your statement that we only consider binary evidence in this paper. But again, this could lead to confusion, because in a t-test setting, data (!= evidence) is not binary, but the test is non-randomized.
But then again, let's assume in the t-test setting evidence = significant. I am now wondering which philosophical standpoints we can model. Because in the manuscript, you often talked about corroboration (which I now changed to confirmation), because I suspect we can not model the philosophical standpoint that comes with "corroboration", e.g. the collection of evidence against the 0-Hypothesis until we reject it.
This is because in this philosophical direction, a non-significant result is not interpreted. Therefore, we can never collect evidence against the alternative (which is H in our notation): I therefore believe we can not model this in our framework.
What do you think about this?