The fact you want to defend the decision interpretation of hypothesis tests, in spite of the fact a simple numerical example demonstrates a huge amount of information loss, is astonishing.
How would anyone know to re-do the experiment if the decision interpretation is accepted? The decision interpretation biases readers into granting too much trust in the experimenter’s report of the data collection procedure, based upon an undisclosed cost function.
There are inevitable subjective inputs into any statistical analysis. The honest thing is to discuss them openly.
“The fact you want to defend the decision interpretation of hypothesis tests, in spite of the fact a simple numerical example demonstrates a huge amount of information loss, is astonishing.”
We follow different Philosophies and that’s all I see with your example.
“The decision interpretation biases readers into granting too much trust in the experimenter’s report of the data collection procedure, based upon an undisclosed cost function.”
Maybe we can talk about this somewhere else? Maybe through discord? I don’t even see how that follows.
I just wonder if we are using different definitions of “arbitrary” here.
Priors based on existing evidence aren’t “arbitrary” in any sense that I understand.
Anyway, a more important point is that the arbitrary criterion in significance testing is the main determinant of the outcome, which isn’t true for any bayesian prior, arbitrary or not.
Then deciding on the alpha level based on the cost of making type 1 errors and the sample size isn’t arbitrary. I reject your important point.
We’re probably not going to agree on this and I don’t want to clog up the thread with a protracted back and forth (this isn’t Twitter!). I’d invite others to comment.
No problem. Have a good one.
I shudder to think of how much harm Fisher did in making such statements.
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