Hi @ClusterFerret68 : Here are a few things to consider (in no particular order).
1. Equivalence testing makes sense. i.e., an x% difference in slopes is of no practical relevance.
2. Traditional significance testing rewards small sample sample sizes (or a poor choice of levels of doses
and the distribution of subjects over the doses); the analyst can mistakenly default to claiming parallelism via not rejecting the null hypothesis of parallelism. While this kind of thinking is not correct (to put it kindly), this is what often happens in the real world of decision making. In this context, an underpowered study (via small sample size or a poor choice of levels of doses
and the distribution of subjects over the doses) has a better chance of "claiming parallelism".
3. Similar to 2 above, traditional significance testing rewards poor precision measurements; an underpowered study has a better chance of "claiming parallelism". In this context, an underpowered study (via poor precision) has a better chance of "claiming parallelism".
4. Traditional significance testing can be a big problem when the precision of the measurement is very good as well; a post hoc explanation of statistical significance may be required when the difference is of no practical importance.
While 1 above appeals to our sense of utility, numbers 2, 3, and 4 are enough, in my view, to abandon traditional significance testing wrt parallelism.
