Image via WikipediaA new post by Andrew Gelman, with a quite wordy title
The single most useful piece of advice I can give you, along with a theory as to why it isn't better known, all embedded in some comments on a recent article that appeared in the Journal of the American College of Cardiology
I would summarize, but I am embarrassed to say I understand very little of it. In a comment, I made an attempt:
I will add edits to this as I learn more.Hello Prof. Gelman,
Are you saying "model building" will naturally lead to applying fruitful transformations that will lead to statistics that do more than only prove "a formally statistically significant difference for a trivial effect"?
(By "model building" you mean the scientist taking responsibility for an abstraction that goes beyond statistics, i.e. causality and value judgments about what is more than a trivial effect.)
I am having trouble translating your description into something I can understand, so I would appreciate your help if I made a hash of things with my little summary.
I feel Pearl's causality graphs (directed acyclic graphs, to be specific) are the appropriate format to present any model. If you want to allow the possibility of "no true zeros", then use multiple models, and "collapse" all the points where you wish to use statistics to show the possibility of "no true zeros", maybe even "collapsing" everything into a single point! The multiple models you then have will now compete in different uses - based on predictive power, accuracy, ability to calculate meaningful error ranges, cost of collecting data, cost of computation, cost of comparison, ability to predict outcomes from interventions, cost of understanding, etc.
"No true zeros" - see Andrew Gelman's Review Essay "Causality and Statistical Learning" Section Heading: "There are (almost) no true zeroes: difficulties with the research program of learning causal structure" http://www.stat.columbia.edu/~cook/movabletype/archives/2010/03/causality_and_s.html
I also have a hard time understanding all this in isolation from a model of a rational being working under a motivating sense of responsibility to make a decision about an action (or remaining inactive). Especially statistical analysis divorced from utility in making a decision. Comprehension is nice, but comprehension that cannot play a part in any morally motivated decision is valueless.