(This article was originally published at Statistical Modeling, Causal Inference, and Social Science, and syndicated at StatsBlogs.)
Our friend K? (not to be confused with X) seeks pre-feedback on this talk:
Can we get a mathematical framework for applying statistics that better facilitates communication with non-statisticians as well as helps statisticians avoid getting “precise answers to the wrong questions*”?
Applying statistics involves communicating with non-statisticians so that we grasp their applied problems and they understand how the methods we propose address our (incomplete) grasp of their problems. Statistical theory on the other hand, involves communicating with oneself and other qualified statisticians about statistical models that embody theoretical abstractions and one would be foolish to limit mathematical approaches in this task. However, as put in Kass, R. (2011), Statistical Inference: The Big Picture – “Statistical procedures are abstractly defined in terms of mathematics but are used, in conjunction with scientific models and methods, to explain observable phenomena. … When we use a statistical model to make a statistical inference [address applied problems] we implicitly assert … the theoretical world corresponds reasonably well to the real world.” Drawing on clever constructions by Francis Galton and insights into science and mathematical reasoning by C.S. Peirce, this talk will discuss an arguably mathematical framework (in the Peirce’s sense of diagrammatic reasoning) that might be better.
*“An approximate answer to the right question is worth a great deal more than a precise answer to the wrong question.” – John Tukey.
P.S. from Andrew: Here’s my article from 2011, Bayesian Statistical Pragmatism, a discussion of Rob Kass’s article on statistical pragmatism.
Key quote from my article:
In the Neyman–Pearson theory of inference, confidence and statistical significance are two sides of the same coin, with a confidence interval being the set of parameter values not rejected by a significance test. Unfortunately, this approach falls apart (or, at the very least, is extremely difficult) in problems with high-dimensional parameter spaces that are characteristic of my own applied work in social science and environmental health.
In a modern Bayesian approach, confidence intervals and hypothesis testing are both important but are not isomorphic [emphasis added]; they represent two different steps of inference. Confidence statements, or posterior intervals, are summaries of inference about parameters conditional on an assumed model. Hypothesis testing—or, more generally, model checking—is the process of comparing observed data to replications under the model if it were true.
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