At the end of Vanessa Didelez’s talk in the Foundations of causal inference workshop at the Isaac Newton Institute today, I asked her whether she would be okay with a mediation publication that only discusses potential interventionist interpretation in the Discussion section of the paper. The immediate reaction from Vanessa was that she does not like this but will not police it. In the discussion afterward, Thomas Richardson showed more disagreement with me. When I raised the potential that requiring scientists to specify separable components of the treatment will make us not popular, Thomas responded that “when I got my academic training we were not asked to be popular” (or something like this). Provoked by this comment, I decided to write a post to articulate my point.
The following is an email exchange with Hyunseung Kang on the nature of randomization inference. This was sparked by a couple of papers by David Freedman and David Lane: A Nonstochastic Interpretation of Reported Significance Levels; Significance Testing in a Nonstochastic Setting.
This post is derived from my talk “Fisher, Statistics, and Randomization” in the Fisher in the 21st Century Conference organized by Fisher’s College, Gonville & Caius. In the first half of that talk, I tried to trace the origin of randomization. Fisher is widely credited as the person who first advocated randomization in a systematic manner. In doing so, he profoundly changed how modern science is being done.
I read a few interesting articles this week on the Fisher-Neyman debate on the foundation of hypothesis testing:
The Fisher, Neyman-Pearson Theories of Testing Hypotheses: One Theory or Two?. Rigorous uncertainty: why RA Fisher is important. Models and statistical inference: The controversy between Fisher and Neyman–Pearson. The first paper is written by Erich Lehmann and argues that the practical aspects of the Fisher and Neyman-Pearson approaches to testing statistical hypotheses are “complementary rather than contradictory”. I agree with this verdict, but I think what is more interesting and useful for modern statisticians is the basic philosophical differences. Lehmann summarized this as “inductive inference versus inductive behaviour”:
Over this Easter weekend, I wrote the following commentary for the reprinting on Leo Breiman’s paper “Statistical Modeling: The Two Cultures” by Observational Studies. This is partly based on a talk I gave last year.