Posted on: November 21, 2009 3:22 PM, by Andrew Gelman
Jimmy points me to this article, “Why most discovered true associations are inflated,” by J. P. Ioannidis. As Jimmy pointed out, this is exactly what we call type M (for magnitude) errors. I completely agree with Ioannidis’s point, which he seems to be making more systematically than David Weakliem and I did in our recent article on the topic.
My only suggestion beyond what Ioannidis wrote has to do with potential solutions to the problem. His ideas include: “being cautious about newly discovered effect sizes, considering some rational down-adjustment, using analytical methods that correct for the anticipated inflation, ignoring the magnitude of the effect (if not necessary), conducting large studies in the discovery phase, using strict protocols for analyses, pursuing complete and transparent reporting of all results, placing emphasis on replication, and being fair with interpretation of results.”
These are all good ideas. Here are two more suggestions:
1. Retrospective power calculations. See page 312 of our article for the classical version or page 313 for the Bayesian version. I think these can be considered as implementations of Iaonnides’s ideas of caution, adjustment, and correction.
2. Hierarchical modeling, which partially pools estimated effects and reduces Type M errors as well as handling many multiple comparisons issues. Fuller discussion here (or see here for the soon-to-go-viral video version).
If you have studied statistics, you may remember Type I and Type II errors. This blog post by Andrew Gelman, from Scienceblogs > Applied Statistics, brings to my attention (probably shamefully late) the prevalence of Type M errors. I am very intrigued and have printed out the article found under “our recent article” in the above quotation. When I manage to wrap my head around this idea a little more, i will post a follow-up. (I am posting on my “general interest” blog as this should interest everyone, not just scientists. Sorry I don’t have a plain language explanation ready yet…)