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Wednesday, July 16, 2014

The Difference Between “Significant” and “Not Significant” is not Itself Statistically Significant

http://www.stat.columbia.edu/~gelman/research/published/signif4.pdf

A paper that I read years ago (via a Cosma Shalizi post on the file drawer problem) and then totally failed to find when I wanted to re-read it.  Up there with the "No Free Lunch Theorem" as being simultaneously blindingly obvious and something that I'd never thought about.

It discusses exactly what the title says.  A highly significant result may be indistinguishable from an insignifcant one, statistically speaking.
Comparisons of the sort, “X is statistically significant but Y is not,” can be misleading.

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