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310 andrew gelman stats-2010-10-02-The winner’s curse


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Introduction: If an estimate is statistically significant, it’s probably an overestimate of the magnitude of your effect. P.S. I think youall know what I mean here. But could someone rephrase it in a more pithy manner? I’d like to include it in our statistical lexicon.


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1 If an estimate is statistically significant, it’s probably an overestimate of the magnitude of your effect. [sent-1, score-1.106]

2 But could someone rephrase it in a more pithy manner? [sent-5, score-0.617]

3 I’d like to include it in our statistical lexicon. [sent-6, score-0.318]


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Introduction: If an estimate is statistically significant, it’s probably an overestimate of the magnitude of your effect. P.S. I think youall know what I mean here. But could someone rephrase it in a more pithy manner? I’d like to include it in our statistical lexicon.

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Introduction: The title of this post by Sanjay Srivastava illustrates an annoying misconception that’s crept into the (otherwise delightful) recent publicity related to my article with Hal Stern, he difference between “significant” and “not significant” is not itself statistically significant. When people bring this up, they keep referring to the difference between p=0.05 and p=0.06, making the familiar (and correct) point about the arbitrariness of the conventional p-value threshold of 0.05. And, sure, I agree with this, but everybody knows that already. The point Hal and I were making was that even apparently large differences in p-values are not statistically significant. For example, if you have one study with z=2.5 (almost significant at the 1% level!) and another with z=1 (not statistically significant at all, only 1 se from zero!), then their difference has a z of about 1 (again, not statistically significant at all). So it’s not just a comparison of 0.05 vs. 0.06, even a differenc

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Introduction: Type S error: When your estimate is the wrong sign, compared to the true value of the parameter Type M error: When the magnitude of your estimate is far off, compared to the true value of the parameter More here.

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Introduction: Gur Huberman asks what I think of this magazine article by Johah Lehrer (see also here ). My reply is that it reminds me a bit of what I wrote here . Or see here for the quick powerpoint version: The short story is that if you screen for statistical significance when estimating small effects, you will necessarily overestimate the magnitudes of effects, sometimes by a huge amount. I know that Dave Krantz has thought about this issue for awhile; it came up when Francis Tuerlinckx and I wrote our paper on Type S errors, ten years ago. My current thinking is that most (almost all?) research studies of the sort described by Lehrer should be accompanied by retrospective power analyses, or informative Bayesian inferences. Either of these approaches–whether classical or Bayesian, the key is that they incorporate real prior information, just as is done in a classical prospective power analysis–would, I think, moderate the tendency to overestimate the magnitude of effects. In answ

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Introduction: If an estimate is statistically significant, it’s probably an overestimate of the magnitude of your effect. P.S. I think youall know what I mean here. But could someone rephrase it in a more pithy manner? I’d like to include it in our statistical lexicon.

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