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Comment by DINKDINK | Hacker News Reader

This author misuses a gaussian distribution by way of claiming that a standard deviation is outrageous...all on a phenomenon that is overwhelmingly likely NOT to be gaussian distributed.

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For anyone who's curious, the procedure used is described in http://www.aliquote.org/pub/odds_meta.pdf. The standardized mean difference is given by:

  log((65/35)/(5/95))/(pi/sqrt(3)) = 1.9646484930140864

The justification for this procedure is that the judges are assumed to make decisions by dichotomizing a continuous variable with logistic distributed error (this one statistical justification for logistic regression; see https://en.wikipedia.org/wiki/Logistic_regression#Latent_var...). The mean difference in the continuous variable is given by the log odds ratio times some constant, and the standard deviation of the continuous variable is pi/sqrt(3) times the same constant. Because the logistic distribution resembles a normal distribution (see https://en.wikipedia.org/wiki/Logistic_distribution and figure in paper), the standardized mean difference given by this method will approximately equal the standardized mean difference of the latent continuous variable.

There's something like a Godwin's law for the Gaussian distribution.

Whoever claims that the other person is making an unwarranted Gaussian assumption has lost the discussion.

He doesn't mention the Gaussian distribution anywhere. He just says the effect size is too big to be plausibly generated by hunger alone.

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