And if the choice of prior has been affected by looking at the results, then the two are correlated. And we know that correlations reduce apparent variance. After all, that is why convolution smoothing techniques exist – to smooth be reducing variance through correlation.

]]>If this criterion were to be applied, for example, to the results shown at the top of this post, there would be no support for claiming an effect. If the details of the experiment/processing/forking paths gave one confidence that the results were distributed normally, then one could narrow the confidence band. One way to get such confidence would be for someone else to repeat the experiment and only process the data in the same way as the published result.

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