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CarlShulman comments on Study shows existence of psychic powers. - Less Wrong
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Failures to set up or follow proper experimental procedures (giving hints, not fully random presentation, etc) or otherwise introducing a slight biasing effect will show an effect which is puny. With low n, this won't be statistically significant, but with high n it will appear very statistically significant.
That's true, statistical significance isn't the most sophisticated statistic. My rule of thumb is looking at the p and d values.