If you follow the principles of classical testing (I do not!), the difference x-y is not significantly different from zero in 26% of the cases when x is significantly different from zero and y is not, or the reverse… This may sound paradoxical to you, however this is what the classical theory says. The paradox is easily explained by the fact that, in this artificial experiment, I know (because I wrote the R code) that x has a mean different from zero and that y has a mean equal to zero. So testing for difference sounds exactly identical to testing for x having a mean different from zero. In a practical problem, one does not know whether any of both means is different from zero, so the test should bear on the difference of the means of x and y.

]]>Interesting! I see that David Aldous also wrote a review of the book on amazon.

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