A Critique of Ioannidis JPA (2005) Why Most Published Research Findings Are False. PLoS Med 2(8)
by Hermann Vetter

Null hypotheses are mostly point hypotheses stating that some (frequency-, mean-) difference, or correlation, is zero. Empirically, an exact value of zero occurs virtually never. Hence H0 is virtually always false. Ioannidis' R is defined as 'the ratio of the number of "true relationships" to "no relationships" among those tested in the field'. H0 being always false means that there are only true relationships, i.e., that R has only a single value (infinity). Hence his analyses involving different values of R do not refer at all to the by far most frequent type of H0, but only to a rare non-point H0 like "boys are better than girls in math", with the negation "boys are equal or lower". This means that his main contention would have to be radically reconsidered for the case of a usual H0.