relax this significance threshold by a factor of ten, or alternatively if the power were lower by a factor of 10, the posterior odds that a ‘hit’ is a true association would also be reduced by a factor of ten. This simple mathematical analysis is little affected by allowing for the fact that true associations come in various sizes with varying power to detect them; the above formula is simply modified by interpreting ‘power’ as the mean power.The above discussion concerns ‘average’ properties of ‘hits’ achieving given significance levels. After the association data are available, a related but different question is whether a particular positive finding is likely to be a true one. For that calculation, the prior odds must be multiplied by the Bayes factor, the ratio of the probability of the observed data under the assumption that there is a true association to its probability under the null hypothesis. As in power calculations, the calculation of Bayes factors requires assumptions about effect sizes (see Methods for details).A key point from both perspectives is that interpreting the strength of evidence in an association study depends on the likely number of true associations, and the power to detect them which,
