Dr Elena Kulinskaya, Statistical Advisory Service, Imperial College
Meta analysis on the right scale

This talk is about an approach to meta analysis and to statistical evidence developed jointly with Stephan Morgenthaler and Robert Staudte, and now written up in our book 'Meta Analysis: a guide to calibrating and combining statistical evidence'  to be published by Wiley very soon. The traditional ways of measuring evidence, in particular with p-values, are neither intuitive nor useful when it comes to making comparisons between experimental results, or when combining them. We measure evidence for an alternative hypothesis, not evidence against a null. To do this, we have in a sense adopted standardized scores for the calibration scale. Evidence for us is simply a transformation of a test statistic S to another one (called evidence T=T(S)) whose distribution is close to normal with variance 1, and whose mean grows from 0 with the parameter as it moves away from the null. Variance stabilization is used to arrive on this scale. For meta analysis the results from different studies are transformed to a common calibration scale, where it is simpler to combine and interpret them.