Inverse effectiveness, multisensory integration, and the bodily self: some statistical considerations

A recent report in Consciousness and Cognition provided evidence from a study of the rubber hand illusion (RHI) that supports the multisensory principle of inverse effectiveness (PoIE). I describe two methods of assessing the principle of inverse effectiveness ('a priori' and 'post-hoc'), and discuss how the post-hoc method is affected by the statistical artefact of 'regression towards the mean'. I identify several cases where this artefact may have affected particular conclusions about the PoIE, and relate these to the historical origins of 'regression towards the mean'. Although the conclusions of the recent report may not have been grossly affected, some of the inferential statistics were almost certainly biased by the methods used. I conclude that, unless such artefacts are fully dealt with in the future, and unless the statistical methods for assessing the PoIE evolve, strong evidence in support of the PoIE will remain lacking.