The principle of inverse effectiveness in multisensory integration: some statistical considerations.

The principle of inverse effectiveness (PoIE) in multisensory integration states that, as the responsiveness to individual sensory stimuli decreases, the strength of multisensory integration increases. I discuss three potential problems in the analysis of multisensory data with regard to the PoIE. First, due to 'regression towards the mean,' the PoIE may often be observed in datasets that are analysed post-hoc (i.e., when sorting the data by the unisensory responses). The solution is to design discrete levels of stimulus intensity a priori. Second, due to neurophysiological or methodological constraints on responsiveness, the PoIE may be, in part, a consequence of 'floor' and 'ceiling' effects. The solution is to avoid analysing or interpreting data that are too close to the limits of responsiveness, enabling both enhancement and suppression to be reliably observed. Third, the choice of units of measurement may affect whether the PoIE is observed in a given dataset. Both relative (%) and absolute (raw) measurements have advantages, but the interpretation of both is affected by systematic changes in response variability with changes in response mean, an issue that may be addressed by using measures of discriminability or effect-size such as Cohen's d. Most importantly, randomising or permuting a dataset to construct a null distribution of a test parameter may best indicate whether any observed inverse effectiveness specifically characterises multisensory integration. When these considerations are taken into account, the PoIE may disappear or even reverse in a given dataset. I conclude that caution should be exercised when interpreting data that appear to follow the PoIE.