Conjunction revisited

The Wellcome Department of Imaging Neuroscience and Institute of Cognitive Neuroscience, University College London, 17 Queen Square, London, WC1N 3AR, UK.
NeuroImage (Impact Factor: 6.36). 04/2005; 25(3):661-7. DOI: 10.1016/j.neuroimage.2005.01.013
Source: PubMed


The aim of this note is to revisit the analysis of conjunctions in imaging data. We review some conceptual issues that have emerged from recent discussion (Nichols, T., Brett, M., Andersson, J., Wager, T., Poline, J.-B., 2004. Valid Conjunction Inference with the Minimum Statistic.) and reformulate the conjunction of null hypotheses as a conjunction of k or more effects. Analyses based on minimum statistics have typically used the null hypothesis that k = 0. This enables inferences about one or more effects (k > 0). However, this does not provide control over false-positive rates (FPR) for inferences about a conjunction of k = n effects, over n tests. This is the key point made by Nichols et al., who suggest a procedure based on supremum P values that provides an upper bound on FPR for k = n. Although valid, this is a very conservative procedure, particularly in the context of multiple comparisons. We suggest that an inference on a conjunction of k = n effects is generally unnecessary and distinguish between congruent contrasts that test for the same treatment and incongruent contrasts of the sort used in cognitive conjunctions. For congruent contrasts, the usual inference, k > 0, is sufficient. With incongruent contrasts it is sufficient to infer a conjunction of k >u effects, where u is the number of contrasts that share some uninteresting effect. The issues highlighted by Nichols et al., have important implications for the design and analysis of cognitive conjunction studies and have motivated a change to the SPM software, that affords a test for the more general hypothesis k >u. This more general conjunction test is described.

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    • "reas specifically involved in coding peripersonal and extrapersonal space , using the following contrasts : ( WN - WO ) ∩ ( ON - OO ) and ( WO - WN ) ∩ ( OO - ON ) , respectively ( Friston et al . , 1999 ) . To this aim , we performed an SPM ' conjunction null ' analysis ( Nichols et al . , 2005 ) . Given the conservative nature of this analysis ( Friston et al . , 2005 ) , we report data with a p - value < 0 . 001 uncorrected . A threshold of 10 was applied on cluster dimension . For all analyses , location of the activation foci was determined in the stereotaxic space of the MNI coordinates system . Those cerebral regions for which maps are provided were also localized with reference to cytoarchitect"
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    • "A compromise is to require evidence that at least r out of n null hypotheses are false, for some user specified r. Such tests of the 'partial conjunction null hypothesis' were used in Friston et al. (2005) and then studied by Benjamini and Heller (2008). The extremes r = 1 and r = n correspond to the usual metaanalysis tests and conjunction testing respectively. "
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    • "had jointly significant AF changes in regions such as the bilateral PSMC, suggesting reproducible high-frequency differences across people (Friston et al., 2005; Nichols et al., 2005). Therefore, our results suggest that the observed AF differences in the high-frequency range are not due to physiological noises but might have functional significance. "

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