Title
Valid conjunction inference with the minimum statistic.
Abstract
In logic a conjunction is defined as an AND between truth statements. In neuroimaging, investigators may look for brain areas activated by task A AND by task B, or a conjunction of tasks (Price, C.J., Friston, K.J., 1997. Cognitive conjunction: a new approach to brain activation experiments. NeuroImage 5, 261–270). Friston et al. (Friston, K., Holmes, A., Price, C., Büchel, C., Worsley, K., 1999. Multisubject fMRI studies and conjunction analyses. NeuroImage 10, 85–396) introduced a minimum statistic test for conjunction. We refer to this method as the minimum statistic compared to the global null (MS/GN). The MS/GN is implemented in SPM2 and SPM99 software, and has been widely used as a test of conjunction. However, we assert that it does not have the correct null hypothesis for a test of logical AND, and further, this has led to confusion in the neuroimaging community. In this paper, we define a conjunction and explain the problem with the MS/GN test as a conjunction method. We present a survey of recent practice in neuroimaging which reveals that the MS/GN test is very often misinterpreted as evidence of a logical AND. We show that a correct test for a logical AND requires that all the comparisons in the conjunction are individually significant. This result holds even if the comparisons are not independent. We suggest that the revised test proposed here is the appropriate means for conjunction inference in neuroimaging.
Year
DOI
Venue
2005
10.1016/j.neuroimage.2004.12.005
NeuroImage
Keywords
Field
DocType
Conjunctions
Developmental psychology,Confusion,Logical conjunction,Statistic,Inference,Null hypothesis,Brain activation,Psychology,Artificial intelligence,Neuroimaging,Cognition
Journal
Volume
Issue
ISSN
25
3
1053-8119
Citations 
PageRank 
References 
260
23.91
2
Authors
5
Search Limit
100260
Name
Order
Citations
PageRank
Thomas Nichols132527.88
Matthew Brett226023.91
Jesper Andersson3194896.07
Tor Wager448171.29
Jean-Baptiste Poline532637.26