Valid conjunction inference with the minimum statistic

By Thomas E. Nichols, Matthew Brett, Jesper L. R. Andersson, Tor D. Wager, Jean-Baptiste Poline. NeuroImage, 2005

1,945 citations recorded by the source corpus.

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., Buchel, 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.

Subfields: Cognitive Neuroscience, Developmental and Educational Psychology

View Paper: https://www.semanticscholar.org/paper/c304fb89f8c02848c039cc41da78b5b2e9851671

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Citations in the corpus

Triangulating a Cognitive Control Network Using Diffusion-Weighted Magnetic Resonance Imaging (MRI) and Functional MRI (2007, methodology): “We performed a conjunction analysis (Nichols et al., 2005) for the parametric conflict-induced slowing effect and outright inhibition by taking the parametric contrast of StopRespond_noncritical Go_noncritical (Z 2.3; p 0.05, corrected for multiple comparisons), binarizing it, and multiplying it by…”
Evidence for a Common Representation of Decision Values for Dissimilar Goods in Human Ventromedial Prefrontal Cortex (2009, background): “In addition, we were able to test for areas that show overlapping correlations with WTP across all three classes of goods (i.e., conjunction null of WTP effects for food, money, and trinkets) (Nichols et al., 2005).”
The cognitive control network: Integrated cortical regions with dissociable functions (2007, methodology): “Tvalues reported with the conjunction analyses are based on a 'conjunction null distribution' derived from all contrasts used in the conjunction (see Nichols et al., 2005).”
Functional Specialization within Rostral Prefrontal Cortex (Area 10): A Meta-analysis (2006, methodology): “When the same region was reported to be activated in two or more independent contrasts, using a conjunction analysis (Friston, Penny, & Glaser, 2005; Nichols, Brett, Anderson, Wager, & Poline, 2005; Price & Friston, 1997), the activation peak was entered into the metaanalysis more than once, corre”
An fMRI investigation of syllable sequence production (2006, methodology): “A minimal speech production network was established by combining the statistical images for each overt speaking condition using a conjunction approach based on the " conjunction null " hypothesis (Nichols et al., 2005).”
Connectivity profiles reveal the relationship between brain areas for social cognition in human and monkey temporoparietal cortex (2013, methodology): “The conjunction between the two maps was determined using the minimum statistic (28).”
Linear mixed-effects modeling approach to FMRI group analysis (2013, neutral): “for omnibus F-test in a regression model or global null hypothesis involved in appropriate conjunction analysis (Nichols et al., 2005).”
Handbook of Functional MRI Data Analysis: Index (2011, background): “Whereas an interaction looks for differences in effects, a conjunction looks for similarities (Nichols et al., 2005).”
Amygdala-frontal connectivity during emotion regulation. (2007, methodology): “…negatively valenced images) and to perform unbiased contrast analysis, we first performed a conjunction analysis with SPM2 (Price and Friston, 1997; Friston et al., 1999; Nichols et al., 2005) to identify amygdala activation that was present across both Maintain and Reappraise task blocks.”
Generalization of value in reinforcement learning by humans (2012, methodology): “Note that although the difference regressors were orthogonalized to the underlying prediction error variables, the validity of conjunction inference using the minimum t statistic does not depend on the conjoined tests being independent (Nichols et al., 2005).”
Modelling neural correlates of working memory: A coordinate-based meta-analysis (2011, methodology): “To compute the conjunction between two ALE analyses, we used the conservative minimum statistic (Nichols et al., 2005), which is equivalent to identifying the intersection between the two cluster-level FWE corrected results (Caspers et al., 2010).”
States versus Rewards: Dissociable neural prediction error signals underlying model-based and model-free reinforcement learning (2010, methodology): “For a formal statistical test of identical voxels in session 1 and 2 that exhibit the correlation with the SPE signal, we also employed a conjunction analysis (Nichols et al., 2005) at an uncorrected statistical threshold of p 0.001.”
The Dynamics of Functional Brain Networks: Integrated Network States during Cognitive Task Performance (2015, positive): “Identifying Regions Related to Global Integration We used a parcel-wise conjunction analysis (Nichols et al., 2005) to identify a set of regions in which the BT and WT were significantly related to drift rate, non-decision time, and pupil diameter.”
Dissociable controlled retrieval and generalized selection mechanisms in ventrolateral prefrontal cortex. (2005, background): “That is, a significant conjunction does not indicate that both contrasts were individually significant at standard thresholds ( Nichols et al., 2005 ) but rather means that both were significant at more lenient thresholds (with a joint probability of a Type I being less than 0.001).”
Striatum and pre-SMA facilitate decision-making under time pressure (2008, background): “Whereas in logic a conjunction is defined as an AND between truth statements, in neuroimaging a conjunction refers to activation caused by task X AND by task Y (17).”