Neuro-doubt: fMRI, meta-analysis, and incorrect p value minimization

The current issue of Neuron includes an article by Mueller, Wang, Fox, Yeo, Sepulcre, Sabuncu, Shafee, Lu, and Liu which accomplishes the admirable task of assessing intersubject variability of fMRI activity in various brain regions. This kind of work is to be commended, since until we fully understand the range of normal brain activity in fMRI it will remain more a research tool and less one of clinical relevance.

The investigators looked at fMRI brain metabolic activity in 23 subjects and derived a per-corresponding-fMRI-cortical-vertex-point coefficient of variation between the subjects (each individual subject had 5 sequential scans).  The investigators noted that several cortical regions, such as the primary visual cortex, which are known to be highly conserved among primate species are also those which showed the least inter-subject variability among human subjects. Areas which are uniquely larger in humans compared to primates such as the macaque were those which showed more variability between human subjects.

The hypothesis that areas of brain similarity that are conserved across species are likely to be similarly conserved between individuals is a logical one, and their newly published meta-analysis supports this.  No problem, good study.

Except that the p value given for the metaanalysis seems quite high for 23 subjects: p < 0.0001, for a Pearson product-moment correlation coefficient r value of just 0.52!

Let us look at the scatter plot:

Figure 3. Functional Connectivity Variability and Evolutionary Cortical Expansion Are Highly Correlated(A) The regional evolutionary cortical expansion between an adult macaque and the average human adult PALS-B12 atlas. Data were provided by van Essen and colleagues (van Essen and Dierker, 2007). On a whole-surface level, evolutionary expansion and functional variability (B) were significantly associated (r = 0.52, p < 0.0001). The correlation was shown in the scatter plot (C) where each 100th vertex is represented by a small circle.


Now, what is the N for the study? 23 subjects? 115 fMRI scans? Thousands of verticies on the 115 scans? I fear that for the statistical package N was not the number of subjects. Let us look at the graph for N versus Pearson r (courtesy of Wikipedia) for significance (here, p< 0.05):

More specifically, if we consider the N to be the number of subjects, at an N of 23 we get a two-tailed Pearson probability of about 0.011. Significant, but over an order of magnitude less that the study reports.

Would an N of 115 (23 times 5, the number of scans) have been a valid N for degrees of freedom? No, because two measurements on the same subject lack true independence of the measure and so should drop the degrees of freedom.

The take home point here is that if even the people doing the basic normal variant work in the fMRI field may use statistical packages so as to overstate their statistical results, the clinical applications people are potentially hosed before they can start.

Here's the abstract:

Individual Variability in Functional Connectivity Architecture of the Human Brain

Mueller, Sophia; Wang, Danhong; Fox, Michael D.; Yeo, B.T. Thomas; Sepulcre, Jorge; Sabuncu, Mert R.; Shafee, Rebecca; Lu, Jie; Liu, Hesheng

Neuron doi:10.1016/j.neuron.2012.12.028 (volume 77 issue 3 pp.586 - 595)

The fact that people think or behave differently from one another is rooted in individual differences in brain anatomy and connectivity. Here, we used repeated-measurement resting-state functional MRI to explore intersubject variability in connectivity. Individual differences in functional connectivity were heterogeneous across the cortex, with significantly higher variability in heteromodal association cortex and lower variability in unimodal cortices. Intersubject variability in connectivity was significantly correlated with the degree of evolutionary cortical expansion, suggesting a potential evolutionary root of functional variability. The connectivity variability was also related to variability in sulcal depth but not cortical thickness, positively correlated with the degree of long-range connectivity but negatively correlated with local connectivity. A meta-analysis further revealed that regions predicting individual differences in cognitive domains are predominantly located in regions of high connectivity variability. Our findings have potential implications for understanding brain evolution and development, guiding intervention, and interpreting statistical maps in neuroimaging. Functional connectivity is most variable in association cortex Connectivity variability is rooted in evolutionary cortical expansion Variability is associated with cortical folding and long-range connection Brain regions of high connectivity variability predict behavioral differences Mueller et al. quantified interindividual variability in functional connectivity across the human brain and identified its relation to evolutionary cortical expansion and some anatomical characteristics.


  1. From the paper, N is the number of voxels , which is a large number, instead of the number of subjects.

    1. Thanks for the update! Even just looking at cortical voxels, that's a N in the thousands that would not change in number between doing the study on 1 subject and doing the study on 100 subjects.

    2. You are absolutely right that the N will not change by the number of subjects involved.
      The figure shown in this post is trying to compare the similarity between two maps-- individual difference map derived from 23 subjects, and the evolutionary expansion map derived from monkey/human templates if I understand right. Each map could come from any number of subjects, e.g., the expansion map comes from a single monkey (or a template from multiple monkeys? Should check Hill et al 2010 ).
      In such comparison, the degree of freedom should be the independent vertices on the cortex mantle.

  2. Since the human map of variance is dependent in its accuracy on number of subjects (and this variance is what interests me) we have two null hypotheses combined in one statistic:

    1. Null difference between monkey and human map. But since the areas of human association cortex marked as most variable hardly exist on the monkey, that null hypothesis is more of less understood as false, I think.

    2. Null difference in variances across the population of individuals between areas on the human cortex. And this one IS dependent on the human subject N (With N of one, we have NO such variance, for example).


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