How Many Subjects Constitute a Study?
Abstract
In fMRI there are two classes of inference: one aims to make a comment about the "typical" characteristics of a population, and the other about "average" characteristics. The first pertains to studies of normal subjects that try to identify some qualitative aspect of normal functional anatomy. The second class necessarily applies to clinical neuroscience studies that want to make an inference about quantitative differences of a regionally specific nature. The first class of inferences is adequately serviced by conjunction analyses and fixed-effects models with relatively small numbers of subjects. The second requires random-effect analyses and larger cohorts.
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Small sample sizes can still inform about the typicality of a feature in a population when the feature is present in most sampled cases.
“However, small sample sizes can be informative about typicality of a feature in a population, when features are identified in the majority of cases sampled[18].”
From In vivo PET imaging of neuroinflammation in familial frontotemporal dementia (2021) · cites this paper as [18]
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“Statistical comparisons between experimental factors used linear contrasts in a random-effects analysis ( Friston, Holmes, & Worsley, 1999 ), after scaling for global signal values in individual subjects.”
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Schmahl, C. G., Bohus, M., Esposito, F., Treede, R., Salle, F. D., Greffrath, W., Ludäscher, P., Jochims, A., Lieb, K., Scheffler, K., et al. (2006) · Archives of General Psychiatry · doi:10.1001/archpsyc.63.6.659 · Cited by 300 · see citing works
“Because of the small sample size and the relatively high variability of the population compared with the single-voxel signalto-noise ratio of the measurements, interindividual variance was not accounted for in voxel-level group analysis, and all contrast maps were computed using a fixed-effects model.(22) To extend ou…”
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“analysis) using across subject variance (random effect analysis) (Friston et al., 1999).”
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Vogt, S., Buccino, G., Wohlschläger, A. M., Canessa, N., Shah, N. J., Zilles, K., Eickhoff, S. B., Freund, H., Rizzolatti, G., & Fink, G. R. (2007) · NeuroImage · doi:10.1016/j.neuroimage.2007.07.005 · Cited by 300 · see citing works
“Data were analysed using a random-effects model (Friston et al., 1999), implemented in a two-level procedure.”
MethodHabituation to painful stimulation involves the antinociceptive system
Bingel, U., Schoell, E., Herken, W., Büchel, C., & May, A. (2007) · Pain · doi:10.1016/j.pain.2006.12.005 · Cited by 298 · see citing works
“At the group level, a random effects approach (Friston et al., 1999) treating individual subjects as a random factor and including non-sphericity correction was applied.”
MethodStriem-Amit, E., Cohen, L., Dehaene, S., & Amedi, A. (2012) · Neuron · doi:10.1016/j.neuron.2012.08.026 · Cited by 293 · see citing works
“a general linear model (GLM) in a hierarchical random-effects analysis (Friston et al., 1999).”
MethodBrain Areas Involved in Interlimb Coordination: A Distributed Network
Debaere, F., Swinnen, S. P., Béatse, E., Sunaert, S. G., Hecke, P. V., & Duysens, J. (2001) · NeuroImage · doi:10.1006/nimg.2001.0892 · Cited by 294 · see citing works
Posture influences motor imagery: An fMRI study
de Lange, F. P., Helmich, R. C. G., & Toni, I. (2006) · NeuroImage · doi:10.1016/j.neuroimage.2006.07.017 · Cited by 293 · see citing works
“Contrasts of the parameter estimates for the 24 main effects (3 POSTURES×2 HAND LATERALITIES×4 ORIENTATIONS) constituted the data for the second-stage analyses, which treated participants as a random effect (Friston et al., 1999).”
MethodEhrsson, H. H., Fagergren, A., & Forssberg, H. (2001) · Journal of Neurophysiology · doi:10.1152/jn.2001.85.6.2613 · Cited by 293 · see citing works
Functional MRI of macaque monkeys performing a cognitive set-shifting task
Nakahara, K., Hayashi, T., Konishi, S., & Miyashita, Y. (2002) · Science · doi:10.1126/science.1067653 · Cited by 286 · see citing works
The neurology of saccades and covert shifts in spatial attention
Perry, R. J., & Zeki, S. (2000) · Brain · doi:10.1093/brain/123.11.2273 · Cited by 282 · see citing works
“The trials were pseudorandomized with the following this is the appropriate analysis for establishing typical features of the human brain (Friston et al., 1999).”
BackgroundNegative BOLD differentiates visual imagery and perception
Amedi, A., Malach, R., & Pascual-Leone, A. (2005) · Neuron · doi:10.1016/j.neuron.2005.10.032 · Cited by 271 · see citing works
“Across-subject statistical parametric maps were calculated by using hierarchical random-effects model analysis (Friston et al., 1999) after transformation into Talairach space (Talairach, 1988).”
MethodBerthoz, S., Eric Artiges, A., de Moortele, P. V., Poline, J., Rouquette, S., Consoli, S. M., & Martinot, J. (2002) · American Journal of Psychiatry · doi:10.1176/appi.ajp.159.6.961 · Cited by 278 · see citing works
“Following random-effect-analysis procedure, we computed the variance across subjects, allowing generalization of the results (44).”
MethodFunctional brain mapping during free viewing of natural scenes
Bartels, A., & Zeki, S. (2003) · Human Brain Mapping · doi:10.1002/hbm.10153 · Cited by 276 · see citing works
Trautmann-Lengsfeld, S. A., Fehr, T., & Herrmann, M. (2009) · Brain Research · doi:10.1016/j.brainres.2009.05.075 · Cited by 274 · see citing works
Processing of the incentive for social approval in the ventral striatum during charitable donation
Izuma, K., Saito, D. N., & Sadato, N. (2010) · Journal of Cognitive Neuroscience · doi:10.1162/jocn.2009.21228 · Cited by 276 · see citing works
“Second, the summary data for each individual were incorporated into a second-level analysis using a random-effect model ( Friston, Holmes, & Worsley, 1999 ) to make inferences at a population level.”
MethodSpectral and Temporal Processing in Human Auditory Cortex
Hall, D. A., Johnsrude, I. S., Haggard, M. P., Palmer, A. R., Akeroyd, M. A., & Summerfield, A. Q. (2002) · Cerebral Cortex · doi:10.1093/cercor/12.2.140 · Cited by 275 · see citing works
Lanius, R. A., Williamson, P. C., Bluhm, R. L., Densmore, M., Boksman, K., Neufeld, R. W. J., Gati, J. S., & Menon, R. S. (2005) · Biological Psychiatry · doi:10.1016/j.biopsych.2005.01.011 · Cited by 260 · see citing works
“This did not allow application of alternative tatistical models, such as random or mixed effects models Friston et al 1999; Kirk 1995).”
MethodKuhtz-Buschbeck, J. P., Mahnkopf, C., Holzknecht, C., Siebner, H. R., Ulmer, S., & Jansen, O. (2003) · European Journal of Neuroscience · doi:10.1111/j.1460-9568.2003.03066.x · Cited by 257 · see citing works
Functional Imaging of Perceptual Learning in Human Primary and Secondary Somatosensory Cortex
Pleger, B., Foerster, A.-F., Ragert, P., Dinse, H. R., Schwenkreis, P., Malin, J.-P., Nicolas, V., & Tegenthoff, M. (2003) · Neuron · doi:10.1016/s0896-6273(03)00677-9 · Cited by 247 · see citing works
“Phantom-limb pain as a percep-subjects pre- and postcoactivation (Friston et al., 1999; Poldrack, 2000).”
Monetary Incentives Enhance Processing in Brain Regions Mediating Top-down Control of Attention
Small, D. M., Gitelman, D., Simmons, K., Bloise, S. M., Parrish, T., & Mesulam, M.-M. (2005) · Cerebral Cortex · doi:10.1093/cercor/bhi063 · Cited by 242 · see citing works
“Random-effects analyses were used to assess group effects by calculating the parameter effects images for each subject across trials and then entering these images across subjects into a one-sample t-test (Friston et al., 1999).”
MethodCognitive effects of nicotine in humans: an fMRI study
Kumari, V., Gray, J. A., Ffytche, D. H., Mitterschiffthaler, M. T., Das, M., Zachariah, E., Vythelingum, G. N., Williams, S., Simmons, A., & Sharma, T. (2003) · NeuroImage · doi:10.1016/s1053-8119(03)00110-1 · Cited by 237 · see citing works
“Data were analysed using a two-stage random effect procedure in order to make inferences about the population as a whole (Friston et al., 1999).”
MethodInfluentialA population-average MRI-based atlas collection of the rhesus macaque
McLaren, D. G., Kosmatka, K. J., Oakes, T. R., Kroenke, C. D., Kohama, S. G., Matochik, J. A., Ingram, D. K., & Johnson, S. C. (2008) · NeuroImage · doi:10.1016/j.neuroimage.2008.10.058 · Cited by 241 · see citing works
“These atlases can be used to align many individual monkeys together to carry out voxel-based analyses (Ashburner et al., 1998; Friston et al., 1999a; 1999b; Woods, 1996; Zeffiro et al., 1997) and such analyses could potentially be conducted with existing tools such as FSL and SPM (Alexander et al.,…”
InfluentialVicarious function within the human primary motor cortex?
Jaillard, A. S., Delon‐Martin, C., Garambois, K., Bas, J. F. L., & Hommel, M. (2005) · Brain · doi:10.1093/brain/awh456 · Cited by 236 · see citing works
Attentional Modulation of Object Representations in Working Memory
Lepsien, J., & Nobre, A. C. (2006) · Cerebral Cortex · doi:10.1093/cercor/bhl116 · Cited by 232 · see citing works
“Whole-brain statistical comparisons were calculated using linear contrasts in analyses of single-subject data, and group effects were determined using a random-effects analysis at a second level (Friston et al. 1999).”
MethodIidaka, T., Omori, M., Murata, T., Kosaka, H., Yonekura, Y., Okada, T., & Sadato, N. (2001) · Journal of Cognitive Neuroscience · doi:10.1162/089892901753294338 · Cited by 233 · see citing works
“Statistical analysis in the present study was conducted according to the random effect model ( Friston, Holmes, & Worsley, 1999 ) so that inferences could be made at the population level.”
MethodTopographic representation of the human body in the occipitotemporal cortex
Orlov, T., Makin, T. R., & Zohary, E. (2010) · Neuron · doi:10.1016/j.neuron.2010.09.032 · Cited by 236 · see citing works
“Group statistical maps were calculated using hierarchical random effects model analysis (Friston et al., 1999), following spatial smoothing (with an isotropic Gaussian kernel of 4 mm full width at half maximum).”
“What”—Then—“Where” in Visual Working Memory: An Event-Related fMRI Study
Postle, B. R., & D’Esposito, M. (1999) · Journal of Cognitive Neuroscience · doi:10.1162/089892999563652 · Cited by 230 · see citing works
“This inferential step cannot be made with the axed-effects group analyses that have been employed in the majority of published neuroimaging studies to date ( Friston, Holmes, & Worsley, 1999; Woods, 1996).”
Method“Stay Tuned”: Inter-Individual Neural Synchronization During Mutual Gaze and Joint Attention
Saito, D. N., Tanabe, H. C., Izuma, K., Hayashi, M. J., Morito, Y., Komeda, H., Uchiyama, H. T., Kosaka, H., Okazawa, H., Fujibayashi, Y., et al. (2010) · Frontiers in Integrative Neuroscience · doi:10.3389/fnint.2010.00127 · Cited by 229 · see citing works
Dissociation between Ventral and Dorsal fMRI Activation during Object and Action Recognition
Shmuelof, L., & Zohary, E. (2005) · Neuron · doi:10.1016/j.neuron.2005.06.034 · Cited by 227 · see citing works
“Across-subjects statistical parametric maps (Figures 2, 4, and 7) were calculated using hierarchical random-effects model analysis (Friston et al., 1999).”
MethodSingh, K. D., Barnes, G. R., & Hillebrand, A. (2003) · NeuroImage · doi:10.1016/s1053-8119(03)00249-0 · Cited by 222 · see citing works
“A random-effects approach is desirable for group analysis, as it allows a quantitative inference of the average effect in the population (Friston et al., 1999).”
BackgroundLee, S. S., & Dapretto, M. (2005) · NeuroImage · doi:10.1016/j.neuroimage.2005.08.003 · Cited by 224 · see citing works
Attention to Action: Specific Modulation of Corticocortical Interactions in Humans
Rowe, J. B., Friston, K. J., Frackowiak, R. S. J., & Passingham, R. E. (2002) · NeuroImage · doi:10.1006/nimg.2002.1156 · Cited by 219 · see citing works
Self-citation
- Authors
- Friston, K. J., Holmes, A. P., & Worsley, K. J.
- Affiliations
- National Hospital for Neurology and Neurosurgery (GB)
- ORCID
- Friston, Karl J.
- Venue
- NeuroImage
- Publisher
- Elsevier BV
- Published
- 1999-07
- Volume
- 10
- Issue
- 1
- Pages
- 1-5
- ISSN
- 1053-8119 (ISSN-L)
- OpenAlex
- W1966363088
- Cited by
- 814
- References
- 0
- Citations by year
- 2026: 2 · 2025: 6 · 2024: 3 · 2023: 7 · 2022: 9 · 2021: 8 · 2020: 17 · 2019: 13 · 2018: 10 · 2017: 15 · 2016: 31 · 2015: 27 · 2014: 22 · 2013: 35 · 2012: 30
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- NeuroImage (publishedVersion)
- PubMed (publishedVersion)
- UCL Discovery (University College London) (submittedVersion)
- Funders
- Wellcome Trust
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced MRI Techniques and Applications
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced Neuroimaging Techniques and Applications
- Keywords
- sample size, functional MRI, statistical inference, population inference, fixed effects model, random effects models, conjunction analysis, clinical neuroscience, functional anatomy, cohort size
- MeSH terms
- Data Interpretation, Statistical, Humans, Magnetic Resonance Imaging, Research Design, Models, Statistical, Cohort Studies, Patient Selection
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