Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences
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Statistical limitations in functional neuroimaging II. Signal detection and statistical inference

Karl Magnus Petersson

Karl Magnus Petersson

Cognitive Neurophysiology R2-01, Department of Clinical Neuroscience, Karolinska Institute, Karolinska Hospital, S-171 76 Stockholm, Sweden ()

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Thomas E. Nichols

Thomas E. Nichols

Department of Statistics, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA ()

Center for the Neural Basis of Cognition, Carnegie Mellon University and University of Pittsburgh, 4400 Fifth Avenue, Pittsburgh, PA 15213, USA

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Jean-Baptiste Poline

Jean-Baptiste Poline

Commissariat VEnergie Atomique, Direction de la Recherche Medicale, Service Hospitaller Frederic Joliot, 4 PI General Leclerc, 91406 Orsay, France ()

Wellcome Department of Cognitive Neurology, Functional Imaging Laboratory, 12 Queen Square, London WC1N 3BG, UK ()

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Andrew P. Holmes

Andrew P. Holmes

Wellcome Department of Cognitive Neurology, Functional Imaging Laboratory, 12 Queen Square, London WC1N 3BG, UK ()

Robertson Centre for Biostatistics, Department of Statistics, University of Glasgow, Boyd Orr Building, University Avenue, Glasgow G12 8QSI, UK ()

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    The field of functional neuroimaging (FNI) methodology has developed into a mature but evolving area of knowledge and its applications have been extensive. A general problem in the analysis of FNI data is finding a signal embedded in noise. This is sometimes called signal detection. Signal detection theory focuses in general on issues relating to the optimization of conditions for separating the signal from noise. When methods from probability theory and mathematical statistics are directly applied in this procedure it is also called statistical inference. In this paper we briefly discuss some aspects of signal detection theory relevant to FNI and, in addition, some common approaches to statistical inference used in FNI. Low–pass filtering in relation to functional–anatomical variability and some effects of filtering on signal detection of interest to FNI are discussed. Also, some general aspects of hypothesis testing and statistical inference are discussed. This includes the need for characterizing the signal in data when the null hypothesis is rejected, the problem of multiple comparisons that is central to FNI data analysis, omnibus tests and some issues related to statistical power in the context of FNI. In turn, random field, scale space, non–parametric and Monte Carlo approaches are reviewed, representing the most common approaches to statistical inference used in FNI. Complementary to these issues an overview and discussion of non–inferential descriptive methods, common statistical models and the problem of model selection is given in a companion paper. In general, model selection is an important prelude to subsequent statistical inference. The emphasis in both papers is on the assumptions and inherent limitations of the methods presented. Most of the methods described here generally serve their purposes well when the inherent assumptions and limitations are taken into account. Significant differences in results between different methods are most apparent in extreme parameter ranges, for example at low effective degrees of freedom or at small spatial autocorrelation. In such situations or in situations when assumptions and approximations are seriously violated it is of central importance to choose the most suitable method in order to obtain valid results.