Overview of Statistical Data Analysis
A major goal of functional MRI measurements is the localization of the neural correlates of sensory, motor and cognitive processes. Hypothesis-driven statistical data analysis is an important tool to identify those brain regions exhibiting increased or decreased responses in specific experimental conditions as compared to other (e.g. control) conditions. Due to the presence of physiological and physical noise fluctuations, observed differences between conditions might occur simply by chance. It is the task of statistical data analysis to explicitly assess the effect of measurement variability (noise fluctuations) on estimated condition differences: If it is very unlikely that an observed effect is solely the result of noise fluctuations, we tend to accept that the observed effect reflects a true difference between conditions. In standard fMRI analyses, this assessment is performed independently for the time course of each voxel. The obtained statistical values - one for each voxel - form a three-dimensional statistical map. In more complex analyses, each voxel will contain several statistical values reflecting estimated effects of multiple conditions.
Standard (univariate) statistical analysis is performed independently for each voxel. Focusing on the time course of a single voxel, the following sections will first describe general principles of statistical data analysis. This is followed by a detailled description of the General Linear Model (GLM), which can be considered the "working horse" of statistical data analysis. The description will then consider the analysis of whole 3D data sets, including specific problems such as the massive multiple comparisons problem. It is then described in detail how data sets of a single-subject is analyzed in various "spaces" including the original recording space (FMR analysis), standard (e.g. Talairach normalized) 3D space (VMR analysis) and cortex space (SRF analysis). Finally it is described how multi-subject data is analyzed using fixed effects group analysis and random-effects group analysis.
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