Statistical Analysis

A wide range of techniques has been applied to look at changes in brain activity (Lange, 1999), with most using some variant of the general linear model (GLM; Friston et al., 1994). The change in BOLD signal intensity over time represents the dependent variable in fMRI studies. Typically, a reference time series is created that denotes what type of event and when it happened during a scanning session. This time series is then convolved with a standard or empirically derived hemodynamic response function (which incorporates the sluggish nature of the hemodynamic response) yielding a suitable estimate or model of the predicted BOLD signal. Each of the independent variables (e.g., different types of task events) is represented by a set of covariates that are shaped like hemodynamic responses and are shifted in time to account for the lag. These can be either categorical variables (such as presence or absence of a task demand) or quantitative variables (such as number of stimuli presented at a time). The covariates are entered into the modified GLM with the fMRI time-series data, and a least-squares procedure is used to derive parameter estimates (i.e., beta values) that scale with the degree to which a given covariate accounts for the variance in the observed data. Similar to traditional statistical methods, these parameter estimates, when normalized by estimates of noise, are used to compute inferential statistics such as t values or F-statistics. These inferential statistics are calculated on a voxel-by-voxel (voxelwise) basis to create statistical parametric brain maps.

Some researchers alternatively perform analyses based on structurally defined regions of interests. This can have advantages when investigators have a specific hypothesis about a specific brain region. However, most investigators prefer a voxelwise approach because it is not constrained by preconceived ideas regarding the volume or location of expected activations. The primary drawback with the voxelwise approach involves the large number of voxels in the brain, causing a high risk of Type I statistical error. Thus one needs to perform an adjustment for the number of independent comparisons in each analysis. Because neighboring voxels are correlated and there exists temporal autocorrelation over time, it is overconservative to apply a simple Bonferroni correction to these data sets. Instead, investigators typically apply corrections based on an estimate of the number of independent resolution elements (RESELs) or adjust the degrees of freedom to account for the nonuniformity in the noise. For instance, an estimate may be made for the number of independent spatial resolution elements by correcting the total size of the volume of interest by the Full-Width at Half-Maximum estimate of spatial resolution (Worsley et al., 1996).

In addition to looking at individual activations, increased attention is being paid to the functional relationships between different brain regions (Mesulam, 1990). Because most psychological phenomena are not mediated by single brain regions, but instead involve networks of brain regions, it becomes essential to understand how these brain regions interact, when their activity is functionally coupled or uncoupled, and the extent to which these changes in functional connectivity are related to experimental variables of interest. Toward this end, researchers have used a number of strategies, ranging from correlation analysis to principle components analysis and structural equation modeling (Mcintosh, 1999).

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