The goal of this study was to compare how multivariate statistical methods for dimension reduction account for correlations between simultaneously recorded neurons. Here, we describe applications of principal component analysis (PCA) and independent component analysis (ICA) (Cardoso J-F, Souloumiac A. IEE-Proc F 1993;140:362-70; Hyvarinen A, Oja E. Neural Comput 1997;9:1483-92; Lee TW, Girolami M, Sejnowski TJ. Neural Comp 1999;11:417-41) to neuronal ensemble data. Simulated ensembles of neurons were used to compare how well the methods above could account for correlated neuronal firing. The simulations showed that 'population vectors' defined by PCA were broadly distributed over the neuronal ensembles; thus, PCA was unable to identify independent groupings of neurons that shared common sources of input. By contrast, the ICA methods were all able to identify groupings of neurons that emerged due to correlated firing. This result suggests that correlated neuronal firing is reflected in higher-order correlations between neurons and not simply in the neurons' covariance. To assess the significance of these methods for real neuronal ensembles, we analyzed data from populations of neurons recorded in the motor cortex of rats trained to perform a reaction-time task. Scores for PCA and ICA were reconstructed on a bin-by-bin basis for single trials. These data were then used to train an artificial neural network to discriminate between single trials with either short or long reaction-times. Classifications based on scores from the ICA-based methods were significantly better than those based on PCA. For example, scores for components defined with an ICA-based method, extended ICA (Lee et al., 1999), classified more trials correctly (80.58+/-1.25%) than PCA (73.14+/-0.84%) for an ensemble of 26 neurons recorded in the motor cortex (ANOVA: P < 0.005). This result suggests that behaviorally relevant information is represented in correlated neuronal firing and can be best detected when higher-order correlations between neurons are taken into account.