Independent component analysis (ICA) is increasingly used for analyzing brain imaging data. ICA typically gives a large number of components, many of which may be just random, due to insufficient sample size, violations of the model, or algorithmic problems. Few methods are available for computing the statistical significance (reliability) of the components. We propose to approach this problem by performing ICA separately on a number of subjects, and finding components which are sufficiently consistent (similar) over subjects. Similarity is defined here as the similarity of the mixing coefficients, which usually correspond to spatial patterns in EEG and MEG. The threshold of what is "sufficient" is rigorously defined by a null hypothesis under which the independent components are random orthogonal components in the whitened space. Components which are consistent in different subjects are found by clustering under the constraint that a cluster can only contain one source from each subject, and by constraining the number of the false positives based on the null hypothesis. Instead of different subjects, the method can also be applied on different recording sessions from a single subject. The testing method is particularly applicable to EEG and MEG analysis.