We discuss the effects of non-independence on region of interest (ROI) analysis of functional magnetic resonance imaging data, which has recently been raised in a prominent article by Vul et al. We outline the problem of non-independence, and use a previously published dataset to examine the effects of non-independence. These analyses show that very strong correlations (exceeding 0.8) can occur even when the ROI is completely independent of the data being analyzed, suggesting that the claims of Vul et al. regarding the implausibility of these high correlations are incorrect. We conclude with some recommendations to help limit the potential problems caused by non-independence.