The ρ statistic is commonly used to infer chronological dates for molecular lineages, especially from mitochondrial DNA sequences obtained in anthropological contexts. Since this approach was described 12 years ago, it has been applied to estimate molecular dates in more than 200 studies, including some published in top-tier journals. However, this method has not been well evaluated, and the accuracy of dates obtained from the ρ statistic remains unknown, especially for genetic data collected from populations with complex demographic histories. Here, molecular dates inferred from ρ are compared against coalescent expectations from a range of demographic models. This exercise reveals considerable inaccuracy. Molecular dates based on ρ have a slight downward bias with large asymmetric variance and commonly exhibit substantial type I error rates, where the true age of a lineage falls outside the 95% confidence bounds derived from the variance of ρ. Furthermore, demography proves to be a strong confounding factor in estimating molecular dates accurately, especially for populations in which bottlenecks, founder events, and size changes have played important historical roles. Therefore considerable caution should be applied to inferences made from molecular dates based on the ρ statistic, many of which may be misleading and warrant considerable skepticism.