Many empirical economists say that the teaching of econometrics is unbalanced, and students are not well-prepared for the serious problems they will encounter with real data. Here, the author considers the problem of noisy data, which is present in most econometric studies, but receives far too little attention. Most econometric studies are done in a world of low signal-to-noise ratios, and educated common sense suggests that we cannot expect precise results in such an environment. Sensitivity analysis shows that the apparent precision of reported econometric results is generally an illusion, because it is highly dependent on error term independence assumptions.